Acoustic Emission Monitoring of CFRP Laminated Composites ...

Acoustic Emission Monitoring of 

CFRP Laminated Composites 

Subjected to 

Multi-axial Cyclic Loading 

A dissertation by 

Rúnar Unnþórsson 

Submitted to the Faculty of Engineering in partial 

fullment of the requirements for the degree of 

Doctor of Philosophy. 

University of Iceland 

Reykjavik, October 2008

Doctoral Committee 

Magnús Þór Jónsson, Professor 

Faculty of Engineering 


Thomas Philip Rúnarsson, Professor 



Jón Atli Benediktsson, Professor 



Opponents 

Kanji Ono, Professor Emeritus 

Henry Samueli School of Engineering and Applied Science, UCLA, 

Los Angeles, California, USA 

Karen Holford, Professor 

Cardi School of Engineering, 

Cardi, Wales, UK. 



VR-II, Hjarðarhaga 2-6, IS-107 Reykjavik, Iceland 

Phone +354 525 4648, Fax +354 525 4632 

verk@hi.is 

www.hi.is 

ISBN: 978-9979-9812-6-8 

Printed in Iceland by Prentsmiðjan Oddi ehf, 2008

To my family.

This page intentionally left blank.

Abstract 

The condition monitoring of machinery is an important eld of study in 

engineering. Its aim is to detect the early development of machine faults, 

and by doing so, facilitate predictive maintenance. This is based on the 

idea that degradation occurs before failure and that by monitoring the 

health of the system, degradation can be identied and corrected before 

breakdown. This can mean huge cost savings for the industry, both in 

terms of safety and productivity. 

Several techniques can be used for condition monitoring. In this thesis a 

technique known as Acoustic Emission (AE) is studied. Acoustic emission 

is a nondestructive evaluation technique which can be used for in situ 

detection of microstructural changes in a material. When these changes 

occur energy is released and elastic stress waves, or acoustic emissions, 

are generated. AE can also be generated by other sources such as friction 

and impacts. The AE technique passively listens to the machinery for 

emissions. When detected, the task is to process them and interpret the 

results. 

This thesis presents an investigation into the acquisition, processing 

and presentation of acoustic emissions during multiaxial cyclic loading of 

an assembly of CFRP composites. The objective of this study is to develop 

a methodology for processing AE to facilitate early damage diagnosis and 

failure prognosis. 

To achieve the objective of the thesis, an experimental setup was designed 

and implemented for acquiring data from 75 nominally identical 

samples of a prosthetic foot while subjected to cyclic loading. The loading 

was applied by means of two pneumatic actuators. The positions and 

loading applied by the actuators were simultaneously acquired with the 

acoustic emissions. The experimental data was then analysed to understand 

how its behavior, within each cycle, evolved as a function of time.

In order to analyse the data new approaches for processing and presenting 

the data were developed and new AE signal features were introduced. 

The principal contribution of this thesis is a methodology for processing, 

presenting, and quantifying AE data so that it can be used for identifying 

multiple AE sources and for tracking their locations relative to the phase 

of a reference signal. The results show that the tracking of AE sources 

can be used to facilitate early damage diagnosis and failure prognosis. The 

methodology is neither limited to AE signals nor to periodic reference signals. 

It can be used to study changes, or artifacts, in other signals using 

either periodic or aperiodic reference signals. Another corollary of the 

work presented here is an algorithm to detect and determine AE hits in 

signals which include large number of overlapping transients with variable 

strengths. Other contributions include new AE features, an AE-based failure 

criterion, and a probability-based approach for providing early warning 

of imminent failure. These last two are based on a 10% displacement failure 

criterion which was used for determining the failure of prosthetic feet.

Ágrip (in Icelandic) 

Líftími vélbúnaðar, sem á að heita eins, er háður notkun, starfsumhver og 

frávikum í bæði efni og smíði hans. Þetta þýðir að framleiðandi búnaðar 

getur í raun ekki útbúið eina viðhaldsáætlun sem gildir fyrir allan búnað 

sömu gerðar nema með því að gera málamiðlanir. Til þess að útbúa sem 

hagkvæmastar viðhaldsáætlanir þarf að aðlaga þær að viðkomandi vélbúnaði 

og uppfæra reglulega. En það getur verið bæði tímafrekt og ertt. Því 

er oft brugðið á það ráð að fylgjast þess í stað með ástandi búnaðarins. 

Ástandseftirlit vélbúnaðar er mikilvægt fyrir öll fyrirtæki sem treysta á 

vélbúnað við starfsemi sína. Markmið með slíku eftirliti er að frumgreina 

bilanir og þar með auðvelda gerð fyrirbyggjandi viðhaldsáætlana. Þetta er 

byggt á þeirri hugmynd að bilanir byrji smátt og ágerist með tíma. Með 

því að fylgjast með búnaðinum þá er hægt að grípa inn í áður en viðkomandi 

vélbúnaður telst vera ónothæfur eða alvarlegar skemmdir myndast. 

Fyrir fyrirtæki getur þannig ástandsstýrt fyrirbyggjandi viðhald þýtt umtalsverðar 

umbætur í öryggi starfsmanna og einnig aukna framleiðni. 

Til ástandseftirlits má velja úr mörgum prófunaraðferðum. Í þessari 

ritgerð er unnið með aðferð sem nefnist Acoustic Emission (AE). Acoustic 

emission er skaðlaus prófunaraðferð sem má nota til þess að greina 

örsmáar breytingar í efni. Þegar þessar breytingar myndast losnar um 

orku sem myndar svipular þrýstibylgjur sem stundum eru kallaðar hljóðþrýstibylgjur 

(AE). Hljóðþrýstibylgjur geta einnig myndast vegna núnings 

og högga. AE er óvirk aðferð því einungis er hlustað á vélbúnaðinn eftir 

hljóðþrýstibylgjum. Þegar bylgjur greinast þá þarf að vinna úr þeim og 

túlka niðurstöðurnar. 

Í þessu doktorsverkefni voru hljóðþrýstibylgjur frá samsettum koltrefjahlutum 

í margása þreytupró rannsakaðar. Allt ferlið frá mælingum, í gegnum 

úrvinnslu og yr í framsetningu var skoðað. Markmiðið með verkefn-

inu var að þróa aðferðarfræði til þess að vinna upplýsingar út úr hljóðþrýstibylgjumælingum, 

til þess að auðvelda ástandsgreiningu og spá fyrir 

um bilanir. 

Til þess að ná fram markmiðum verkefnisins var mælitækni útfærð og 

notuð til að mæla gögn á meðan 75 koltrefja gervifætur voru þreytuprófaðir. 

Fæturnir voru allir sömu gerðar og með sömu laguppbyggingu. Tveir lofttjakkar 

voru notaðir til þess að setja álag á fæturna. Staða tjakkana og 

álagið var mælt samtímis hljóðþrýstibylgjumælingunum. Mæligögnin voru 

síðan greind til þess að skilja hvernig hegðun þeirra, innan hverrar þreytulotu, 

þróaðist sem fall af tíma í þreytuprónu. Við úrvinnslu og framsetningu 

gagnanna voru nýjar aðferðir þróaðar og nýjar kennistærðir kynntar. 

Í verkefninu var þróuð aðferðarfræði til úrvinnslu og framsetningar á 

hljóðþrýstibylgjum þannig að hægt er að greina og staðsetja skemmdir 

miðað við fasa viðmiðunarmerkis. Niðurstöður sýna að með því að fylgjast 

með stöðu skemmda fást upplýsingar sem auðvelda ástandsgreiningu og 

má nota til þess að spá fyrir um bilanir. Aðferðafræðin takmarkast hvorki 

við hljóðþrýstibylgjur né lotubundin viðmiðunarmerki. Hana má nota til 

þess að greina breytingar, eða truanir, í annars konar merkjum frá bæði 

stöðugum og óstöðugum kerfum. Einnig var þróuð aðferð til þess að greina 

og ákvarða hljóðbylgjuskot (e. AE hit) í merkjum þar sem svipular hljóðþrýstibylgjur 

bæði skarast og eru mjög mismunandi að styrk.

Preface 

This dissertation has been prepared in partial fullment of the requirements 

for a Ph.D. degree in Engineering at the University of Iceland. The 

research was carried out at the Department of Mechanical and Industrial 

Engineering at the University of Iceland and in the testing laboratory at 

Össur hf.


Acknowledgements 

There are many people whom I wish to thank for their support and guidance 

throughout this research project. First and foremost I thank my advisor, 

Professor Magnus Thor Jonsson, for making the research possible. His 

guidance, encouragement, support, patience, and the discussions we had 

are greatly appreciated. My advisor, Professor Thomas Philip Runarsson, 

I thank for his friendship, suggestions and discussions, and also for all his 

frank, critical comments. 

The experimental part of this research was carried out at the test facility 

at Össur hf. I would like to thank Össur for this and for providing the 

prosthetic feet for testing. I thank everybody at Össur who assisted me 

during this time, especially Stefán Jóhann Björnsson, for his invaluable 

support and constant interest in my work. 

Special thanks go to my friends and colleagues with whom I shared 

an oce during the largest part of the study: Benedikt Helgason, Guðrún 

Sævarsdóttir and Halldór Pálsson. Their personal and professional support 

is deeply appreciated. 

To Niels Henrik Pontoppidan, at the Technical University of Denmark, 

thank you for all your help, especially during my visit to DTU. Also, thanks 

go to Jens Forker and Hartmut Vallen at Vallen GmbH, Jason Dong at 

Physical Acoustic Corporation, Bjarni Gíslason, Lilja Magnúsdóttir, and 

all the sta at the Faculty of Engineering. 

I gratefully acknowledge the nancial support provided through grants 

from the following funds: The University of Iceland Research Fund, the 

University of Iceland Research Equipment Fund, the Icelandic Research 

Council (Rannis) Research Fund, the Icelandic Research Council Graduate 

Research Fund, and the Memorial Fund of Helga Jonsdottir and Sigurlidi 

Kristjansson.

I thank my family, who have always supported me. I thank my parents, 

especially my father for always being ready to discuss new ideas and for 

helping me with the design and fabrication of parts which I needed for 

my study. Special thanks to Sigurþóra Bergsdóttir, my partner in life, for 

her love and endurance. Last but not least, I thank my children, Bergur 

Snær, Margrét Rán and Eyjólfur Felix for their unconditional love and 

inspiration.

Contents 

Abstract 

Ágrip (in Icelandic) 

Preface 

Acknowledgements 

v 

vii 

ix 

xi 

1 Introduction 1 

1.1 Motivation and Research Objective . . . . . . . . . . . . . 1 

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 3 

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

2 Carbon Fibre-Reinforced Polymer Composites 7 

2.1 CFRP Composites . . . . . . . . . . . . . . . . . . . . . . 7 

2.2 Defects and Damage Mechanisms . . . . . . . . . . . . . . 9 

2.3 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

2.4 Discussion and Summary . . . . . . . . . . . . . . . . . . . 20 

3 Acoustic Emission 23 

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 24 

3.2 AE Hit Determination . . . . . . . . . . . . . . . . . . . . 39 

3.3 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

3.4 AE Source Tracking . . . . . . . . . . . . . . . . . . . . . . 57 

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 

4 Experiments 65 

4.1 The Prosthetic Foot . . . . . . . . . . . . . . . . . . . . . 65 

4.2 Test Setup & Procedure . . . . . . . . . . . . . . . . . . . 68

xiv 

4.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . 70 

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 

5 Results 77 

5.1 Fatigue Behaviour of the Vari-ex foot . . . . . . . . . . . 78 

5.2 Load-Displacement . . . . . . . . . . . . . . . . . . . . . . 82 

5.3 Impending Failure Warning . . . . . . . . . . . . . . . . . 92 

5.4 AE-Based Failure Criterion . . . . . . . . . . . . . . . . . 106 

5.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . 113 

6 Conclusion 133 

6.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 134 

6.2 Directions for Future Research . . . . . . . . . . . . . . . . 136 

Bibliography 155 

List of Tables 157 

List of Figures 163 

List of Algorithms 165

"If all diculties were known at the outset 

of a long journey, most of us would never 

start out at all." 

Dan Rather 

1 Introduction 

The subject of this thesis is the structural health monitoring of brereinforced 

polymer composites subjected to multiaxial cyclic loading. The 

technique used for monitoring is a passive non-destructive technique known 

as acoustic emission monitoring. This chapter introduces the motivation 

behind this thesis and its objective. The contributions and outline of the 

thesis are also presented here. 

1.1 Motivation and Research Objective 

Carbon Fibre-Reinforced Polymer (CFRP) composites have many interesting 

properties, such as high strength-to-weight ratio and excellent corrosion 

and fatigue tolerance. Despite this, damage in composites develops early 

in service 14 

and continues to accumulate throughout the service life. The 

fatigue tolerance can be attributed to resistance to inhomogeneous damage 

growth, which is a property of highly inhomogeneous materials. 3 

The high 

damage tolerance of composites means that composites are able to meet 

their in-service requirements for a prolonged period of time while damages 

accumulate and grow. 

Fatigue is a stochastic process inuenced by several random factors such 

as material variations, manufacturing variations and in-service variations. 

Due to the uncertainties involved, the true system cannot be accurately

2 Chapter 1. Introduction 

represented by a mathematical fatigue model. In other words, all fatigue 

models will have a certain level of model uncertainty. In addition, fatigue 

is also inuenced by the orientations, locations and the types of damage 

mechanisms introduced in the composite. As a result, the fatigue model 

needs to be continually updated and revised while the composite is inservice. 

The information required for updating the model can be obtained 

using non-destructive condition monitoring techniques. 

By combining condition monitoring techniques with fatigue modelling, 

critical material degradation processes can be identied, failure predicted, 

and preventive actions planned. This approach is known as condition-based 

maintenance. By using eective condition based maintenance, instead of 

corrective (after failure) or preventive (calendar-based) maintenance, companies 

can make substantial savings. The savings will be in the form of 

extended part life, reduced number of unexpected breakdowns, lower risk 

of secondary failure, and increased safety. Consequently, there is a denite 

advantage in being able to detect, monitor and evaluate individual damage 

mechanisms before the failure of a composite. 

Acoustic Emission testing is a non-destructive condition monitoring 

technique which can be used for in situ monitoring of composite fatigue. 

Acoustic emissions (AE) are transient stress (pressure) waves which are 

generated by the energy released when microstructural changes occur in 

materials. 5, 6 

The stress waves travel through the composite and when they 

reach the surface, they cause it to vibrate. AE waves can be measured 

using very sensitive transducers which respond to surface displacements 

of several picometers. The AE technique can detect delamination, matrix 

5, 710 

cracking, debonding, bre cracking and bre pull-out. Hence, the high 

sensitivity of the AE technique may potentially enable early detection of 

damage. 

However, there's no such thing as a free lunch; the high sensitivity of 

the AE technique means that the measured AE signal may contain a high 

number of AE transients from sources in both the composite and the environment. 

The sources in the composite include damage growth, rubbing of 

crack surfaces and friction between the bres and the matrix due to their 

dierent material properties. The varying material properties will result in 

an anisotropic speed of propagation. 11 

In addition, reection and attenuation 

of the AE waves add to the complexity. Attenuation can be caused 

by geometric spreading, dispersion, internal friction and scattering. 12 

Fur-

1.2 Contributions 3 

thermore, the AE waves from damage growth can be buried in the AE 

generated by the friction and rubbing of crack surfaces. 6 

As a result, multiple 

AE transients with varying amplitude, duration, and frequency can 

be emitted in each cycle and simultaneously. The values of the AE signal 

features from cumulated damage usually fall in the same range as those 

4, 13 

that result from damage growth. Hence, designing the entire process 

from data acquisition through processing and analysis to interpretation of 

the AE signal emitted from composites subjected to cyclic loading is a 

challenging task. 

The research objective of this thesis is to make a valuable contribution 

towards the goal of using AE to facilitate early damage diagnosis and 

failure prognosis of CFRP composites subjected to cyclic loading. In order 

to achieve this objective the acquisition, processing, and presentation of 

the acoustic emissions is investigated. 

1.2 Contributions 

One contribution of this thesis is an algorithm to detect and determine 

AE hits in signals which include large number of overlapping transients 

with variable strengths. The algorithm is designed to overcome important 

limitations of threshold-based approaches in determining hits in this type 

of AE signal; for example, when the signal's amplitude between transients 

does not fall below the threshold for a predetermined period of time. The 

algorithm was presented in Acoustic Emission-Based Fatigue Failure Criterion 

for CFRP by Runar Unnthorsson, Thomas P. Runarsson and Magnus 

T. Jonsson 14 and used in four articles by the same authors. 1417 

The AE hits are frequently used as a damage measure. For this purpose 

AE hit count, AE cumulative hit count and AE hit rate are often 

recorded and interpreted. However, the time between the hits has not 

been studied. In this thesis three AE features are proposed and used to investigate 

whether useful information can be obtained by studying the time 

between the hits. These features are the inter-spike interval (ISI) feature, 

the hit pattern feature and the trough-to-peak pattern feature. The rst 

two features were presented in On Using AE Hit Patterns for Monitoring 

15, 18 

Cyclically Loaded CFRP and the trough-to-peak pattern feature was 

presented in An AE Feature for Issuing Early Failure Warning of CFRP

4 Chapter 1. Introduction 

Subjected to Cyclic Fatigue. 17 

The ISI feature is the timing between two 

sequential hits, and the hit pattern feature is essentially a technique for 

fusing AE features, extracted from each AE hit, and for nding and locating 

patterns which appear within the fused data representation. The 

trough-to-peak pattern feature is made by using a variant of the ISI feature 

as a input to the hit pattern feature. Furthermore, four Entropy-based features 

are studied in order to assess whether they are useful for condition 

monitoring CFRP subjected to multiaxial cyclic loading. The results of 

this study were presented in AE Entropy for Condition Monitoring CFRP 


The study of these features and the results 

form another contribution of this thesis. 

The main contribution of this thesis is a methodology for processing, 

presenting, and quantifying AE data for the purpose of identifying and 

tracking the locations of multiple AE sources. The locations are determined 

relative to the phase of a reference signal. This methodology was presented 

in Monitoring The Evolution of Individual AE Sources in Cyclically loaded 

16, 20 

FRP Composites. The results show that the tracking of AE sources 

can be used to facilitate early damage diagnosis and failure prognosis. The 

methodology is neither limited to AE signals nor to periodic reference 

signals. It can be used to study changes, or artifacts, in other signals using 

either periodic or aperiodic reference signals. 

Other contributions are an AE-based failure criterion 14 and a probabilitybased 

approach for providing an early warning of imminent failure. 17 

These 

two contributions are based on a 10% displacement failure criterion, which 

is used in this study. 

1.3 Outline 

The thesis is divided into 6 chapters, including this introduction chapter. 

Chapter 2 provides an introduction to bre-reinforced composites, their 

construction and properties. It also presents a detailed review of the cause 

and eect of the various defects and damage mechanisms which can be 

found in bre-reinforced polymer (FRP) composites. 

The subject of Chapter 3 is acoustic emissions (AE). The chapter starts 

with a background and literature section. The section, which is based on 

NDT Methods for Evaluating Carbon Fiber Composites , 21 

opens with a

1.3 Outline 5 

description of how AE is generated, measured, and processed. The various 

factors which can aect the propagation and waveform of the acquired 

AE are also discussed and the traditionally used methods for analyzing 

the AE signal are introduced. The section ends with a literature review 

of experimental results obtained using these methods and pattern recognition 

and classication approaches. The rest of the chapter introduces, 

formulates and discusses a hit determination procedure, new AE features, 

and a methodology for processing, presenting and quantifying AE data so 

that it can be used for identifying multiple AE sources and tracking their 

locations. 

In order to obtain AE data suitable for achieving the objective of this 

thesis an experimental procedure was designed and implemented. Seventy- 

ve nominally identical samples of a prosthetic foot were subjected to multiaxial 

cyclic loading up to failure. Chapter 4 describes the prosthetic foot, 

the experimental procedure, and the equipment used. 

Chapter 5 presents the results of the analysis of the experimental data. 

First, a general description of the fatigue behaviour is presented, followed 

by the results of three studies. The hypothesis of the rst study is that 

the probability distribution of an AE feature can be used to provide early 

warning signs of imminent failure in the feet. Failure is dened by a 10% 

displacement-based failure criterion. In order to investigate this hypothesis, 

the probability distributions of several AE features are estimated and 

evaluated. Because the warning signs are based on an estimated probability 

distribution it will not be able to detect and issue warnings for all 

impending failures. Hence, for the purpose of supplementing these results 

a second study is conducted to investigate whether an AE-based failure criterion 

equivalent to the 10% displacement criterion can be designed. The 

third and the nal study is a case study on the fatigue evolution of one 

prosthetic foot. The aim is to improve the results of the two prior studies 

by facilitating a damage diagnosis and a failure prognosis. The hypothesis 

of the study is that the methodology designed for identifying and tracking 

the locations of multiple AE sources can be used for this task. 

Chapter 6 concludes the thesis by summarizing its contributions and 

outlining some possible directions for future work.


"Prediction is very dicult, especially about 

the future." 

Niels Bohr 

2 Carbon Fibre-Reinforced 

Polymer Composites 

This chapter introduces Carbon Fibre-Reinforced Polymer (CFRP) composites 

to the reader. The rst section provides an introduction to brereinforced 

composites, their construction and properties. It is followed 

with a section which presents a detailed review of the cause and eect of 

the various defects and damage mechanisms which can be found in brereinforced 

polymer (FRP) composites. The rst two sections are based on 

NDT Methods for Evaluating Carbon Fiber Composites . 21 

The third section 

discusses the stiness degradation of FRP composites during fatigue 

and reviews some stiness-based fatigue modelling studies. 

2.1 CFRP Composites 

Approximately 80 years elapsed between the time when Sir Joseph Wilson 

Swan, in 1878, and Thomas Alva Edison, in 1879, independently produced 

incandescent lamps with carbon laments 22 

to the point at which carbon 

bres became a commercial product. The need for lighter and more heatresistant 

building material for the military and space applications was the 

23, 24 

main reason for increasing interest in carbon bres. This interest was 

an impetus for improving production methods 25 

which in turn made it

8 Chapter 2. Carbon Fibre-Reinforced Polymer Composites 

possible to manufacture cheaper bres. Recent years have seen an increasing 

interest in the use of carbon bres for applications in the automotive, 

aerospace and biomedical industries. Their popularity stems largely from 

their advantageous material properties such as high strength-to-weight ratio, 

fatigue strength, corrosion and heat resistance. 

The scope of this thesis is limited to carbon bre-reinforced epoxy composites, 

also referred to as carbon bre-reinforced polymer (CFRP) composites. 

Hence, the discussion in the remainder of this chapter is limited 

to bre-reinforced polymer (FRP) composites. 

A composite material is a nonhomogeneous material made by combining 

two or more dierent materials. Each of the constituent materials retains 

its own distinctive properties, while the composite will have properties 

which are a complex function of the proportion of each constituent and 

their interactions. When used in composites, carbon bres are used to 

reinforce materials such as metals, carbon, ceramics, and polymers. The 

reinforced material is referred to as the matrix. The composite will have 

properties which cannot be achieved with the matrix (cured resin) and the 

bres independently. 26 

The material properties of an epoxy resin are vastly dierent from carbon 

bres. Hence, the properties of a carbon/epoxy composite can be split 

into matrix dominated and bre-dominated properties. Many of the important 

properties of a composite are determined by the matrix. The matrix 

transfer loads internally to all the bres, determines the maximum service 

temperature, supports bres under compression and provides resistance to 

damage growth. 27 

In addition, the matrix provides interlaminar shear and 

impact tolerance. 28, 29 The bre-dominated property is tensile strength. 29 

Hence, the matrix dominates the transverse and compressive properties, 

but the bres dominate the axial tensile properties. 

Laminated composites are constructed by adding thin layers of sheets 

and resin. The bres come as chopped strand mats, woven and unidirectional 

sheets. Chopped strand mats consist of chopped bres that are 

evenly distributed and randomly orientated. The bres are held together 

with a binder. The strength of the mats is equal in all directions in the 

plane of the laminate. Woven sheets are formed from interlacing yarns, 

and are strongest in the direction of the bres, i.e. in two directions. The 

orientation of all bres in a unidirectional sheet is in the same direction.

2.2 Defects and Damage Mechanisms 9 

Their strength is therefore almost solely concentrated in that direction. 

Prepregs are mats and sheets which have been pre-impregnated with resin 

before being stored. 

The strength of carbon bre composites depends on the volume ratio 

of bres versus matrix. 30 

The higher the ratio, the stronger the composite. 

Properties of composites usually depend on the direction in 

27, 31 

which they are measured. This is called anisotropy. Metals are generally 

isotropic, which means that their strength and other properties are independent 

of direction. Composites therefore oer more design parameters, 

which is something that most designers welcome. The three dierent types 

of sheets oer many interesting possibilities for a designer. The stacking 

sequence and orientation of sheets can be used to obtain desired properties. 

It is possible to design a composite that can be easily bent, but hard to 

twist and vice versa, depending on the orientation of the bres. Also, it is 

possible to design a composite that shows negligible heat expansion over 

certain temperature intervals. This is because the coecient of thermal ex- 

24, 32 

pansion for carbon bres is negative, but positive for the epoxy matrix. 

Hence, the increasing demand for carbon bres can also be attributed to 

the fact that the material properties of composites can be engineered by 

changing the stacking sequence and orientation of bres. 

All the benets oered by CFRP composites, however, do not come 

without a cost; numerous defects and damage mechanisms can occur in 

these composites. The reasons why defects and damages occur can be 

diverse, but once they have occurred further damage is more likely to 

develop. This is because both the defects and the damages weaken the 

composite, which is required to meet its in-service requirements. 

2.2 Defects and Damage Mechanisms 

The initiation of defects and damage mechanisms in laminated CFRP composites 

can be roughly divided into three stages: during the manufacturing 

of bres and prepregs, during the construction of the composite, and during 

the in-service life of the composite. The following overview is divided 

into three parts, each corresponding to one of these stages.


2.2.1 Defects in Fibres and Prepregs 

Carbon bres can be made from many types of precursor materials, but 

rayon, pitch, and PAN have been used when mechanical properties are 

important. 31 

Rayon was used in the rst generation of carbon bres, but 

due to expensive production methods and high mass losses it isn't popular 

today. 33 

The main advantage that pitch-based bres have over their PANbased 

counterparts is that the precursor material is cheaper. 25 

The bres, 

however, have lower tensile and compressive strength, and although these 

properties can be improved it is expensive to do so. 25 

PAN, or polyacrylonitrile, is the most used precursor material for making 

carbon bres. The production of a bre starts by melting the polymer, 

pumping it through small holes and stretching it until it becomes a very 

thin bre (10-12µm). At the same time the precursor bres are oxidized 

in air at 200-300 ◦ C. 34 

Internal voids and surface defects are randomly generated 

in the bres during this process. 31 

During oxidization the bre becomes 

black and its material structure changes; hydrogen atoms disappear 

and oxygen atoms are added. If the core of a thick bre doesn't oxidize 

the bre will become hollow later in the production. Hollow bres have 

higher strength to weight ratio than solid bres. The oxidization process 

is the key limiting factor in the production, even though the time required 

has been reduced from hours to minutes. 25 

The next step is carbonation, 

where the precursor bres are heated up to 1000-3000 ◦ C, 24 

but now in an 

inert gas. According to S. Chand, 25 

nitrogen is often used for temperatures 

up to 2000 ◦ C, and argon for higher temperatures. The exact temperature 

used depends on the properties required. In general, the tensile modulus 

increases with higher temperatures. 25 

According to Landis et al., 35 

volatile materials are released during the 

heating process, resulting in a material that is almost pure carbon, or 92- 

99%. If the temperature exceeds 3000 ◦ C the bres turn into graphite, a 

soft material which has been used as a dry lubricant or a pencil lead. The 

dierence between carbon and graphite bres lies in how the carbon atoms 

are connected. In graphite bres the atoms are arranged in sheets. In each 

sheet they are connected in a hexagonal structure similar to chicken wire. 

The bonds between the atoms in each sheet are very strong, but the bonds 

between adjacent sheets are very weak. The weak bonds will break under 

stress and the sheets slide past one another. This is what makes graphite


a good lubricant. The structure of carbon bres is dierent; the sheets 

appear as though they have been laid in the direction of the bre and then 

crumpled. This results in a complex interaction between the sheets and 

makes it dicult for them to slide. 

After the carbonization process the bres are surface-treated and sized. 

These two last steps inuence how the bres will perform in a composite. 

By surface treatment the surface area of the bres can be increased, resulting 

in better bonding. 36 

The purpose of sizing is to protect them from 

24, 37 

corrosion, handling and to improve the resin bonding. If the bonding 

is too strong the impact resistance of the composite will decrease. 38 

During 

the production of carbon bres, the bres travel at high speed trough the 

machinery and occasionally rub against it. 39 

The sizing that is applied to 

the bres is intended to protect them from abrasion, but if they become 

scratched the sizing is damaged and the bre will lose strength. If the 

sizing fails the bonding between the bre and the matrix is more likely 

to break. Debonding of the bre/matrix interfaces (see Fig. 2.1) will render 

the matrix unable to distribute stresses to the bre, which results in 

reduced stiness and dierent damping characteristics for the composite. 40 

Figure 2.1 

Shows matrix cracks, broken bres, debonding and delamination. 

Woven prepreg material and unidirectional tapes are produced by impregnating 

the carbon bres in resin and allowing it to partially cure. During 

this process various random defects can be built into the defects, e.g. 

bre and tow misalignment. 41 

Material property data from suppliers of carbon 

bre/epoxy prepregs is commonly obtained using standards provided 

by the American Society for Testing and Materials (ASTM), e.g. ASTM 

D3039 for tensile strength, ASTM D790 for exural strength and SACMA 

SRM 1R-94 for compression strength. The test procedures outlined in


these standards are based on quasi-static loading of coupons. Quasi-static 

loading does not provide adequate characterization of the composite material 

under dynamic loading because the polymer responds dierently to low 

and high strain rates. 4244 

Random defects can be introduced during the 

production and handling of bres, so the material property parameters, like 

all other experimentally obtained data, follow probability distributions. 

2.2.2 Defects in Laminated Composites 

Careful quality control is important throughout the manufacturing process 

of a CFRP composite, from lay-up to nal nishing. This is because 

of the large number of defects which can be generated and other factors 

which can aect the mechanical properties of the composite. During the 

lay-up process, it is important to remove wrinkles when new layers are 

added. Wrinkles (Fig. 2.3) can cause air entrapment and resin build-up. 45 

They can therefore weaken the composite and render the design useless. 

Air entrapment, sometimes called voids, can occur between the bre lay- 

Figure 2.2 

Shows what happens when air gets trapped between layers. 

ers (Fig. 2.2) because air gets trapped between layers during the lay-up process. 

According to Schwartz 26 

voids and porosity can be caused by volatile 

entrapment during resin curing. Schwartz also remarks that if they are only 

partially entrapped then blisters are generated. Blisters are generated in 

the outermost layers. Voids and blisters weaken the composite and can 

also induce the formation of other types of damage. Foreign objects that 

get trapped between layers weaken the composite (Fig. 2.3). Examples of 

foreign inclusion are: oily residues left on the prepregs due to hand lotion


used by personnel, dust, hair, grease and other impurities. According to 

Adams and Cawley 45 

stresses can develop around foreign inclusions. These 

stresses can cause delamination and other damage. This has been used in 

research in order to manufacture composites with damage. 4649 

Delamination 

(Fig. 2.1) is when the bonds between layers break. It is the most 

common type of damage in composites. 5052 

The weakest bonding between 

layers is where voids and too much resin is located. When the inter-layer 

breaks, the stiness and buckling resistance decreases. 46 

Therefore, both 

too much and too little resin increases the risk of delamination. 

Figure 2.3 

Shows foreign inclusion and a wrinkle. 

It is important to use a suitable amount of resin for in the application, 

because temperature, stress and moisture can cause damage to the 

matrix. 45 

The ability of the matrix to distribute stresses can change during 

fatigue loading, hence aecting the endurance limit of the composite. 40 

Density variations, due to either too little or too much resin, can have 

serious consequences for the composite. According to Gaylord 53 

too little 

resin results in inadequate bonding between layers and the formation 

of voids and porosity. Too much resin lowers the volume fraction of - 

bres and increases the risk of cracks (Fig. 2.1). If the cure temperature of 

the resin is too high or the resin cures too fast then crazing can occur. 53 

This is characterized by very ne cracks on the surface and in the matrix. 

Crazing generally occurs where there is excessive resin or gel coat. The 

orientation of the bres is one of the composite design parameters. Fibre 

misalignment can therefore change the design and generate dierent load 

distribution than was anticipated by the designer. In some cases this will 

cause the matrix to take up the load and the composite will break.


Lay-ups are commonly consolidated in autoclaves using vacuum bagging, 

which is used to compress the part and squeeze out excess resin. This 

reduces the resin content, removes entrapped air, and as a result makes the 

part both lighter and stronger. During vacuum bagging, layers can slide 

and hence alter the design. This process depends on a large number of variables, 

including the mould geometry, locations of the resin outlets, resin 

temperature, vacuum pressure, and curing. The last three are functions of 

both time and location and must be repeated exactly the same way every 

time. Also, the moulds must be designed in order to ensure correct vacuum 

pressure and resin ow throughout the part. During the curing of the 

resin it warms up and its volume reduces due to polymerization shrinkage 

but the bres are unaected. This generates internal stresses between 

the matrix and the bres. 54 

When the composite cools down, additional 

stresses are generated because the matrix and the bres have a dierent coecient 

of thermal expansion. 54 

The stresses generated are called residual 

stresses. The residual stresses aect several properties of the composite, 

e.g. strength, fatigue and chemical resistance. The stresses can be reduced 

by extending the curing time. 

The nal nishing touches include cutting/drilling, grinding and assembling. 

These operations can easily cause damage to the composite. 

The most common reason for damage is forces that are applied perpendicularly 

to the direction of the bres. Composites, however, have very 

little strength in that direction. 55 

When the cutting tool used for the 

cutting/drilling operations enters and exits the material it can induce delamination. 

56 

Furthermore, localized defects such as bre pullouts, and 

55, 57, 58 

burning of the resin can also be initiated. The grinding operations 

can result in a higher temperature than the curing temperature; hence, 

the material property may be degraded. 59 

Low-velocity impacts such as 

dropping the composite part, dropping tools on the part, and mechanically 

hitting the composite during assembly can initiate delamination, break - 

46, 58, 6063 

bres, and generate cracks. Furthermore, mechanical joining of 

composite parts, such as bolting, will produce stress concentrations which 

can initiate damage growth. 64 Hence, improper selection of washer sizes 65 

and over-torquing 58 

can cause detrimental local damage around the bolt 

holes. Cut or broken bres weaken the composite. Fibre failure can be 

attributed to improper handling, imperfections, and both tensile and compressive 

stresses. Stresses can develop around the area where the bre


breaks. These stresses can cause other bres to break. 

2.2.3 Damages Initiated In-Service 

Damages initiated during in-service can be caused by a number of environmental 

and operational factors. The mechanical properties of epoxy matrices 

degrade when exposed to ultraviolet radiation, thermal cycling, high 

temperatures and moisture. Ultraviolet radiation, e.g. from the sun, causes 

matrix loss which results in a decline in the exural properties. 66 

Due to 

the dierent coecients of thermal expansion between bres and matrix, 

thermal changes cause the two materials to expand dierently and create 

stresses at the bre/matrix interface. These thermal stresses can lead to 

matrix cracking and debonding. 67 

Matrix cracking can lead to matrix loss 

68, 69 

which results in a drop in the matrix-dominated properties. In a high 

temperature environment, close to the glass temperature (Tg) of the epoxy 

matrix, the matrix softens, which results in a drop in the interlaminar 

shear strength and the exural stiness. The matrix also absorbs moisture, 

28, 67, 70, 71 

which has a plasticizing eect and leads to dimensional changes. 

Absorption leads to dimensional changes and lowers the glass transition 

temperature. 27, 28, 6971 This causes degradation in matrix-dominated properties 

such as stiness, shear strength, compressive strength, impact toler- 

28, 68, 72, 73 

ance and fatigue. 

Because the epoxy is brittle it is vulnerable to many types of impacts, 

such as dropping tools, stone and hail impacts to a car body, impacts to 

aircrafts from birds, hail and other objects, and wave impacts on the hull 

of a ship. In some instances impacts will only leave barely visible impact 

damage (BVID) on the impacted surface. 7476 

According to Komorowski 

et al., 77 

cyclic loading, moisture, temperature and viscoelastic eects can 

signicantly reduce the depth of the impact dents and make them BVID. 

In their paper, Hosur et al. 60 

inferred that the impact damage increases 

with depth and the maximum delamination occurs near the unimpacted 

side. 

When a slip in a bolted joint is initiated, wear and energy losses occur. 

78 

Under repetitive loading this can result in load-relaxation of the 

bolted joint, which can lead to accelerated damage growth. Cyclic fatigue 

of a composite is inuenced by the defects and damage mechanisms located 

randomly throughout the volume of the composite. Some of these


material aws will grow with repeated loading and cause premature failure. 

Furthermore, cyclic fatigue is also inuenced by factors such as the loading 

frequency and the load ratio. 7982 

The evolution of composites during 

cyclic fatigue is discussed separately in the next section. 

2.3 Fatigue 

In order to gain an understanding of the physical processes that occur 

during the fatigue degradation of FRP composites, the research has been 

limited to certain laminate sequences, geometries, and specic loading con- 

1, 83, 84 

ditions. 

The fatigue of composites has mainly been studied using standardized 

test coupons. These coupons are sometimes made with notched edges or 

with a hole. The following loading conditions have been predominant in the 

published literature: tension-tension, 8, 9, 83, 8589 90, 91 

tension-compression, 

compression-compression 92 and bending. 2, 93 Gamstedt and Sjögren stated 

that tension-compression loading is common in service applications and 

is more destructive than tension-tension loading for composites containing 

transverse plies. 91 

They concluded that this was due to more rapid debonding 

growth around the transverse bres in tension-compression loading, 

which caused earlier initiation of transverse cracks. 

Many models have been proposed for the task of predicting fatigue life 

and failure of composites. Some have been based on laminate analysis, 9496 

some on nite element analysis, 65, 97100 and others on measurable quantities 

such as stiness. Composites are widely used in applications where stiness 

is critical. Changes in stiness can be monitored by using displacement 

and loading measurements, both of which are readily obtainable while a 

composite is in-service. 

The stiness degradation of composites during cyclic loading can generally 

be divided into three stages: initial (I), gradual (II), and a nal (III) 

stage. 2, 87, 101, 102 This division is demonstrated schematically in Fig. 2.4. 

Dyer and Isaac also observed two stages in glass/polyester composites and 

concluded that the number of stages and the amount of damage within 

each stage depends on the laminate structure, matrix material, and bre 

type. 83 

Early during stage I damage starts to accumulate at an increasing rate.

2.3 Fatigue 17 

Figure 2.4 

Schematic progression of fatigue damage in composites. 

According to Daniel 103 

the duration of this stage, in an idealized case, 

is from 1 cycle to a few hundred cycles. The damage is mainly microcracks 

104 (transverse matrix cracks 2 ) and debonding. Debonding is incipient 

to micro-cracks transverse cracking. 91 

Other damage mechanisms 

such as the breaking of low strength bres, small edge delamination and 

8, 9, 104 

bre pullout can take place simultaneously. The reduction in stiness, 

at this stage, is mainly due to the development of transverse matrix 

cracks. 82 

A drop of the order of 10% in Young's modulus, or stiness, 

105, 106 

is often observed. However, an increase in stiness has also been 

reported. 107109 Sung and Jianping observed that stiness increases in E- 

glass/vinyl ester composites. 107 

They attributed the stiness increase to 

the viscoelasticity of the matrix and the alignment of bres to the loading 

direction. Kahn et al. 108 

tested woven Carbon Fabric with polyester resin. 

They explained that the stiness was usually observed in the beginning of 

cyclic testing. Ruggles-Wrenn et al., 109 

using a urea/urethane matrix, attributed 

the stiness increase to the straightening of bres. The fact that 

some investigations only report two stages (for an example, see the review 

by Dyer and Isaac 83 ), can be attributed to a short initial stage, i.e. if it is 

only few cycles, it may not be considered a stage. 

For a given load level, there is a limit on how many micro cracks can 

exist in the composite. Hence, the number of micro cracks will eventually


reach saturation point and the rate of new damage start to decline. When 

saturation occurs the matrix cracks start to form a regularly spaced pattern. 

This pattern was discovered by Reifsnider, who called it the "Characteristic 

Damage State" (CDS). 106 

The formation of CDS is located at the 

end of stage I, as shown in Fig. 2.4. Reifsnider determined that the saturation 

state is a property of the laminate and does not depend on the load 

history, environment, or residual stresses. The properties of the laminate 

include the material system, geometry, and both the properties and the 

orientation of the individual layers. Reifsnider explained that although the 

CDS does not depend on the loading history, it does depend on the maximum 

loading, i.e. if the maximum load level is not increased, the pattern 

will remain roughly unchanged during the cyclic life. Changes in material 

properties, i.e. corrosion and any damage which changes the load distribution, 

will also change the CDS. The micro-matrix cracks do not cause 

catastrophic failure when their number is low. However, as the number of 

cracks increases they can start to coalesce and form regions of high stress 

concentration. Stress concentrations can cause the development of critical 

damage mechanisms, e.g. delamination and bre breakage. For this reason, 

the state when the number of micro cracks reaches saturation point 

(CDS) is generally considered to be the starting point for the formation of 

critical damage mechanisms. 

Stage II begins after the CDS stage has been reached. In this stage 

micro cracks start to coalesce and delamination begins. 8 

This stage is characterized 

by a gradual, steady damage growth rate. 104 

Both the stiness 

reduction and damage accumulation become almost linear with the number 

of cycles, but at dierent rates. The gradient depends on the stress amplitude. 

103 

This stage accounts for approximately 80% of the fatigue life. 

Occasional deviations from linearity are often due to local delamination 

initiation which occurs when transverse cracks link up. 8 

In the third and nal stage the rate of damage accumulation increases 

rapidly 104 and the stiness decreases signicantly. 99 The damage accumulation 

is mainly due to irregular delamination growth, 2 

e.g. coalescence 

of delamination cracks. 92 

Damage accumulation in this stage ends in a 

catastrophic failure. The nal failure depends on several factors, such as 

the geometry, the loading conditions and the lamina sequence. In some 

composites failure can be in the form of a delamination, but in others the 

damage growth can change into bre breakage.

2.3 Fatigue 19 

Van Paepegem and Degrieck presented a fatigue damage model based 

2, 101 

on the residual stiness approach. In order to include the nal failure 

in the model, the authors needed to include strength properties. This was 

done by using a modied version of the Tsai-Wu static failure criterion. The 

results show that the model, despite the fact that it is one-dimensional and 

delamination was not considered, is capable of simulating the three stages 

in stiness degradation. 

Kim and Zhang used a normalized fatigue modulus for lifetime predictions 

of unidirectional Glass/Vinyl Ester composites. 107 

They observed 

stiness increase in the rst stage which they attributed to viscoelasticity 

of the matrix and also to the alignment of the bres with the loading direction. 

The normalized fatigue modulus was, on the contrary, monotonously 

decreasing throughout the fatigue life. For this reason the authors concluded 

that the normalized fatigue modulus better represents damage accumulation. 

The results also showed that the damage rate obeys power 

law. 

According to Zhang and Hartwig composites with a brittle epoxy matrix 

exhibit higher fatigue resistance than those with a ductile thermoplastic 

matrix (e.g. PEEK). 110 

Many microcracks form in the brittle matrix, but 

bres are more likely to break in a ductile matrix during fatigue. Thus, it 

is better to distribute the stress intensity over many crack tips instead of 

only few. The micro-cracks are most likely to be one reason of increased 

stiness during fatigue testing, due to rubbing resistance generated when 

opening and closing the cracks. 

Lee et al. presented a residual stiness degradation model for composites 

subjected to spectrum loadings. 111 

Model parameters need to be 

evaluated, but once they have been established the model can be used for 

predicting statistical distributions of the residual stiness and fatigue life. 

The model includes all types of damage because any damage will be re- 

ected in the stiness degradation and hence in the model parameters. The 

service data can also be used to track the stiness reduction of a composite 

in service. The model was validated using experimental data. The results 

show that the model and experimental data agree. The whole approach 

seems quite solid; however, the results depend largely on good evaluation 

of parameters. 

The load-displacement information can be used for generating new mea-


sures for evaluating composites. Such measures include non-linearity and 

energy loss, also known as hysteresis. Huang et al. estimated the dissipated 

energy from the load-displacement curves for predicting failure in 

composites. 112 

Although it is an interesting approach, their model did not 

treat laminates with delamination and was only tested using static load. 

Dzenis does not believe that hysteresis will be useful for monitoring 

damage development. 87 

He believes that the cumulative damage increments 

will be too small to have a signicant eect on the stress-strain diagram. 

There are, however, other ways of working with hysteresis. Thompson 

et al. analyzed the hysteresis loops of three dierent wood-based panels: 

OSB, chipboard, and MDF. 113 

Four parameters were extracted from 

the loops and monitored. The rst parameter, the loop area, represents 

the energy dissipated during one loop. The second parameter, the dynamic 

modulus, is the gradient of the line drawn from the two extreme points of 

each loop. The third parameter, the fatigue modulus, is the gradient of the 

line from the origin to the upper extreme point of each loop. This parameter 

combines the eects of both fatigue and creep. The last parameter, 

the microstrains, represents the deection. Thompson et al. demonstrated 

how the information provided by these parameters could be interpreted. 

Kim and Matthews suggested that the Specic Damping Capacity (SDC) 

would be an interesting way of presenting the variations in loop area. 114 

SDC is dened as the ratio of the energy dissipated in one cycle to the 

total energy stored in the same cycle. They also pointed out that since the 

area of one loop represents energy, the SDC can be computed as the ratio 

of one loop area to the next one. Using this technique Guild reported that 

SDC allowed him to detect cracks in unidirectional composites, which were 

not detectable by visual inspection. 115 

The technique also allowed them to 

detect cracks which were not discernable using an infrared camera. 

2.4 Discussion and Summary 

This chapter introduced carbon bre-reinforced polymer composites. A 

brief introduction was given on the properties of the constituent materials, 

the advantageous material properties of composites and also how one can 

design the properties of an composite. Emphasis was put on discussing 

what faults and defects can be found in composites, their formation and

2.4 Discussion and Summary 21 

how they aect the service life of the composite. The stiness degradation 

of composites during fatigue was also discussed. The discussion of the 

stiness degradation ended with a review of some stiness-based fatigue 

modelling studies. 

Despite the progress being made in understanding the damage process 

of composites, a rigorous failure theory is still lacking. Several fatigue 

models and failure theories have been published, 1, 116118 but they have been 

1, 84, 116 

limited to certain laminate sequences and specic loading conditions. 

Consequently, they need to be extended and adapted when dierent laminate 

sequences, geometries, and dierent loading conditions are required. 

Intuitively, by adapting existing fatigue models less accurate models are 

obtained. This is especially true when they are extended and adapted to 

complex shaped composites which will be subjected to complex fatigue 

loading. 

As mentioned in the introduction, in-service condition monitoring can 

be used to update and continually improve the fatigue models. These 

techniques can also be used by designers of laminated composites. The 

designers can rely on the available theory and experience only up to a 

certain point. In the end a "make and test" 116 approach is must be taken in 

order verify the design and ensure that it meets the certications required, 

such as those made by ISO 1 , ASTM 2 

and more. Certication tests are 

commonly destructive, time-consuming and costly. 

By using condition monitoring techniques during fatigue testing of composite 

prototypes, designers can obtain valuable information about the fatigue 

damage evolution. If detrimental damage mechanisms are observed 

early during testing the test can be stopped, the design improved, and a 

new prototype tested. By shortening the test time the amount of time required 

for this iterative process can be shortened considerably. This means 

that both the time to market and the corresponding cost will be reduced. 

Furthermore, by using the same techniques for condition monitoring during 

design and subsequently in-service, the information obtained during the design 

phase can possibly be used to develop a condition-based maintenance 

schedule. 

1 International Organization for Standardization 

2 American Society for Testing and Materials


"Enjoy the Silence." 

Depeche Mode 

3 Acoustic Emission 

Many non-destructive evaluation methods can be used for condition-monitoring 

composites. These include coin-tapping, vibrational, visual, thermal 

infrared, ultrasonic, eddy current and acoustic emission inspection. Factors 

which inuence the selection of a method include the cost involved, 

the time required to make measurements, access to the composite and the 

suitability of the method. In this thesis acoustic emission testing is studied, 

i.e. the acquisition, processing and presentation of acoustic emissions. 

The acoustic emission technique is a passive, non-destructive and sensitive 

technique which can be performed in situ without interrupting the 

operation of a composite. 

This chapter starts with an background section where the AE phenomenon 

is introduced, the AE technique presented and a literature review 

of experimental results obtained using the AE technique is provided. The 

background section is based on NDT Methods for Evaluating Carbon Fiber 

Composites. 21 

The remainder of the chapter introduces, formulates and discusses the 

contributions of this thesis related to AE signal processing. In Sect. 3.2 an 

AE hit determination algorithm is presented. The algorithm was presented 

in Acoustic Emission-Based Fatigue Failure Criterion for CFRP by Runar 

Unnthorsson, Thomas P. Runarsson and Magnus T. Jonsson 14 

and used 

in. 1417 

In Sect. 3.3 two new features based on the time intervals between hits 

are presented and also a well known feature from Information Theory, i.e.

24 Chapter 3. Acoustic Emission 

the entropy. The entropy is studied here for its use for condition monitoring. 

The features based on the time intervals between hits were presented 

and studied in On Using AE Hit Patterns for Monitoring Cyclically 

Loaded CFRP 15, 18 and in An AE Feature for Issuing Early Failure Warning 

of CFRP Subjected to Cyclic Fatigue. 17 

The results of the entropy study 

were presented in AE Entropy for Condition Monitoring CFRP Subjected 

to Cyclic Fatigue. 19 

The last section, or Sect. 3.4, presents the main contribution of this 

thesis. It is a methodology for processing, presenting, and quantifying AE 

data for the purpose of identifying and tracking the locations of multiple 

AE sources relative to a reference signal. This methodology was presented 

in Monitoring The Evolution of Individual AE Sources in Cyclically loaded 

16, 20 

FRP Composites. 

3.1 Background 

Acoustic Emission (AE) is a term used for transient stress waves which are 

generated by the energy released when microstructural changes occur in a 

material. 5, 6 

AE is measured using a passive, non-destructive measurement 

technique. The energy is provided by an elastic stress eld in the material. 

The stress eld can be generated by stressing the material, for instance 

using mechanical-, thermal-, pressure- and chemical stressing. These types 

of stress all contribute to fatigue failure and are commonly encountered 

in-service. The stress waves travel through the material and, when they 

reach the surface, cause it to vibrate. AE signals are acquired by measuring 

the minute surface displacements with sensitive transducers. From the 

acquired AE signal it is possible to detect delamination, matrix cracking, 

5, 710 

debonding, bre cracking and bre pull-outs. 

Acoustic Emission signals can be roughly divided into three types: 

bursts, continuous and mixed. 119 

Bursts are transient signals generated 

by the formation of damage, e.g. ber breaking and delamination. Continuous 

AE signals are generated when multiple transients overlap so that 

they cannot be distinguished and the envelope of the signal amplitudes 

becomes constant. Continuous AE can be generated by electrical noise 

and rubbing. The mixed type signal contains both bursts and continuous 

signals and it is the type which is normally encountered in-service.

3.1 Background 25 

If a composite is stressed and microstructural changes occur, then an 

AE is generated. If the stress is removed and then reapplied, then no AE 

should be generated unless higher stress is applied. This phenomenon is 

called Kaiser Eect and is valid for most materials. AE, however, can be 

generated at stress levels below those previously applied. This is known as 

the Felicity Eect. One reason for this eect is material degradation, i.e. 

damages can occur and grow at lower stress levels. Other sources which can 

contribute to the eect are the opening and closing of cracks, the rubbing 

of delamination surfaces and the rubbing of parts. AE is also generated 

under loading because of the dierent material properties of the bers and 

the matrix. 120 

AE that comes from other sources, such as machinery and 

electricity, are considered to be disturbances or noise. AE noise from the 

environment is generally strong; hence, it has the potential to be a huge 

problem. However, the noise is commonly located at frequencies that are 

much lower than the AE generated by a material damage, and therefore it 

is not as big problem as it could be. 7 

3.1.1 Propagation 

As the stress waves propagate from the AE source they are inuenced 

by a variety of factors. These factors include propagation velocities, attenuation, 

reection, refraction, discontinuities and the geometry of the 

material. 

The propagation velocity of an elastic stress wave depends on the wave 

type, material properties and frequency. Stress waves can be split into two 

classes depending on where in the material they travel: body waves and 

surface waves. The body waves travel inside the material as either P-waves 

or S-waves. P-waves are compressional waves and S-waves are shear waves. 

P-waves generally propagate at higher velocities than S-waves. 121 

Two special 

types of shear waves can occur: SH-waves and SV-waves. These two 

types of waves are polarized so that the wave propagations are respectively 

on a horizontal and a vertical plane. The surface waves, as their name indicates, 

travel along the surface of the material, hence they are in essence 

plane waves. Their propagation velocities are typically smaller than the 

velocity of S-waves 122 

and since they only spread out in two directions 

their amplitude attenuation is less than body waves. Rayleigh and Love 

waves are two special surface waves. Rayleigh waves are vertically polar-


ized (surface SV-waves) and Love waves are horizontally polarized (surface 

SH-waves). Both are dispersive and the amplitudes decreases exponentially 

with depth. Flexural waves, or Lamb waves, are a special class of 

waves which occur in plates which are bounded by two surfaces, e.g. laminated 

composites. There are three fundamental classes of Lamb waves, 

analogous to the body waves: LP, LSH, and LSV. 123 

Two modes of Lamb 

waves are observed in thin plates: extensional (symmetric) and exural 

(antisymmetric) modes. The largest component of the extensional mode 

lies in the plane of the plate, while the largest exural mode component is 

out of the plane. 124 

The wave velocity in isotropic and homogeneous materials depends on 

the density and stiness of the material. Fiber-reinforced composites are 

anisotropic and inhomogeneous; hence, the wave velocity is anisotropic. 

Furthermore, the wave velocity is a function of frequency, 123 

i.e. high and 

low frequency waves will separate as they propagate. This separation is 

referred to as dispersion and results in an amplitude decrease. A parameter 

which describes the resistance of a material to transfer waves is the 

acoustic impedance. This parameter is analogous to electrical impedance. 

The acoustic impedance depends both on the wave type and the frequency. 

It is dened as the product of the material density with the velocity of the 

wave type. When the waves come across inhomogeneities such as defects, 

interfaces between the constituent materials of the composite, and the surface 

of the composite, they will reect and refract. The actual response 

depends on the acoustic impedance of the two adjacent materials and the 

angle of incidence between the wave and reecting boundary. Assuming 

that the wave's energy is conserved, the energy per unit area of the wave 

decreases as the surface area of the wave increases. Hence, the rate of decrease 

depends on how the wave propagates, e.g. as plane-, spherical- or 

cylindrical waves. The wave's energy, however, is not conserved. Due to 

internal friction, part of the energy is converted into heat. Consequently, 

when a stress wave nally arrives at the transducer its waveform parameters 

will have changed. For these reasons, the analysis and interpretation 

of AE signals is a complex subject.


3.1.2 Measurements 

AE waves generate small surface displacements which can be measured 

by using appropriate transducers which respond to surface displacements 

to the order of several picometers. Several types of transducers can be 

used for this: piezoelectric, capacitance, electromagnetic and optical. The 

last two are non-contact, but electromagnetic transducers are considerably 

less sensitive than piezoelectric transducers. Optical sensors, e.g. laser, 

are free of resonance and can be absolutely calibrated by measuring the 

correct amplitude of the AE. 125 

Piezoelectric transducers are the most popular and are either of a broadband 

or a resonance type. The transducers are made by using a special 

ceramic, usually Porous Lead Zirconate Titanate (PZT). Figure 3.1 shows 

a schematic view of a piezoelectric transducer and how an AE is converted 

into an electric representation. The vibration of the composite is transferred 

to the PZT inside the transducer through the wear plate. When the 

PZT element vibrates it generates an electric signal. The transducer's signal 

is, therefore, a 1D voltage-time representation of the 3D displacementtime 

wave that it senses. 

Figure 3.1 An illustration of a typical resonant AE transducer and how an AE 

is converted into an electric representation. 

Measurements using piezoelectric transducers are sensitive to how the 

vibration is transferred to them. The main factors that aect this are: the


surface of the composite, the transducer's pressure against the composite, 

and the coupling medium. 126 

The presence of a transducer aects the 

vibration of the composite; however, this is unavoidable when using contact 

transducers. The direction of the waves also aect the transducer's 

response. This is because AE transducers are nearly always designed to 

measure the components of the AE waves that are normal to the surface. 127 

Although the stress waves typically have components in the normal direction 

this directionality means that the response to identical waves arriving 

from dierent direction will not be the same. 

The selection of transducers is most often based on their frequency 

response curves, also known as calibration curves. These curves can be 

absolute or relative. The most typical calibration curves are relative displacement 

and pressure response curves. Relative curves are useful for 

comparison of transducers. The curves are generated by exciting transducers 

with continuous sine waves. The resulting response curves do not 

provide information about the response to signals arriving from dierent 

directions. The frequency response of a resonance transducer can vary 

by several decibels for dierent frequencies. This is demonstrated by the 

rugged response curves shown in Fig. 3.2. 

Figure 3.2 Two calibration curves for the same resonant AE transducer. The 

red curve is the result of a pressure calibration and the green is the result of a 

displacement calibration (reproduced with permission from Vallen GmbH). 

AE transducers behave like displacement sensors for very low frequencies, 

but with increasing frequency their response becomes much more like


that of velocity sensors, and for even higher frequencies the response approaches 

that of pressure transducers. 128 

For piezoelectric sensors the transition 

range from displacement to pressure response is from several kHz to 

a few MHz, i.e. the transition is not immediate. The transition depends 

on variety of factors, such as the coupling, the sensor's characteristics, the 

test specimen's properties, etc. 

At Vallen Systeme GmbH pressure and displacement curves are generated 

by connecting an exciter face to face with the corresponding transducer. 

129 

In both cases continuous sine waves are used for excitation. Pressure 

curves are generated by exciting the sensing area uniformly, but displacement 

curves are performed by using an exciter with small aperture 

size. The displacement calibration is an attempt to simulate line excitation 

of a travelling displacement wave. Figure 3.2 demonstrates the dierence 

between these two calibration methods. The red curve is the result of a 

pressure calibration and the green curve is the result of a displacement 

calibration. The resulting response curves are more relevant for continuous 

and long duration AE signals than for transient AE signals. Some 

authors have deconvolved the AE signal with the frequency response of 

the transducers as an attempt to minimize the eect of the rugged frequency 

response of resonant transducers. The transducer's response 

86, 130 

to transient signals is, however, dierent from the response to continuous 

waves. Hence, the convolution may not work as intended or even make 

things worse. 

In order to determine the placement of sensors and calibration of the 

measuring equipment the method of breaking pencil leads on the surface of 

the composite is often used. This method is also known as a Hsu-Nielsen 

source. For this procedure a mechanical pencil and Pentel 2H 0.3 mm 

lead is used. In a paper by Higo and Inaba 126 

it is reported that, when 

Dr. Hsu rst suggested this procedure in the year 1975, 0.5 mm lead 

was used. The reason for changing the diameter is because the properties 

of the lead have changed. Change in properties will result in dierent 

AE signal when they break. In order to produce a consistent AE signal 

a Teon guide collar is sometimes put on the tip of the pencil. Hsu- 

7, 12, 131133 

Nielsen source has also been used for generating AE in research. 

According to Prosser and colleagues 133 

pencil lead breaks can simulate 

impact damage and delamination AE. Other ways of articially generating 

AE signals include using pulse generators or spark guns. 134


3.1.3 AE Features 

Over the years many research projects have been conducted with the aim of 

extracting useful information from AE signals. The extracted information 

is stored in n-dimensional data structures, known as features. A number 

of techniques can be used for studying AE features. These techniques 

include trending-, statistical- and classication techniques. Here, the AE 

feature extraction approaches, the corresponding features, and the rst 

interpretation steps are described. For this, the approaches are grouped 

into four types: activity-, hit-based-, frequency-, and waveform analysis. 

Classication approaches will be discussed later in this chapter. 

Activity analysis is the process of detecting trends and abrupt changes 

in AE features over time. Common features used in this analysis include 

135, 136 

the number of AE hits and the signal's energy. The features are 

extracted and compared regularly. Additional parameters are sometimes 

acquired at the same time and used for reference. Activity analysis is 

mainly represented graphically by plotting the features against time. The 

activity can be studied by plotting either the absolute feature values or 

their cumulative sum against time. 135 

Two ratios are often used when load is used as a reference parameter, 

namely the Felicity ratio and the Shelby ratio. The Felicity ratio is the ratio 

of the lowest load that generates a certain amount of AE activity, during 

loading, against the highest load in last cycle. 137 

The ratio was described 

by Dr. Timothy Fowler and has been used as an indicator of damage 

with mixed results. 137 

Instead of looking at the loading of a composite the 

Shelby ratio looks at the unloading. The Shelby ratio is therefore analogous 

to the Felicity ratio. The Shelby ratio is dened as the ratio of the lowest 

load that generates a certain amount of AE activity, during unloading, 

against the previous maximum load. 120 

If the level of AE activity isn't 

reached then the ratio is dened as 1.0. The Shelby ratio, described by 

Dr. Marvin A. Hamstad, is useful for detecting damage that generates AE 

from friction. This ratio hasn't been used much in the literature, but if an 

AE is generated from friction it is believed that it can provide important 

information about the condition of a composite. 89


Hit-based Analysis is the analysis of AE hits using a certain set of 

features, or waveform parameters. AE hits are the portions of a measured 

AE waveform which satisfy a given detection criterion. The purpose of the 

detection criterion is to determine the presence of AE and discriminate it 

from background noise, or continuous AE. Because AE is mainly transient 

stress waves, the term AE hit is usually understood as an isolated and 

separated transient from the acquired waveform. 

There are many detection techniques which can be used for determining 

AE hits. A common technique used in real-time commercial parameterbased 

AE systems is to compare the AE signal against a certain threshold. 

The threshold is typically set on the positive side of the signal and held 

in a xed position, but it can also be oating. A hit is detected by comparing 

the AE signal against the threshold, and if the signal surpasses the 

threshold a hit is detected. Three parameters are commonly used with 

this detection technique: a hit denition time (HDT), the hit lockout time 

(HLT), and the peak denition time (PDT). A timing parameter is triggered 

every time the threshold is crossed. If the time which has elapsed 

since the timing parameter was last triggered equals the HDT parameter, 

then the hit has ended. The HLT parameter species the amount of time 

which must pass after a hit has been detected and before a new hit can be 

detected. The PDT parameter species the time allowed, after a hit has 

been detected, to determine the peak value. 

Conventional AE hit-based features include amplitude, duration, energy, 

number of peaks above certain threshold (ring-down count) and rise 

time. 136 

Figure 3.3 illustrates how these and other common hit based features 

are related. 

New features can be designed by processing existing ones. The processing 

includes, but is not limited to: adding, subtracting, multiplying, and 

dividing two or more features. New features can also be made by ltering 

and extracting statistical information from the features in the set, e.g. 

variance, skewness and kurtosis. 

Trend analysis of hit-based features is widely used. Sometimes trending 

is carried out by plotting the cumulative sum of the feature. In some applications 

trending can be sucient, e.g. when monitoring of the AE signal's 

power alone is of interest. In many cases, however, further analysis is required. 

In some cases more information about a feature can be gleaned by


Figure 3.3 

Illustration of conventionally used AE hit-based features. 

studying its statistical parameters and its correlation with other features. 

The statistical distribution of a feature can be estimated from a histogram 

of its values. The shape of the histogram can provide useful information, 

e.g. the shape of the amplitude histogram can help to identify 

the damage mechanism which generates the AE. 135 

Correlation analysis 

is often performed using cross-plots by plotting one feature as a function 

of another. For this task, the following feature pairs are often used: AE 

counts vs. amplitude, AE counts vs. duration, and duration vs. amplitude. 

These plots can further help with the identication of the damage mechanism. 

Correlation analysis can also be performed in higher dimensions, 

but the correlation of four and more features may be dicult to visualise. 

One of the advantages of using AE features is that they provide a huge 

data reduction compared with a full waveform acquisition, but there are 

several practical disadvantages. First, the fact that the same type of damage 

can emit AE signals with dierent amplitudes makes it dicult to 

set the threshold. Second, AE signals in composites suer from high attenuation, 

which means that signals close to the transducer are stronger 

and more likely to be detected than those generated further away. Third, 

the rugged frequency response of resonance AE transducers means that 

frequencies which are spaced only a few tens of kilohertz apart, will be


magnied dierently. The magnication can dier by several decibels. Finally, 

if only the AE features are stored then the analysis is limited to 

these features; it is impossible to study dierent results using other threshold 

settings. 

Frequency analysis involves the study of the frequencies contained in 

the AE signal and how they can be used to help identify dierent sources. 

Frequency analysis is most often conducted using the Fast Fourier Transform 

(FFT). Commonly used frequency features include frequency centroids, 

peak frequency, and the power in frequency bands (subbands). 136 

In order to perform an accurate interpretation of these spectral features 

one must take into account all the waveform shaping which the AE undergoes 

(see Sections 3.1.1 and 3.1.2 and also the last paragraph). Consequently, 

dierent results will be obtained using dierent materials, geometries, 

transducers and setups. If one is only interested in detecting changes, 

then trending analysis of the features can be used. Trending analysis allows 

the detection of trends and abrupt changes without the need to interpret 

the value of the features accurately. 

AE signals are mainly transient stress waves, meaning that they are 

time-varying signals. AE signals can also be non-linear. Power spectrum 

analysis, for instance using FFT, only shows which frequencies exist in 

the signal and how they are distributed. This is because the FFT is not 

designed to analyze transient signals, but rather continuous signals. Timefrequency 

representations are methods designed to analyze time-varying 

signals. Among the methods that have been used for this task are the 

Short-Time Fourier Transform (STFT) and the Wavelet Transform (WT). 

These transforms are most commonly interpreted by visual inspection. 

The STFT is an enhanced version of the standard FFT. The idea behind 

the STFT is to divide the signal into portions where it is stationary. A 

window function is used to extract the portions from the original signal. 

The portions are then processed using FFT. Hence, the STFT is basically 

a FFT with a window function. The time-frequency localization obtained 

is from the location of the window functions. The frequency localization 

suers due to the limited size of the window. For a given window size, the 

STFT has a constant localization resolution at all times and frequencies. 

By increasing the window size, the frequency localization can be improved, 

but then the time localization gets worse, and vice versa. This problem


is related to the Heisenberg's Uncertainty Principle, which can be applied 

to time-frequency localization of signals. Basically what it says is that we 

cannot know both the exact localization of time and frequency. 

In the recent years there has been increasing interest in using methods 

based on the Discrete Wavelet Transform for analyzing AE signals. The 

Discrete Wavelet Transform (DWT) was designed to improve the STFT, 

within the boundaries set by the Heisenberg's Uncertainty Principle. Both 

these transforms are linear. Instead of using a xed window the DWT uses 

scaled windows. 138 

The DWT has a good time and poor frequency localization 

at high frequencies, and good frequency and poor time localization at 

low frequencies. The transform has at least two serious drawbacks. First, 

it is not time-invariant, which means that small shifts in the signal can generate 

completely dierent coecients. Second, due to its ability to detect 

sharp changes, the wavelet transform is sensitive to noise. 

Waveform analysis of AE signals is the study of fully digitized AE 

waveforms their shapes and modes of propagation. Full waveform acquisition 

and analysis of high frequency AE signals places a high demand on 

the computer memory, the data storage, and on the computing power. At 

the same time it oers nearly endless possibilities for signal manipulation 

and feature extraction. Furthermore, the digitized waveform can be reused 

to study the eects of dierent threshold settings and signal processing on 

hit-based features. 

By analyzing the full AE waveform more information about the damage 

mechanisms can be obtained than when using only hit-based features. 

Additional information about the damage mechanisms, and the material, 

can in some cases be obtained by studying Lamb waves, i.e. Lamb wave 

velocity can be related to the modulus of the material. 139 

The two propagation 

modes of Lamb waves are the lowest order symmetric (S 0 ) and the 

antisymmetric (A 0 ) Lamb modes. The two modes are also known as exural 

and extensional modes. These two modes have dierent properties, 

e.g. the exural mode components are sensitive to dispersion but extensional 

mode components are not. The analysis technique in which 

124, 140 

the properties of these modes are studied is known as modal AE.


3.1.4 AE Analysis 

A number of investigations into the behaviour of AE signals have revealed 

that the evolution of the cumulative AE count, during cyclic testing of 

composites, can be divided into three stages: initial (I), gradual (II), and 

8, 9, 86, 141 

a nal (III) stage. These three stages are analogous to the three 

stages in the stiness degradation, depicted schematically in Fig. 2.4. Stage 

I is characterized by high AE activity which is associated with the formation 

of new damage mechanisms 86 

arbitrarily located throughout the material. 

At the end of the stage the activity decreases and becomes nearly 

87, 99 

constant. The AE activity during stage II is mainly due to friction 86 

and a 

constant rate of delamination. 8 

Occasional new damage will result in high 

AE activity bursts which will change the AE activity rate temporarily. 8 

During stage III the AE activity increases rapidly until failure. 

During the cyclic testing of composites AE is generated by both actual 

damage progression and cumulative damage, i.e. friction. AE from cumulative 

damage can be generated many times but AE from the formation 

of new damage occurs only once; hence, the majority of the emissions are 

related to cumulative damage. The values of AE features from cumulated 

8, 87 

damage usually fall in the same range as the ones from damage growth 

and it can be very dicult to distinguish between the two types. Because 

important AE events can get buried in the AE signals generated by friction 

6, 86 

and the rubbing of crack surfaces attempts have been made to lter out 

8, 87, 89 

AE events from these damage mechanisms. Several approaches have 

been used; for example, thresholding the AE features, coupling the AE 

to the load, 8 limiting the analysis to a part of the loading cycle, 87, 89 and 

conducting frequency analysis. 86 

Thresholding AE features can be dicult 

both due to attenuation and the fact that the same type of damage can 

produce AE with dierent amplitudes. 133 

As suggested and investigated 

by Dzenis, 87 

it is intuitive to assume that more AE from friction ought to 

be generated during unloading and more AE from new damage during the 

loading of a composite. Hence, by splitting the fatigue cycle into loading 

and unloading Dzenis determined that fatigue damage in unnotched laminate 

develops mainly during loading. Awerbuch and Ghaari concluded 

that frictional AE should not be eliminated as it may provide important 

information about the condition of a composite. 89 

They argued that damage 

detection could be made easier by using frictional AE, since damage


growth, i.e. a material change, produces AE only once, but the resulting 

rubbing of damage surfaces generates AE many times. 

Dierent and in some cases contradictory results have been published 

using amplitude features. According to Duesing, 11 Barré and Benzeggagh 

142 and Ativitavas et al. 143 ber breakage emits high AE amplitudes 

whereas Ono explains that high amplitudes are caused by rapid advances 

of delamination and carbon ber fracture is characterized by low amplitude 

signals. 144 

Godin et al. claimed that conventional AE feature analysis 

cannot be used to distinguish between dierent AE sources and suggested 

that more advanced methods, such as multivariate analysis and classiers, 

should be used. 145 Similar comments were made by Tsamtsakis et al.; 8 

they suggested that new parameters, such as force or displacement, should 

be added. 

Ativitavas et al. developed an amplitude ltering technique using a 

normalized load to lter out low amplitudes, and claimed that a reliable 

isolation of AE signals due to ber breakage was obtained. 143 

The intuitive 

reason behind this is that it requires more energy to break the bers than it 

does to damage the matrix, because the bers have higher Young's modulus 

and higher strength. Hence, high amplitude AE is generated when the 

bers break. This idea was veried by comparing the cumulative signal 

hits (with respect to the loads of the ltered signal) with cumulative signal 

strength and the cumulative number of ber breaks. The results showed 

strong correlation. 

Acoustic Emission frequency analysis techniques have mostly been limited 

to classical approaches like the FFT. When used, the aim has been to 

determine frequency bands which can be related to certain damage mechanisms. 

The results presented by Bochse determined the frequency bands 

for three types of damage. 146 

Frequencies due to matrix cracks were found 

to reside in the 100 to 350 kHz band, and ber breakage was given the interval 

between 350 to 700 kHz. The sources were classied according to the 

criterion that 70% of the signal power had to lie within either frequency 

band. If not, the source was expected to be debonding. Similar results 

were presented in a paper by de Groot et al. in which the frequency spectrum 

between 50 to 600 kHz was analyzed. 49 

They determined that matrix 

cracks emit frequencies between 90 to 180 kHz, ber pull-out release frequencies 

between 180 to 240 kHz, debonding produces frequencies between 

240 to 310 kHz, and that bre breakage gives AE with frequencies above


300 kHz. Iwamoto et al. used both feature and frequency approaches in 

their study based on bridging ber failure in unidirectional CFRP composites. 

147 

They discovered that bridging ber failure generates a large amount 

of AE energy which lies in the 600 to 700 kHz frequency region. The results 

of power spectrum analysis research studies tend to agree with this. The 

exact location and size of the frequency intervals detected, however, dier 

slightly. 

Kamala et al. used Wavelet-based analysis of AE signals obtained during 

uniaxial fatigue loading of CFRP composites. 86 

By using the Wavelet 

transform they were able to analyze the AE signal at dierent levels. Their 

results showed that 95% of the AE signal is located at levels with central 

frequencies of 120, 250 and 310 kHz and that friction-related emissions 

have frequencies between 250 to 300 kHz. 

Hamstad et al. studied the application of WT in order to identify AE 

sources in an aluminum plate. 148 

The signals were articially generated 

using nite element code. The WT was calculated using a freeware wavelet 

software tool, AGU-Vallen Wavelet. They studied the ratio of the WT 

coecients of extensional to exural Lamb wave modes. The results showed 

that, when the sources were located at the same depth, it was possible to 

use the ratios to distinguish dierent source types. When, however, the 

sources were located at dierent depths the discrimination between sources 

was worse. 

According to Surgeon and Wevers, 131 

plate wave theory makes it possible 

to study the eects of attenuation and dispersion theoretically. They 

also report that several advantages of using modal analysis have been identied 

in the literature, i.e. the method is better at detecting, distinguishing 

and locating AE sources. Prosser was able to eliminate noise by analyzing 

the waveform of dierent damages. 124 

He found that cracks create mainly 

extensional mode waves and both delamination and impacts create primarily 

exural mode waves. The AE noise he was dealing with was generated 

by grip damage and was mainly made of exural mode waves. By using this 

information, he was able to distinguish between noise and matrix cracks. 

The waveform of AE can also be used to get better localization of AE 

sources than when using conventional triangularization methods. Prosser 

located sources by matching similar phase points of the acquired AE waveforms. 

This resulted in extremely accurate source location. By 

124, 140 

using


waveform analysis of AE acquired using 4 sensors, Prosser was also able 

to see from his measurements that the cracks initiated at the edge of a 

composite specimen. 149 

Pattern recognition and classication have been applied to the features 

extracted from AE signals; however, pattern recognition for AE features 

has not been established as a reliable tool. The main reason is that the 

interpretation of AE data is not straightforward. In fact, it can be dicult 

even for an experienced AE specialist. 

Ebenezer et al. used time-frequency based methods for classifying timevarying 

transient AE using the Matching Pursuit decomposition (MPD) 

algorithm. 150 

This algorithm uses a dictionary which is formed using timeand 

frequency-shifted versions of selected signals. The signals selected 

represent each class which is to be detected. Several samples are used for 

each class. The results show that the MPD is well suited for AE signal 

classication. The main drawback is high computational complexity, but 

the authors proposed techniques to reduce it, such as using a pre-classier. 

Pon Varma et al. compared several methods of AE classication. 151 

These methods were: 2-D matched ltering using spectrogram and the reassigned 

spectrogram; the narrowband Ambiguity Function (AF), which is 

a 2D FFT of the Wigner distribution; the cross AF; and the matched pursuit. 

Their results on real data show that the matched pursuit performed 

best. Articial Neural Network (ANN) was studied by Bhat et al. by 

suppressing noise. 85 

The ANN was trained to learn dierent noise sources. 

The input features used were rise time, energy, ring-down counts and peak 

amplitude. The results showed 90-99% classication accuracy. Diculties 

in discriminating the noise from the AE signal due to overlapping characteristics 

was the main reason for not obtaining a higher level of accuracy. 

Classication of AE signals was also studied by Rippengill et al. 152 

They started with four features and reduced them to two by using Principal 

Component Analysis (PCA). Bursts were extracted by setting the 

threshold to six standard deviations from the mean. The authors mention 

that the component with least variance may in fact be the one that has the 

most discriminant power and the PCA method may erroneously discard it. 

The data was clearly separable using conventional AE features. For automatic 

classication, however, the authors used two statistical methods 

and an ANN. The statistical methods were Gaussian statistical methods,

3.2 AE Hit Determination 39 

whereby they used multidimensional Gaussian distribution as a discriminant 

function for quadratic discriminant analysis, and kernel density estimation 

(KDE). The ANN was a standard multi-layer perceptron (MLP) 

trained with backpropagation. Each class had an output, with a total of 

three. The classication results were quite good, as was to be expected. 

Clustering of features has also been used. This provides a convenient 

way of detecting when changes in the AE signal occur. Clustering of Principal 

Components was studied by Kaveh et al. 153 

The authors of the study 

used PCA as a convenient way of summarizing the signicant statistical 

characteristics of a group of random signals in terms of an orthonormal 

basis set. They looked at the rst eigenvectors and their frequency distribution. 

Self-Organizing Maps (SOM) were studied for clustering, classication, 

and discrimination of transients. An alternative to PCA is the 

Hebbian algorithm. Yang and Dumont used Hebbian algorithm to extract 

features, from AE signal, which they used as input for ANN. 154 

The objective 

was to automatically classify the AE from ve dierent types of 

wood. The classication accuracy obtained was 90% for both raw and 

compressed data; however, using the compressed data less training time 

and better generalization was achieved. Omkar et al. used fuzzy c-means 

clustering to classify AE from dierent sources. 134 

The data points had four 

input features: event duration, peak amplitude, rise time, and ring-down 

count. The AE came from four dierent sources (classes): Hsu-Nielsen 

source, spark gun, pulse generator and from noise. The classication accuracy 

of pencil and spark signals was above 93%, but for the noise and 

pulse source the accuracy was around 80%. The authors partly attributed 

this to overlapping between the classes. 

3.2 AE Hit Determination 

In complex systems, where high AE activity is observed it may become 

dicult to separate individual transients using a pure threshold-based approach. 

There can be several reasons for this, such as variable amplitude 

of the continuous AE within a loading cycle, and overlapping of transients, 

which can be simultaneously emitted from the many AE sources 

in the material. These transients have varying strength, duration, shape 

and frequency. Hence, as the complexity of the AE signal increases, more


advanced signal processing methods are required to detect and separate 

transients. 

In the remainder of this section the approach used in this study for 

locating and determining hits is described. This approach is designed to 

overcome the abovementioned limitations of pure threshold-based hit detection. 

Figure 3.4 shows a ow chart of the procedure. In the rst step, 

the acquired AE signal is processed in order to extract descriptive features 

for detection. The resulting signal is called a detection function, or novelty 

function, and can be in any suitable domain of interest, e.g. in both the 

time and the time-scale/time-frequency domains. For detecting and locating 

hits, the detection function is input to a peak-picking algorithm which 

automatically detects hits based on the trough-to-peak dierence of local 

troughs and peaks. In the nal step, the detected transients are compared 

against a threshold, both to locate the hits more accurately and to lter 

out weak hits, for instance those from background noise. 

Figure 3.4 

Flow chart of the AE hit determination procedure. 

3.2.1 Detection functions 

Assuming an acceptable signal-to-noise ratio (SNR), most transients can 

be detected in the time domain using the temporal characteristics of the


signal, i.e. the amplitude. Temporal amplitude increase is one of the 

key properties of transients and is, for example, used in threshold-based 

hit determination. The signal's instantaneous energy can also be used 

in a detection function. The energy can be calculated by squaring the 

amplitudes: 

E[i] = |x[i]| 2 ∆t (3.1) 

where x is the acquired AE signal and the use of square brackets serves 

as a reminder that the values are discrete. Because the sampling interval 

∆t is a constant it will not aect the peak-picking and can be omitted. 

In acoustics, the energy is commonly expressed in base-10 logarithm scale, 

known as the decibel (dB). The logarithm transformation changes the dynamic 

range of the signal by enhancing low values, while compressing high 

values. The logarithmically converted energy can be expressed by 

E log10 [i] = 10 log 10 |E[i]| = 10 log 10 

∣ ∣ x[i] 2∣ ∣ = 20 log10 |x[i]| . (3.2) 

Equation 3.2 shows that the transformed energy is a logarithmic transformation 

of the raw signal envelope multiplied by 20. Because hits will 

be determined by peak-picking the detection function, the multiplication 

can be omitted. Also, in order to ensure that the detection function is 

positive and remove the need to deal with numbers less than one, whose 

logarithms are negative, the rectied signal values are incremented by one. 

The resulting detection function is: 

DF [i] = 20 log 10 |1 + |x[i]|| (3.3) 

Because the detection function is based on the raw signal envelope, it 

may be too jagged to accurately perform peak-picking. Hence, in order to 

improve peak-picking the detection function can be ltered. 

Another property of transients is their broadband frequency response; 

hence, this property can be used to detect them. In the time-frequency domain 

the temporal energy of the signal can also be used to detect and isolate 

transients. For this purpose the short-time Fourier transform (STFT) can 

be used to generate the detection function. Figure 3.5 and Alg. 1 describe 

how the STFT-based detection function is computed.


Figure 3.5 

Illustration of how the STFT-based detection function is generated. 

The computation procedure starts by dividing the AE signal into segments 

of k samples. The segments overlap by d samples. For each segment, 

the discrete Fourier transform (DFT) is computed using k samples, i.e. no 

zero padding is used. Then the results are converted into the decibel scale 

by applying a logarithm (base 10) to the complex modulus (magnitude) of 

the DFT coecients. The coecients for each segment are then summed 

up. Each coecient is multiplied by 20. The multiplication can be omitted 

because it only scales the detection function, i.e. the peak-picking results 

will be the same with adjusted parameters. 

The number of elements in the detection function, DF, is equal to 

the number of segments. For this reason, the elements are mapped to 

the corresponding data points in the AE signal; the mapping is stored in 

a vector MAP. The time resolution is controlled by the length of the 

segments. The additional information found from overlapping is obtained 

by interpolation. 

Given the reduction in the time resolution and the computational cost 

involved, the STFT-based detection function does not compare well against 

the previous detection function, which was in the time domain.


1 

2 

3 

4 

5 

6 

Algorithm 1: STFT-based detection function 

Data: signal, k, d 

Result: DF, MAP 

Segments ← signal divided into k sample segments with d sample overlap; 

MAP ← map the segments to corresponding data points in the signal; 

for i=1 to number_of_segments do 

DFT ← Calculate Discrete Fourier Transform of segment i; 

DF [i] ← sum (20log 10 (|DFT |)); 

end 

3.2.2 Peak-Picking and Hit Determination 

In order to locate hits from the detection function a peak-picking procedure 

is used. This procedure is illustrated in Fig. 3.6. The small troughs and 

peaks in the detection function are incrementally removed until it contains 

only troughs and peaks which have trough-to-peak dierence above the 

trough-to-peak threshold, T tp . The hits are then found from the remaining 

troughs in the detection function. This procedure can be split into two 

algorithms: Alg. 2 and Alg. 3. Algorithm 2 is used for locating troughs 

and peaks in an input signal. The algorithm starts by creating an empty 

vector, Locs, of the same length as the input signal. This vector will be the 

output of the algorithm and contains the locations of all detected troughs 

and peaks. The derivative, or slope, of the input signal is used to determine 

troughs and peaks. The slope is computed by subtracting a time-shifted 

version of the input signal from itself. Peaks are detected by rst nding all 

samples which have zero or positive slope. If the next sample in time has 

negative slope then a peak is detected. The procedure for nding troughs 

is similar; in this case all samples with zero or negative slope are found 

rst and if the next sample in time has positive slope a trough has been 

detected. The end points are treated separately. In both cases, the rst 

thing to check is whether a peak, or a trough, has been determined at the 

ends. If not, then a trough is determined if a peak is closest to the end, 

and vice versa. 

Algorithm 3 is used to remove troughs and peaks which have trough-topeak 

dierence below a specied threshold, T tp . They are removed incre-


Figure 3.6 

Illustration of the incremental peak picking procedure. 

mentally by increasing the threshold, a, from 1 to T tp in steps. The larger 

the increments, the larger the hit location error may be. Smaller increments, 

however, increase the computational cost. After each removal step, 

Alg. 2 is used to re-evaluate the troughs and peaks from the remaining 

list. The re-evaluated list is then used for the next step. The hit locations 

determined by the peak-picking procedure are the trough locations in the 

nal list. 

After the hits have been located they are compared against a determination 

threshold, T AE . This threshold is the same as that used in thresholdbased 

hit detection. Here this threshold is used to lter out weak hits, i.e. 

only hits which exceed the threshold are determined as hits. The threshold 

is also used to extract threshold-based features.


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

Algorithm 2: Trough- and Peak-Picking Algorithm 

Data: signal 

Result: Locs 

Locs ← zero vector of the same size as signal; 

peaks: 

tmp_indices1 ← indices of all samples with positive slope (and 0); 

tmp_indices2 ← indices of samples in tmp_indices1 for which the 

adjacent samples with indices tmp_indices1 +1 have negative slope; 

Locs [tmp_indices1 [tmp_indices2 ]+1] ← (+1); 

valleys: 

tmp_indices1 ← indices of all samples with negative slope (and 0); 

tmp_indices2 ← indices of samples in tmp_indices1 for which the 

adjacent samples with indices tmp_indices1 +1 have positive slope; 

Locs [tmp_indices1 [tmp_indices2 ]+1] ← (-1); 

end points: 

nz_indices ← nd the indices of non zero entries in Locs; 

if abs (nz_indices [rst entry]) ≠ 1 then 

Locs [1] ← (−1)×nz_indices [1] 

end 

if abs (nz_indices [last entry]) ≠ length of signal then 

Locs [1] ← (−1)×nz_indices [last entry] 

end 

1 

2 

3 

4 

5 

6 

Algorithm 3: Trough- and Peak-Removal Algorithm 

Data: Locs, signal, T tp 

Result: NewLocs 

for a=1 to T tp do 

Remove trough/peak entries in Locs which have trough-to-peak 

dierence below a; 

Locs_tmp ← Algorithm 2 (signal [Locs ])); 

Locs ← map the entries in Locs_tmp to entries in signal; 

end 

NewLocs ← Locs;


3.2.3 Hit Determination Approach Illustrated 

Continuous parameter-based AE systems commonly use a pure thresholdbased 

hit detection with a xed or a oating threshold. However, in some 

situations neither may be appropriate. When the xed threshold is set, it 

is tuned to the AE signal, i.e. the noise level, at the start of monitoring. As 

the component under monitoring degrades and the signal level increases, 

the threshold may not be used to detect individual transients. That is, 

the threshold-based approach may not be able to separate transients if the 

signal does not fall below the threshold for a sucient period of time. In 

some situations a oating threshold can be used to overcome this problem; 

however, a oating threshold may not be appropriate if the signal level 

varies. This is because it can be dicult to set the appropriate response 

time of the oating threshold; if it is set too fast it can be aected by 

strong transients. 

An approach for hit determination has been introduced in this section. 

This approach is designed to handle the abovementioned limitations of 

the threshold-based hit determination approaches. In order to accomplish 

this, hits are rst detected by peak-picking a detection function and then 

compared against a threshold in order to both lter out weak hits and 

to extract hit-based AE features. The threshold comparison is optional. 

Hence, the approach is able to detect and separate transients even though 

the signal does not fall below the threshold. The separation is accomplished 

by splitting the transients at the point of lowest amplitude between them. 

Figure 3.7 illustrates this. 

The detection functions can be created in the time domain as well as in 

the time-scale/time-frequency domains. In some instances transients are 

only separable in the time-scale/time-frequency domains, where wavelets 

and Cohen's class of time frequency representation (TFR) are used respectively. 

Both approaches have been shown to provide a good representation 

of signals, and for this reason they have been receiving increasing attention 

in the recent years. The successful detection of transients, using either 

wavelets or Cohen's class of TFR depends strongly on the wavelet function 

and the distribution function respectively. 

The resolution of the approach presented here can be ne-tuned by adjusting 

the threshold, T tp , used to lter out small local troughs and peaks 

in the detection function. If a high resolution is required, namely to detect


Figure 3.7 Illustration of how the hit determination approach presented here 

is able to detect and separate overlapping transients which the threshold-based 

procedure cannot. 

pulsations in the signal, then the time domain is the appropriate choice. 

This is due to the inherent trade-o between the time and frequency resolution 

of the time-scale-/time-frequency-based approaches. The transformation 

of the detection functions into the decibel scale is useful when the 

transducer cannot be placed at the location of damage and the AE signal 

suers from high attenuation. Furthermore, the transformation produces a 

detection function which makes it possible to use one setting for automatic 

hit determination of both strong and weak hits. 

The following numerical example may be used to demonstrate the hit 

determination approach. It shows the ability of the approach to work with 

and detect transients, which have amplitudes that dier in magnitudes, 

using the same settings. 

Figures 3.8 3.9 illustrate automatic hit detection results which can 

be obtained using the Fourier transform-based detection function. The 

detection function is computed using 128 sample window and 120 sample 

overlap. All processing of the signal is performed on the amplied signal 

as obtained from the A/D converter; no corrections are made due to the 

amplications made by the preamplier and the transducer. The signal 

depicted in Fig. 3.8a consists of weak, intermediate and strong AE tran-


sients. The duration of each type is 5 microseconds and they are arranged 

in order of increasing amplitude. The weak transients are low-amplitude 

transients, all with amplitudes equal to, or less than, 85 mV; the intermediate 

transients are at most 650 mV, and the strong AE transients are 

roughly ten times stronger, or up to 6.2 V. 

Figure 3.8b shows the rst 5 microseconds of the signal in Fig. 3.8a in 

more detail. The resulting detection function, depicted on a scale to t in 

the gure, is shown above the AE signal. The weak transients are located 

in this part of the signal. In addition, the location of the troughs and peaks, 

as determined by Alg. 2, are shown respectively by triangles pointing down 

and up. The threshold for the trough/peak determination, T tp , is 304 dB 

V-s. The parts of Fig. 3.8a which correspond to the intermediate and the 

strong transients are shown in Fig. 3.9a and Fig. 3.9b respectively. The 

strong transients have been soft-clipped by the preamplier. 

(a)An AE signal and the corresponding 

detection function. 

(b)The rst 5 microseconds of the AE 

signal are shown in the left gure. 

This segment contains the 

weak transients. 

Figure 3.8 The left gure shows an AE signal which consists of weak (0-5 ms), 

intermediate (5-10 ms) and strong transients (10-15 ms). Above the AE signal 

is the STFT-based detection function. The right gure shows the weak transients 

in more detail, the detection function, and the detected troughs and peaks.


(a)The segment of the AE signal in 

Fig. 3.8a which contains intermediate 

transients (510 ms). 

(b)The segment of the AE signal in 

Fig. 3.8a which contains strong 

transients (1015 ms). 

Figure 3.9 

Fig. 3.8a. 

The intermediate and strong transients of the signal shown in


3.3 Features 

This section presents two features which can be used for condition monitoring. 

The rst feature is based on a fundamental concept in Information 

Theory the entropy. The entropy can be used to estimate the randomness 

in a signal. The reason for estimating the randomness is based on the 

assumption that measurement noise can be kept constant during monitoring. 

Consequently, an increase in the randomness of an AE signal will be 

due to increased AE activity, either from cumulated damage or damage 

growth. The entropy-based feature can therefore be used to monitor the 

AE activity. The second feature is based on the spacing between hits. Hit 

and ring-down counts have been used extensively for interpreting AE data. 

Both are pulsations in the signal, but on dierent time scales. Given the 

success that has been achieved using these two features, the time between 

the pulses may provide valuable additional information. 

In addition, a methodology for coding AE features into a vector and 

searching for patterns in the coded representation is also put forward. By 

monitoring the evolution of hit patterns and detecting changes, it may be 

possible to detect the inception of critical damage mechanisms before the 

onset of catastrophic failure. 

3.3.1 Entropy 

Information entropy was introduced by C. E. Shannon in 1948. 155 

In his paper 

Shannon developed a method of measuring the randomness of a signal, 

or its uncertainty. The randomness is information encoded in the signal 

and the entropy increases with more information. Shannon recognized that 

the form of the measure was the same as the entropy in statistical mechanics 

and, for this reason he also called his measure 'entropy'. Shannon's 

formula for the entropy is 

H SHANNON (X) = − ∑ λ 

P r(x = λ) log(P R(x = λ)). (3.4) 

The signal's values are denoted by x and are considered to be discrete 

random variables. The possible signal values are denoted by λ, and P r(x = 

λ) is the probability mass function (PMF) of X. Consequently, the entropy

3.3 Features 51 

is a function of the signal's probability mass function, but not the values 

themselves. Without any constraints, the maximum entropy is attained 

when all values are equally probable, i.e. when the signal is white noise. 

The entropy is the minimum weighted average number of units, per value, 

required to encode the signal. The unit of measurement depends on the 

choice of the logarithm base, i.e. by choosing 2, 10, or e as the base the 

units will be bits, hartleys, or nats respectively. The base can be changed 

by using the law of logarithm, i.e. 

log a (X) = log a (b) log b (X). (3.5) 

In practice, computing the entropy can be challenging because the underlying 

distribution is often unknown, for instance the AE signal measured 

during cyclic testing of CFRP. Consequently, the entropy needs to be estimated. 

This can be done by estimating the probability mass function using 

statistical methods or by estimating the entropy directly using data compression. 

A normalized histogram of the random variable can be used 

156, 157 

to estimate the probability mass function. By using a histogram to estimate 

probabilities, the entropy is estimated with respect to a model which 

assumes that the frequencies of the signal's values are constant within the 

signal segment. The histogram can be normalized to sum to one by 

n i = 

m i 

∑ k 

i=1 m i 

for i = 1, . . . , k (3.6) 

where k is the number of bins and m i is the number of observed signal 

values that fall in bin i. The normalized values of the histograms represent 

the proportion, or probability, of the corresponding signal's values. In 

the frequency domain, the frequency can be considered to be the random 

variable and the normalized spectrum to be the probability mass function. 

The spectrum is normalized by 

x i = 

X i 

∑ N 

i=1 X i 

for i = 1, . . . , N (3.7) 

where X i is the magnitude of the i th frequency component of the spectrum, 

e.g. the amplitude if an amplitude spectrum is used. Based on this 

probability mass function, entropy can be computed using Shannon's formula. 

By considering the spectral amplitude to be the random variable, a


dierent entropy can also be dened and computed using Shannon's formula; 

the probability mass function of the amplitude intensities can be 

estimated using a histogram. When the probabilities are based on discrete 

Fourier transform, or histograms, the entropy is estimated with respect to 

a static model. These two entropies will be referred to as the frequency 

entropy and the spectrum entropy respectively. 

The Shannon entropy is properly dened as the minimum entropy over 

all possible models, i.e. it is an entropy computed using Shannon's formula 

and the correct probability mass function. In other words, it is the theoretical 

upper limit on lossless data compression that can be achieved for a 

156, 157 

given signal. Consequently, the entropy can be used to evaluate compression 

algorithms to determine whether there is room for improvement. 

Conversely, compression algorithms can be used to estimate the entropy of 

data. The compressed data can be written to a le and the le size then 

converted from bytes to nats using: 

H COMP RESSION = 8 log e(2)File_Size 

length_of_signal . (3.8) 

Where File_Size, the size of the compressed le in bytes, is multiplied 

by 8 to convert to bits. Equation 3.5 is used to change from bits (base 2 

logarithm) to nats (base e logarithm). The results are then averaged over 

all values (samples) by dividing the results with length_of_signal. If 

the header of the compressed le is included in the le, then the entropy 

estimate will be higher. If the AE signal length is kept constant then the 

error due to the header will be approximately same for all computations. 

Among the best lossless compression approaches are those based on 

a scheme known as prediction by partial matching (PPM). The PPM 

compression scheme is divided into two steps: modelling, from which the 

scheme takes its name, and coding. Arithmetic coding is used to code the 

output of the modeller. Arithmetic coding is a highly eective technique 

which can code data close to its entropy with respect to the model. 157 

The 

PPM modeller works with the data in a symbol-wise manner and its output 

is a set of conditional probabilities for the symbols. The probabilities 

of the symbols are estimated adaptively and used to predict the next unseen 

symbol. For predicting the modeller uses nite context models of k 

symbols which immediately precede the one to be predicted. The number 

k is also referred to as the model order and is specied by the user before


the data compression is initiated. During the modelling for each symbol, 

the modeller begins by looking up how many times the current context 

of length l c = k has occurred before. If the context has been observed 

before, followed by the symbol, the symbol can be coded using a probability 

of n c /n, where n c is equal to the number of times the context has 

been observed followed by the symbol and n is the number of times the 

context has been observed. If the context hasn't been encountered before, 

or it has only been followed by dierent symbols, an escape character is 

passed to the modeller. When the modeller receives the escape character it 

switches to a context that is one symbol shorter, i.e. to a context of length 

l c = k − 1. Again, if the current context hasn't been observed before, or 

has only been followed by dierent symbols, another escape character is 

passed to the modeller and it starts to look for contexts which are one symbol 

shorter. This can be repeated until the context length becomes l c = −1 

symbols. When this occurs, all symbols from the alphabet are considered 

equally probable. Equiprobability is undesirable since it does not provide 

an accurate model; however, it poses no problem for accurate coding. The 

arithmetic coder is able to proceed even though the model is inaccurate; 

however, a higher number of bits may be required to encode the data. 

Intuitively, better compression is achieved with more accurate modelling. 

Fortunately, the context of l c = −1 symbols is only considered at most 

once for each symbol, and as the modelling proceeds the data statistics 

improve and lower values of l c become less and less frequent. Every time 

an escape character is sent (i.e. whenever the modeller is unable to code a 

symbol) the probability of observing a novel symbol, when presented with 

the current context, is updated. By assigning a probability to the escape 

character the modelling can be improved. For a detailed description of 

the PPM scheme and examples, the reader is referred to Text Compression 

156 

and Managing Gigabytes: Compressing and Indexing Documents 

and Images. 157 

Dierent variants of the PPM compression scheme have been introduced 

in order to improve the PPM compression and to speed up calculations. 

One variant suggested by Howard 158 is referred to as method D, 

or PPMD, and estimates the conditional probability of observing a particular 

symbol given a specic context to be (2n c − 1)/(2n), where n c is 

the number of times which the modeller has seen the symbol being preceded 

by the context and n is the total number of symbols preceded by


the current context. The escape probabilities are estimated by n u /(2n), 

where n u is the number of unique symbols preceded by the current context 

and n has the same meaning as before. Another variant was introduced 

by Dmitry Shkarin in Improving the Eciency of the PPM Algorithm 159 

(in Russian) under the name PPM with information inheritance, or PP- 

MII. Shkarin presented the PPMII a year later in English. 160 

The PPMI 

uses an additional model in order to get better estimation of the escape 

probabilities. In order to overcome the lack of statistical information when 

estimating the escape probabilities of long contexts, the PPMII allows the 

longer contexts to inherit statistics from shorter contexts. The inheritance 

reduces the computational cost compared with other approaches to this 

problem. 160 Starting with a code from Nelson, 161 Shkarin implemented his 

improvements, and several other variations, and made them available in 

the public domain under the name PPM by Dmitry (PPMd). 

3.3.2 Hit Patterns 

One of the fundamental elements of music is rhythm. Rhythm can be 

determined by the relation between note accents (attack) and the rests between 

notes. 162 

The term can be used to refer to either a repetitive pulse, 

or a beat, which is repeated throughout the music or a temporal pattern 

of pulses. The modelling and the interpretation of temporal patterns are 

of interest to people working in dierent disciplines. In the eld of music 

information retrieval rhythm-based features have been extracted from audio 

and used to classify music styles, 163 

e.g. blues, disco, polka, etc. In the 

eld of computational neuroscience, patterns in spike trains are studied in 

order to understand the "language of the brain". 164 

For this reason, it is 

of interest to investigate whether patterns exist in AE signals. 

The rst step in working with temporal patterns is to determine the 

pulses. The detection of pulses usually begins with the processing of the 

signal in order to make the detection more accurate. The resulting signal is 

called a detection function. An example of a detection function is one made 

using a model called a rhythm track. 165 

The rhythm-track model is based 

on the assumption that the audio can be considered to be a random signal 

and the signal's energy increases signicantly when a pulse occurs. The 

resulting rhythm track, which can be created using the hit determination 

approaches introduced in Sect. 3.2, contains the locations of all the pulses.


An intuitive rhythm track is a vector, of the same length as the signal, 

containing ones where the pulses start and zeros elsewhere. The placement 

of the ones can also be based on any of the pulse's properties, for instance, 

the peak values. 

Interpreting patterns in the rhythm-track is a non-trivial task. This is 

because similar patterns can be generated dierently. For example, closely 

spaced transients can be attributed to factors such as rapid AE release, 

reections, and simultaneous emissions from multiple sources. In Extracting 

Information from Conventional AE Features for Fatigue onset Damage 

Initiation in Carbon Fiber Composites 166 

AE features were successfully 

fused and processed to improve classication results. These results provided 

an impetus to investigate the fusion of AE features further. As a 

result, a methodology for fusing AE features, and for nding and locating 

patterns within the fused data representation, has been elaborated. This 

methodology can be used to fuse and code AE hit-based features with information 

from the rhythm track, i.e. the inter-spike intervals (ISI). Other 

intervals can also be used, such as trough-to-peak intervals. The additional 

information provided by the waveform-based features comes at higher computational 

cost, but may help to distinguish and interpret rhythm track 

patterns which are generated dierently, or at dierent locations. 

The fused and coded features are collected in a vector, called a coding 

vector, where each hit is represented by a subvector. The length of the 

subvector depends on both the number and type of features used, and is 

the same for all hits. In order to limit the number of patterns in the coding 

vector the features are rst processed and then quantized to a relatively 

small set of integers. The quantization suggested here is rst to transform 

the processed features logarithmically (log 10 ), then shift, scale, and round 

the results so that they are represented by integers ranging from 1 to 

N F EAT URE , where N F EAT URE is an integer number chosen by the user. 

The scaling operation requires the user to know the extreme values of 

the features. If the extreme values can only be approximated then the 

coded elements will be occasionally out of the range. In order to solve 

this, hard limits can be used, i.e. if the values go out of range then they 

will be set to the allowable maximum. However, the limits do not have 

to be critical; if the coded elements are allowed to exceed the limit then 

relatively few new patterns will be added. Henceforth, the processing and 

quantization will be referred to as coding. The coding of each element


depends on the corresponding feature. The quantization reduces the memory 

and computational cost, which can become prohibitive if continuous 

feature values are used. 

Figure 3.10 illustrates how the coding vector is generated when two 

element subvectors are used. The elements of the subvectors, shown in the 

gure, are the coded maximum amplitude of the hit and the coded interspike 

interval (ISI) between the peaks of the current hit and the previous 

hit. The coding of the ISI is made by rst logarithmically transforming 

(log 10 ) the time between the peak amplitudes of successive hits, measured 

in milliseconds. The results are then quantized so that each ISI is represented 

by integer values ranging from 1 to N ISI . The coding of the peak 

amplitudes is performed in a similar way. The amplitudes are logarithmically 

transformed (log 10 ) and quantized to integer values between 1 and 

N AMP . 

Figure 3.10 The generation of the coding vector illustrated using two element 

subvectors for each hit. The two elements are coded maximum amplitude and 

coded ISI respectively. 

The procedure for searching for hit patterns in the coding vector is 

illustrated in Fig. 3.11. The length of each hit pattern, L, must be an 

integer multiple of the subvector length. The locations where a pattern,

3.4 AE Source Tracking 57 

H P , is observed are stored in an observations vector, O P , where P = 

1, . . . , N P and N P is the number of hit patterns. Each observation vector 

is of same length as the original AE signal and initially contains only zeros. 

The locations where a pattern, H P , is observed within the AE signal are 

indicated by ones in the corresponding observation vector. The ones are 

placed where the patterns start. 

Figure 3.11 

The procedure for nding hit patterns in the coded representation. 

3.4 AE Source Tracking 

This section describes a methodology for simultaneous tracking of multiple 

AE sources. The methodology is designed to be used for monitoring 

objects subjected to repetitive loading conditions. By using the images 

generated by the methodology, one can identify and locate interesting AE 

signals for further study, or for tracking, which otherwise would be dicult 

to accomplish due to the overwhelming number of sources with similar 

characteristics. 

An intuitive approach to condition monitoring using AE signals is to 

keep track of one or more waveform parameters, which characterize the 

AE from the source of interest. Each parameter, however, will follow a 

probability distribution, which changes when the source (damage) changes. 

Because of the parameter uctuations and the high rate of AE with similar


parameter values, waveform parameters alone are not sucient for distinguishing 

between sources. Additional indication is therefore needed. For 

an example, if an AE source always emits an AE at the same load level, 

then the load level of AE occurrence is sucient to distinguish between 

the sources. However, when a source evolves, e.g. a growing delamination 

crack, the load level of AE occurrence changes. 

Figure 3.12 

Schematic overview of the proposed experimental methodology. 

Figure 3.12 shows a schematic overview of the proposed methodology. 

The rst step of the approach is to split the AE signal into segments of 

length equal to the period of one cycle. Care must be taken to ensure that 

the segments all start at the same phase of the cycle. A reference signal, 

such as displacement or load, can be measured simultaneously and used 

for segmenting. In the next step, each segment, s, is bandpass ltered into 

N subbands. The decomposition of the AE signal into subbands helps to 

detect band-limited sources which might otherwise go undetected. The 

user selects the type of ltering, the number of subbands (N) and the 

individual subband bandwidths. Figure 3.13 illustrates these two steps. 

A lter bank representation of the discrete wavelet transform (DWT) 

oers a convenient method for decomposing the AE signal into subbands. 

In the lter bank, the conventional discrete wavelet decomposition, at each


The AE signal is segmented and each segment is split into N sub- 

Figure 3.13 

bands. 

level, is computed by ltering the input signal with low and high pass lters, 

producing two sequences, and keeping only their even numbered coef- 

cients. All subsequences of the original signal are called wavelet packets, 

and together they form a wavelet packet tree. Figure 3.14 shows a conventional 

DWT tree and full tree corresponding to J = 4 level decomposition. 

Each packet retains the necessary information in order to reconstruct 

the signal in the corresponding subband. This means that packets from 

dierent levels can be used to fully reconstruct the original signal if, together, 

they span the full bandwidth. This is illustrated in the left image 

in Fig. 3.14. 

Alternatively, the signal can be split into subbands using a technique 

known as phaseless ltering. 167 

Phaseless ltering is used on the AE signal 

in order to avoid phase delay. The ltering is made phaseless by ltering 

twice. After the rst ltering, the signal is reversed, ltered and reversed 

once again. 

In the third step of the methodology, a feature vector is generated from 

each subband segment. Each feature vector is generated in two stages. In 

the rst stage, the AE feature of interest is extracted from the segment.


Figure 3.14 The left image shows a wavelet packet tree corresponding to conventional 

DWT and the packet numbers. The right image shows a full 4 level 

wavelet packet tree and the packet numbers. 

Both the positions within the segment and the feature values are logged. 

In the second stage, the segment is partitioned into K intervals and the 

features extracted within each interval are processed. The user selects 

the number of intervals, K. The results from the processing are output 

in a feature vector (K × 1). Depending on the processing in the second 

stage, the rst stage can in some cases be omitted, e.g. when the energy 

in each interval or the maximum amplitude is computed. Figure 3.15 

illustrates this procedure by showing how a a feature vector is generated 

when the maximum amplitude in each interval is used. Each subband 

segment is rst rectied and partitioned into K intervals and then the 

maximum amplitude within the interval is found, i.e. a piecewise constant 

envelope is generated. The envelope is then down-sampled by a factor L/K, 

where L is the length of the subband segment. The resulting feature vector 

contains one sample from each interval of the envelope. The amplitude- 

ltering and down-sampling process extracts the amplitude of the strongest 

transient in each interval. Hence, the tracking capability is limited by this 

ltering. However, the ltering is performed in all the subbands, which 

consequently improves the tracking ability because the AE energy from


dierent sources often resides in dierent subbands. Down-sampling also 

helps keep the data manageable since the number of samples acquired 

during one fatigue cycle is high. 

Figure 3.15 For each subband segment, the new feature vector is computed by 

rst rectifying the signal, then computing a piecewise constant envelope, and 

nally down-sampling the envelope. 

In the fourth step, each new feature vector is appended to previous 

vectors from the same subband and an intensity image is generated. Figure 

3.16 illustrates this procedure. Intensity images are a convenient way 

to visualize the range of data, i.e. the higher the amplitude, the brighter 

the image pixels. A bright pixel in an intensity image shows the location 

of an AE source with a high feature value. The horizontal location shows 

the location relatively to the phase of the reference signal. The vertical location 

shows the corresponding segment. AE sources which emit AE with 

a high feature value in each cycle generate paths in the image. Random 

AE sources, however, do not. The paths can be used both to monitor the 

sources and to isolate the signal for further analysis. In the fth and the 

nal step, image processing is performed in order to enhance the images 

and to make the paths more prominent.


Figure 3.16 For each subband, new feature vectors are appended to previous 

vectors and an intensity image is generated. 

3.5 Summary 

This chapter introduced acoustic emissions and provided a background to 

their use in this thesis. Acoustic emissions are generated by microstructural 

changes in materials; hence, by measuring the AE signals damages can be 

detected and monitored before they become serious. Furthermore, the 

information extracted from AE has the potential to be used to predict the 

service life of a composite or, alternatively, to detect an imminent failure. 

Hence, the usability of the composite may be extended. 

However, AE signals from composites subjected to multiaxial loading 

can be dicult to interpret. This is because multiple simultaneous emissions 

with varying amplitude, duration and frequency can be generated in 

each cycle. These emissions will reect, disperse and attenuate during the 

propagation. Hence, interpretation of the AE signal is non-trivial. 

In order to address the problem of working with and interpreting such 

AE signals, this chapter introduced an AE hit determination approach, 

three AE features and a method for nding and locating patterns which 

appear in the AE signal. Furthermore, a methodology was presented for

3.5 Summary 63 

quantifying and visualizing AE behaviour in order to identify, locate and 

track evolving AE sources. The next chapter provides a description of the 

test specimens, the instrumentation and the experimental setup designed 

to obtain AE data for studying the methods and features presented in this 

chapter.


"Door meten tot weten" 

[Through measurement to knowledge] 

Heike Kamerlingh Onnes 

4 Experiments 

This chapter presents the experimental setup designed in order to acquire 

the data used in this work. The data is acquired while fatigue testing 75 

nominally identical samples of a prosthetic foot. The prosthetic foot is 

introduced in the rst section. The second section presents the test machine, 

the mounting of the prosthetic foot and the failure criterion used for 

stopping the fatigue tests. The third section provides a description of the 

equipment used for the data acquisition and the settings used. Also presented 

in the third section are the data acquisition problems and solutions 

which occurred during the implementation of the experimental procedure. 

4.1 The Prosthetic Foot 

The Vari-Flex consists of three CFRP composite components: a dual part 

heel and split-toe foot. In addition, a shock-absorbing crepe is glued under 

the forefoot. The foot assembly is illustrated in Fig. 4.1. All components 

are curved with both varying thickness and width. Figure 4.1a depicts 

the varying thickness and Fig. 4.1b shows how the toe is split. A male 

pyramid is bolted to the top of the foot component. The pyramid provides 

a convenient way of fastening feet to endoskeletal pylon components and 

the test machine. 

The layer orientation and sequence are similar for all the components. 

The four outermost layers, on each side, are woven carbon/epoxy prepregs

66 Chapter 4. Experiments 

(a)A side view of the Vari-Flex. The diagram 

shows the varying thicknesses of the components. 

(b)An isometric view of the Vari- 

Flex. 

Figure 4.1 The assembled Vari-Flex. The Vari-Flex is made up of two heel parts 

and one toe part. 

(Newport 301 3K), laid at 45 ◦ . Between the outer layers unidirectional 

carbon/epoxy prepreg tapes (Newport 301 34700) are laid at 0 ◦ . The 

number of the unidirectional tapes diers between components and their 

lengths are varied in order to obtain varying stiness, resulting in a tapered 

thickness. Around the holes extra unidirectional carbon/epoxy prepreg 

tapes are laid at 90 ◦ for added strength. 

The components are manufactured using an open mould technique. Figure 

4.2a shows the mould used for the lay-up of the toe components. The 

woven prepregs are hand-laid, but the unidirectional tapes are laid by an 

automatic tape-laying machine. The machine rolls the laminate in order to 

consolidate it and remove air pockets. The lay-up is then vacuum-bagged 

and cured in an autoclave. Each layout produces a panel out of which 

the parts are cut. Eight toe components are cut out of each panel. Figure 

4.2b shows the resulting panel after the toe components have been cut 

out. A 5-axis CNC water cutter is used for water cutting the components 

out of the resulting panel. The CNC machine is also used to make bolt 

holes. The cut edges are ground in order to remove streaks. The streaks 

are removed for several reasons, including aesthetics, preventing injuries 

from the sharp edges, and because they can have detrimental eect on the 

fatigue performance.

4.1 The Prosthetic Foot 67 

(a)The mould used for the lay-up of the 

toe components. 

(b)A panel after the components have 

been cut out. 

Figure 4.2 A mould for the toe components and the resulting panel after the 

components have been cut out. 

After the components have been postprocessed they are visually inspected 

and assigned to a stiness category. Although components cut out 

from the same panel have the same laminate structure, there are a number 

of factors which cause stiness variations between the components. By 

assigning components to dierent stiness categories, they can be better 

matched to the weight, activity level, and personal preferences of amputees. 

The stiness category is determined by the load, F L , required to bend 

the components by a certain distance in a quasi-static bending test, e.g. 

47.3 mm for the split-toe foot. The following formula is used to calculate 

the stiness category of the split-toe foot: 

Cat = 6.7 ln(F L ) − 42.3 (4.1) 

One decimal's precision is used: the whole number is used to indicate 

the category and the decimal for the subcategory. 

A total number of 75 Vari-Flex feet are tested. These feet are all of same 

size, size 26, and from the same stiness category, Cat 5.x. Fifty-six feet are 

taken from production and seven defective feet were specially made. The 

defects in these feet components are introduced by not heating the prepreg 

tapes suciently during lay-up. This results in loss of adhesiveness and 

air entrapment. The remaining 12 feet are taken from scrap. These feet 

do not pass visual inspection due to minor surface defects, i.e. porosity in


the woven plies. 

4.2 Test Setup & Procedure 

The fatigue tests are performed in an ISO 10328 Foot/Limb test machine 

at Össur's testing facilities. The machine is run under PID closed loop 

control. The machine and the software used to control the tests are from 

Bose Corporation. In the test, a foot is placed in the test machine where 

two actuators are used to ex the foot using 90 ◦ phased sinusoidal loading. 

One actuator loads the forefoot and the other loads the heel. Figure 4.3 

shows the displacement and the loading on both the forefoot and heel 

during one fatigue cycle. 

The actuators and the pylon to which the foot is attached can be adjusted 

vertically on the test machine. Consequently, the measured position 

values can vary between tests. Figure 4.3 shows a schematic representation 

of the experimental setup. The actuator that exes the forefoot is rotated 

20 ◦ from the vertical; the other actuator that exes the heel is rotated −15 ◦ 

from the vertical. The foot is rotated 7 ◦ out of the vertical plane dened 

by the movement of the actuators. 

Figure 4.3 Schematic representation of the experimental setup for both the AE 

and the position measurements. 

The cyclic fatigue tests at Össur are performed according to ISO 10328 

specications. The maximum loading is based on the stiness category of

4.2 Test Setup & Procedure 69 

the toe unit and the minimum loading is set to 50 N. In order to pass a 

test a foot is required to withstand 2.000.000 cycles at 1 3 Hz and then a 

residual strength test. Hence, the time to complete one successful test can 

be up to 23 days. 

For this study, accelerated tests are used. The tests are accelerated by 

increasing the maximum loading by 50% and placing a 2 ◦ plastic wedge 

between the heel and the toe components. Figure 4.4 shows the maximum 

load as a function of stiness category and the Vari-Flex with a wedge. 

The wedge is used by amputees in order to stien the foot. The increased 

load and the use of the wedge result in considerably shorter fatigue tests. 

(a)The maximum load amplitude as a function 

of stiness category. 

(b)The Vari-Flex with a wedge 

between the toe and the heel 

units. 

Figure 4.4 Shows both the maximum loading as a function of stiness category 

and the Vari-Flex with a wedge. 

During one test, both the minimum and maximum loads are constant, 

with allowable variation of ±2%. The operating frequency is 1.0 Hz. It 

takes the test machine, after a test has started, approximately 1000 2000 

cycles to reach the specied maximum and minimum load values. After 

this run-in period, the limits of the failure criterion are dened. The failure 

criterion is a heuristic criterion used in-house at Össur. It denes a failure 

when a 10% change in the displacement of either actuator, with respect to 

initial value, is observed. All fatigue tests are run until the failure criterion 

is met. 

Because the foot exes when loaded, the location of the contact point 

between an actuator and the foot changes. Hence, the displacement used


in the criterion is not of a xed point on the foot, but of the contact point. 

Figure 4.5 shows the shape of the foot at the two extreme loading conditions, 

in each fatigue cycle, and how the contact points of the actuators 

change. 

(a)The Vari-ex with the forefoot loaded. 

(b)The Vari-ex with the heel loaded. 

Figure 4.5 The shape of the Vari-ex at the two extreme loading conditions in 

each fatigue cycle, i.e. forefoot loaded (left) and heel loaded (right). The images 

are made by tracing video frames of a foot in a test. 

4.3 Data Acquisition 

In this section, the equipment used for the data acquisition during fatigue 

testing of the Vari-Flex will be discussed. Table 4.1 lists the equipment 

along with the settings used. 

The VS375-M AE transducer and the AEP3 preamplier from Vallen 

Systeme GmbH are used to obtain the AE. Figure 4.6 shows the frequency 

response of the transducer. The rugged response curve in the gure shows 

that the frequency response can vary by several decibels for dierent frequencies. 

The transducer is located in the area between the two bolts which are 

used to fasten the foot to the pyramid. This is the only accessible part of 

the foot which has a at surface; however, it bends slightly and returns in

4.3 Data Acquisition 71 

Table 4.1 The measurement equipment used for acquiring AE and the position 

of the forefoot's actuator during fatigue testing. 

AE acquisition 

VS375-M An AE transducer with resonance at 375 kHz 

AEP3 Preamplier, 

49 dB gain 

110 kHz high pass lter (54 dB/octave) 

630 kHz low pass lter (30 dB/octave) 

DCPL1 Decoupling box 

PS3003 Linearly regulated laboratory power supply 

29.9 VDC 

PCI-6250 16 bit A/D converter 

1250 kHz sampling rate on one channel 

Position measurements 

L-Gage Q50A Infrared displacement sensor 

Fast response mode used 

PCI-6024E 12 bit A/D converter 

500 kHz sampling rate on one channel 

each fatigue cycle. Figure 4.7 demonstrates this. Consequently, the contact 

area changes from full face to line contact, which aects the frequency 

response characteristics of the transducer. In order to maintain full face 

contact, a special shim was machined for fastening the foot, see Fig. 4.8b. 

The presence of the shim aects the surface AE waves, but maintaining 

full face contact and preventing possible frictional AE is considered more 

important. The electrical insulation provided by the ceramic wear plate of 

the transducer is not sucient because the shim can touch the aluminium 

case and, by doing so, creating an earth loop noise. For this reason, the 

case is insulated by wrapping it with an electrical insulation tape. The insulation 

tape also prevents earth loop noise associated with the ne carbon 

bre dust which comes from grinding the CFRP components. Although 

the grinding is performed in a special room, the dust nds its way around 

the facilities and causes conductivity problems in electrical equipment, e.g. 

bridging the electrical isolation of the transducers. 

The transducer is held by a plastic c-clamp and a heavy duty high


Figure 4.6 

The frequency response of the VS375-M transducer. 

(a)The transducer has a full face contact 

when the forefoot is unloaded. 

(b)The contact area bends slightly 

when the forefoot is loaded, resulting 

in a line contact. 

Schematic illustration of the bending of the transducer's contact sur- 

Figure 4.7 

face.


(a)The shim used to ensure full face 

contact with the transducer. 

(b)The AE transducer in place, with 

electrical insulation tape wrapped 

around the housing. 

Figure 4.8 

The shim (left) and the isolated AE transducer (right). 

vacuum silicon grease from Wacker Chemie GmbH is used as coupling 

medium. The c-clamp is shown in Fig. 4.9a. Prior to each measurement 

the coupling is veried by a Hsu-Nielsen method and the noise activity is 

checked. This is necessary due to electrical disturbances which can come 

from machinery at the testing facilities, such as the ventilation system. 

The primary purpose of using the plastic wedge is to prevent sticking of 

the surfaces, of the split-toe and the heel. When pressed up against each 

other the surfaces stick and when separated a loud audible sound, and a 

strong AE signal, is generated. 168 

Figure 4.9b shows the resulting damage 

after one fatigue test. The wedge eliminates this problem. 

The gain of the preamplier is set to 49 dB. The preamplier is equipped 

with a 9th order 110 kHz high pass lter (54 dB/octave) and a 5th order 

630 kHz low pass lter (30 dB/octave). Both lters have near-Butterworth 

characteristics. The power to the preamplier is provided via a BNC coaxial 

cable from a DCPL1 decoupling box, made by Vallen Systeme GmbH. 

The decoupling box has protection diodes to prevent damage in case of a 

reverse connection. These diodes cause a voltage drop of about 1.2 Volts. 

For this reason an input voltage between 29 VDC and 30 VDC to the 

decoupling box is recommended. 169 

Furthermore, a linear regulated power 

supply is also recommended as switching power supplies may add unwanted 

noise. Hence, 29.9 VDC is provided using Velleman PS3003 a linearly


(a)The c-clamp used to hold the transducer 

during fatigue testing. 

(b)The supercial damage on the heel 

components due to sticking, after 

one fatigue test. 

Figure 4.9 The c-clamp used to hold the transducer during the fatigue testing 

(left) and the resulting supercial damage due to sticking of the split-toe component 

and the heel. 

regulated laboratory power supply. According to the specications, the 

output of the preamplier is 10 Volt peak-to-peak, or 5 Vp. If the AE signal 

input to the amplier is too strong, the preamplier starts to saturate, 

becomes nonlinear, and the output will be soft-clipped. The soft-clipping 

starts at about 10,5 11 Vpp and at 15 Vpp, or 7,5 Vp, the output will be 

hard-clipped. The gain settings of the preamplier are based on 28 VDC 

supply. The actual amplication, however, depends on the input voltage 

to the AEP3 preamplier. With less than 28 V the saturation point is 

earlier and the gain goes down slightly. The coaxial cable which provides 

power to the preamplier is also used for transferring the AE signal from 

the preamplier to the decoupling box. The decoupling box decouples the 

AE signal from the DC power. The decoupled analog AE signal is then 

fed to a PCI-6250 16 bit Analog/Digital (A/D) converter, from National 

Instruments Corp., for full waveform digitization. 

Due to the geometry and structure of the Vari-Flex, the forefoot's actuator 

always meets the 10% displacement criterion before the heel's actuator. 

For this reason, only the position of the forefoot's actuator is measured. 

A L-Gage Q50A infra-red displacement sensor from Banner Engineering 

Corp. is used to measure the position of the actuator. The sensor is shown 

in the lower left corner of Fig. 4.3. Figure 4.10 shows the resolution of the

L-GAGE 


Using the 

5 

4 

Response Speed 

To control the re 

follows: 

Resolution (mm) 

Fast Speed (4 

Slow Speed ( 

Window Limits 

Window limits m 

(using the gray w 

button. 

The Q50A senso 

programming) m 

Figure 4.10 The NOTE: resolution Resolution is independent of the L-Gage of color (90% Q50A Kodak sensor. White Card Ato 6% fast Black) response speed NOTE: is All LED in 

used. The gure is taken from a specications sheet provided by the manufacturer. changes s 

Figure 3. L-GAGE Q50A resolution 

sensor. The response 

Q50A (infrared 

speed ofmodels) the sensor 

range 

is set 

50 - 

to 

200 

fast 

mmresponse, or 4Indicator ms; Status 

Q50AV (visible models) range is 50 - 150 mm 

hence, the accuracy of the sensor is ±0.4 mm and ±2.0 mm at the minimum 

and maximum positions of the actuator respectively. The analogue Range LED 

Indicator 

signal from the displacement sensor is digitally converted by a PCI-6024E (green/red) 

12 bit A/D converter (manufactured by National Instruments Corp.). 

9 

The position of the forefoot's actuator and the AE signal are measured 

Teach/Output 

simultaneously 8 at 500 Hz and 1.25 MHz sampling rates respectively. Software, 

developed 7 in LabView is used to acquire the data automatically, (yellow/red) for 

LED 

2.2 seconds every 5 minutes. After the data acquisition, the data is trimmed 

6 

so that it represents exactly one fatigue cycle, starting at the lowest position 

of the forefoot's actuator. The data is also high-pass ltered in order 

5 

6% Reflectance Black Card 

TEACH-Mod 

4 

to remove DC and other low frequency disturbances. Phaseless ltering, 

Push-Button Pro 

mentioned in 3 Sect. 3.4, is used in order to avoid phase delay. A fth-order 1. Press the Teac 

elliptic lter2 

with 1 dB passband ripple and corner frequency of 80 kHz 

18% Reflectance Kodak Grey Card 

(hold is button i 

used. The stopband 1 attenuation is set to 30 dB at 50 kHz. No corrections sensor is wait 

are made to the signal due to the amplication made by the preamplier 

0 

and the transducer. 50 

100 

150 200 2. Position the ta 

Distance (mm) 

green, indicat 

NOTES: 

Color sensitivity is independent of response time 

button. This w 

Q50A (infrared models) span is 50-200 mm 

LED will flash 

Q50AV (visible models) span is 50-150 mm 

window limit; 

Color Sensitivity (mm) 

3 

2 

1 

0 

50 

Fast Response Slow Response (90% 

Reflectance Kodak White 

Card to 6% Reflectance 

Black Card) 

100 

Distance (mm) 

150 200 

Figure 4. L-GAGE Q50A color sensitivity (This represents the 

expected change in output when the target color is 

changed from a 90% reflectance Kodak White Card to a 

3. Position the ta 

push button a 

Teach LED wil


4.4 Summary 

This chapter presented an accelerated fatigue testing procedure which was 

designed for testing 75 nominally identical samples of a prosthetic foot 

(also introduced) and for simultaneously acquiring both AE and position 

data. In order to shorten the test time a higher loading amplitude and 

a wedge was used. Frequently the damage mechanics change depending 

on the stress level, however, preparatory tests showed that the damage 

mechanisms leading to nal failure were the same as observed under normal 

fatigue testing conditions. 

The AE and the actuator's position data acquired during the accelerated 

fatigue testing will be studied in the next chapter using the techniques 

presented in Chapter 3.

"Information is a source of learning. But 

unless it is organized, processed, and available 

to the right people in a format for 

decision-making, it is a burden, not a bene- 

t." 

William Pollard 

5 Results 

This chapter presents the results from the analysis of the acquired experimental 

data. It starts with a general description of the observed fatigue 

behaviour during the fatigue testing of the 75 Vari-ex feet studied in this 

thesis. In Sect. 5.2 a static nite element analysis of the Vari-Flex, under 

the two extreme loading conditions, is presented. Section 5.2 also contains 

a brief study and discussion of the position measurements, stiness 

evolution and the load-displacement relationship. 

The aim of the study presented in Sect. 5.3 is to investigate whether 

the probability distribution of an AE feature can be used to provide early 

warning signs of imminent failure. This work was presented in An AE 

Feature for Issuing Early Failure Warning of CFRP Subjected to Cyclic 

Fatigue. 17 

Because the approach is based on estimating probabilities, it 

will not be able to issue warnings for all feet. For this reason, an AE-based 

failure criterion can be used simultaneously to prevent failures from passing 

undetected. Section 5.4 provides the results of a study conducted in order 

to determine whether an AE-based failure criterion can be designed to be 

equivalent to the 10% displacement failure criterion used in this work. The 

study was presented in Acoustic Emission-Based Fatigue Failure Criterion 

for CFRP. 14

78 Chapter 5. Results 

The chapter ends with a case study in which the fatigue evolution of 

one Vari-ex foot is analysed based on the experimental data. The case 

study approach is selected because it allows for an in-depth analysis of the 

experimental data and at the same time oers the opportunity to investigate 

whether, and then how, the results obtained using the methodology 

presented in Sect. 3.4 can be used to facilitate early damage diagnosis and 

failure. The results of the case study have been partially presented in 

Monitoring The Evolution of Individual AE Sources in Cyclically loaded 

16, 20 

FRP Composites, On Using AE Hit Patterns for Monitoring Cyclically 

Loaded CFRP and AE Entropy for Condition Monitoring CFRP 

15, 18 


5.1 Fatigue Behaviour of the Vari-ex foot 

The cyclic endurance of the feet, as dened by the 10% displacement criterion, 

is depicted in Fig. 5.1. Superimposed is a Weibull distribution which 

follows a two-parameter Weibull distribution with a = 68.08 (shape) and 

b = 1.65 (scale). The parameters were obtained using the maximum likelihood 

estimate function MLE in Matlab. The 95% condence interval for 

the shape is (58.90 78.70), and (1.40 1.93) for the scale. 

Visual inspection during fatigue testing showed that the failure of all 

feet began as interlaminar cracking, rst in one half of the split-toe foot and 

then later in the other half. In all cases, the side which rst failed was the 

one which was exed more. In other words, because the feet were rotated 

7 ◦ out of the plane dened by the actuators, the two halves of the split-toe 

foot were loaded unequally. Two types of nal failure modes were observed. 

One was delamination caused by cracks which propagated through the 

composite. In some cases the delamination extended to one or both ends 

of the toe-unit. The other failure mode was local buckling delamination, 

or interlaminar cracks. The buckling delamination occurred because of the 

propagating delamination cracks, which weakened the composite. Some 

feet had a combination of both failure modes, i.e. one mode in each half 

of the split-toe foot. Figure 5.2 is a composite image showing the side of 

ve split-toe feet after failure. The feet were painted grey and statically 

loaded in order to make the damages more salient. Feet numbered 1, 2 and 

3 (from left) show buckling failure, and feet 4 and 5 delamination.

5.1 Fatigue Behaviour of the Vari-ex foot 79 

Figure 5.1 The fatigue life distribution of the feet according to the 10% displacement 

criterion. A two-parameter Weibull distribution t is superimposed. 

Splinters, or tear outs, were commonly observed on the side of the 

split-toe foot. These splinters were located in the area from mid-foot to 

the ankle. The reason for the formation of splinters is the varying width 

of the split-toe feet. The ends of the cut unidirectional bres in the widest 

section of the split-toe foot are only held together by the matrix, which 

eventually fails due to repeated compression and tension loading. Three 

types of splinters were identied and classied based on their length (L) 

and thickness (T): a) small splinters (L ≈ 40 mm, T ≈ 1 mm) which 

formed early in the tests, b) medium splinters (L ≈ 80 mm, T ≈ 2 mm), 

and c)large splinters (L ≈ 120 mm, T ≈ 5 mm). The length was measured 

from the visible root to the tip and the thickness was estimated at the root. 

The cross-section of the large splinters had a right-triangular shape with 

one leg dened by the vertical side of the foot. The other leg is dened by 

the interlaminar region between the woven layers at the lower side and the 

unidirectional layers; the two legs of the triangle are parallel to the surface. 

Figure 5.3a) shows where the cut bres are located. If a splinter is


Figure 5.2 The side of ve split-toe feet components after failure. The components 

are statically loaded. 

located at the lower half of the foot component, i.e. below the center 

line, the splinter pushes out when the second half of the heel's loading 

starts (750 1000 ms) and snaps back in when the loading of the forefoot 

starts (0 250 ms), often producing an audible sound. Similar behaviour 

was observed for splinters located above the center line, except that the 

splinter pushes out when the forefoot is nearly fully loaded (250 500 ms) 

and snaps back in when then unloading starts (500 750 ms). 

Counting from either side in Fig. 5.2, feet number 1, 3 and 5 have 

splinters which are slightly pushed out due to the loading. The splinter 

on the leftmost foot was made more noticeable by placing a piece of paper 

between the split-toe foot and the splinter. 

Quasi-static failure tests were also carried out on few split-toe feet, 

both by pushing and pulling the forefoot. These feet failed suddenly and 

completely. The failure mode was bre breakage located at the mounting. 

Figure 5.3b shows the location of failure. Matrix-dominated failure 

was, however, both observed and expected in the fatigue tests. It was expected 

based on prior fatigue testing experience at Össur (using lower load 

amplitude).

5.1 Fatigue Behaviour of the Vari-ex foot 81 

(a)Shows the area where the cut bres 

end. For many feet, the ends of 

these bres broke away and formed 

splinters which rubbed against the 

feet. 

(b)The location where the sudden 

quasi-static failure occurs. 

Figure 5.3 Shows both the positions of the two actuators during one fatigue cycle 

and the loading on the foot. 

5.1.1 Discussion and Summary 

The failure of all the feet tested was traced to delamination. The feet 

were rotated 7 ◦ out of the plane dened by the actuators, hence one side 

of the foot exed more (higher stresses) than the other side in each cycle. 

Because of the higher stresses involved, the rst splinters and delamination 

cracks formed on the side which exed more. Until recently, the splinters 

which form on the sides have not been considered detrimental to the fatigue 

behaviour of the prosthetic feet. However, the visual observations made 

during the testing of the 75 prosthetic feet suggested that these splinters 

might have an important role in the fatigue behaviour. 

In the next section, the stresses within the split-toe foot will be studied. 

An analysis of the stresses can possibly help explain why delamination is 

the critical damage mechanism and why it only occurs during fatigue.


5.2 Load-Displacement 

This section presents a static nite element analysis of the prosthetic foot 

and a study on the stiness evolution of the 75 tested feet. 

5.2.1 Static Finite Element Analysis 

A static nite element analysis of the Vari-Flex, performed by Lilja Magnúsdóttir, 

was used to develop a better understanding of the stresses acting 

in the foot. In the analysis, the following factors were not taken into account: 

the 7 degree rotation of the foot out of the plane dened by the 

actuators, the wedge and the woven layers. The element model used for 

the analysis was based on a 3D solid model made in SolidWorks. Due to 

the tapered design of the components, an area model was needed. The 

area model was generated by dividing the 3D model into areas, each with 

a constant number of layers. The area model is depicted in Fig. 5.4a. The 

nite element model, shown in Fig. 5.4b, was constructed from the area 

model using the ANSYS SHELL99 element. The maximum loading of the 

actuators was set to 1950 N and the minimum to 50 N. The deection was 

veried against experimental data from the fatigue tests. The comparison 

revealed a dierence which was within few millimeters. 

Figure 5.5 shows the axial stresses on the unidirectional bres at the two 

extreme positions of the actuators. Figures 5.5a and 5.5c show respectively 

the axial stresses in the top and the bottom layers when 1950 N is applied 

to the forefoot and 50 N to the heel. When loaded this way, the top layers 

are in compression, and the bottom layers are in tension. Figures 5.5b 

and 5.5d show the axial stresses in the same layers when the heel is loaded 

1950 N and the forefoot 50 N. In this loading condition, the sign of the 

stresses have reversed; the top layers are in tension, and the bottom layers 

are in compression. 

Figure 5.6 shows the shear stresses at the two extreme positions of the 

actuators. Figure 5.6a and Fig. 5.6c show respectively the shear stresses 

in the top and the bottom layers when 1950 N is applied to the forefoot 

and 50 N to the heel. The maximum shear stresses occur in these outer 

layers. Because the shear stresses in the top layers are positive, while those 

in the bottom layers are negative, the top layers press against the bottom

5.2 Load-Displacement 83 

(a)An area model was used to divide 

the 3D solid model. The lengths of 

the areas were determined so that 

the number of layers in each area 

was constant. 

(b)The resulting element model. The 

model was made using a SHELL99 

element a linear layered structural 

shell. 

Figure 5.4 

in the foot. 

The area model and the element model used for studying the stresses 

layers. This is due to the curved geometry of the split-toe foot. Hence, 

a fully delaminated foot is able to maintain a reasonable stiness when 

the foot is loaded this way. Conversely, when the heel is loaded the shear 

stresses reverse their sign, shown in Figs. 5.6b 5.6d, and the top layers 

pull against the bottom layers, i.e. they try to separate. The layers are 

held together by the interlaminar bonding, i.e. the matrix. Consequently, 

a delaminated foot is not able to maintain usable stiness when subjected 

to this type of loading. 

According to the manufacturer of the unidirectional carbon bre tapes, 

Newport Adhesives and Composites Inc., the tensile strength, compression 

strength, and the short beam shear strength in 0 ◦ are 2030 MPa, 1241 MPa 

and 91 MPa respectively. 170 

Table 5.1 shows the maximum axial and shear 

stresses as determined by the nite element analysis. Upon comparing the 

values in Table 5.1, which are conservative, with the those provided by the 

manufacturer, one can conclude that the shear strength of the composite is 

the limiting factor in the strength of the Vari-Flex. Consequently, matrix-


(a)The stresses (compression) in the top 

unidirectional layers when the forefoot 

is at maximum loading. 

(b)The stresses (tension) in the top unidirectional 

layers when the heel is at 

maximum loading. 

(c)The stresses (tension) in the bottom 

unidirectional layers when the forefoot 


(d)The stresses (compression) in the bottom 

unidirectional layers when the heel 


(e)The colour coding for the compressional and tensional stresses (values are 

in MPa). 

Figure 5.5 Shows the compressional and tensional stresses at the two extreme 

positions of the forefoot's actuator.


(a)The shear stresses in the top unidirectional 

layers when the forefoot is at 


(b)The shear stresses in the top unidirectional 

layers when the heel is at maximum 

loading. 

(c)The shear stresses in the bottom unidirectional 

layers when the forefoot is 

at maximum loading. 

(d)The shear stresses in the bottom unidirectional 

layers when the heel is at 


(e)The colour coding for the shear stresses (values are in MPa). 

Figure 5.6 

actuator. 

Shows the shear stresses at the two extreme positions of the forefoot's


dominated failure is to be expected. 

Table 5.1 The maximum stresses found by the nite element analysis of the 

Vari-Flex foot. 

Type of Loading 

1950N @ forefoot 1950N @ heel 

Max. tension 482 MPa 497 MPa 

Max. compression 584 MPa 380 MPa 

Max. shear 493 MPa -569 MPa 

5.2.2 Stiness Evolution 

For all the feet tested, the failure was determined by the displacement 

of the forefoot's actuator; the displacement of the heel's actuator never 

changed by 10%. The solid curve in Fig. 5.7 shows, in percentages, how the 

displacement of the forefoot's actuator evolves on the average as a function 

of percentage of life. The curve is constructed by averaging all displacement 

evolution curves. The grey area represents one standard deviation from the 

mean. As one can observe, the scatter is larger than the mean value of the 

data. Hence, this suggests that a parameter which represents the changes 

in the displacement is not appropriate for monitoring. When lower loading 

is used, i.e. normal loading, the changes will be smaller and the signal-tonoise 

ratio may become too low. 

The dashed curve is a log 10 transformation of the solid curve. The 

log 10 transformation produces a curve with a similar shape to the curve in 

Fig. 2.4; hence, the three stages of damage accumulation can be identied 

using displacement measurements. On the average, a small increase in 

displacement is observed during the rst 95 percent of the lifetime, but 

during the last 5% the displacement increases rapidly. The high standard 

deviation is mainly due to uctuations in individual displacement curves, 

i.e. the temporal slope of the curves can be both positive and negative. 

Instead of presenting the information provided by the position measurements, 

as displacement it can be split into two parameters: the maximum 

and minimum positions. Because constant amplitude is used, the extreme


Figure 5.7 The solid curve shows the mean displacement change and all values 

within one standard deviation from the mean. The dashed curve is a log 10 

transformation of the solid curve. 

positions can be used to estimate the upward and the downward bending 

stinesses. The upward bending stiness and the downward bending 

stiness can evolve in dierent ways, hence, the extreme positions can be 

used to obtain more information than when only studying the displacement. 

More involved methods can also be used to detect changes in the 

bending stinesses which occur between the extreme positions, e.g. by analyzing 

the shape of the load-displacement curves. Figure 5.8 shows the 

evolution of the extreme positions for four sample feet. The initial value 

of each curve has been subtracted. Figure 5.8a shows an example of when 

the upward bending stiness decreases at similar rate, as the downward 

bending stiness increases. When the extreme positions change by nearly 

equal magnitude in the same direction, the change will not be reected 

in the displacement. Hence, the change will pass undetected when performing 

displacement monitoring. Figure 5.8b shows an example of opposite 

behaviour; the upward bending stiness increases while the downward 

bending stiness decreases. 

The curves depicted in Fig. 5.8c have both negative and positive slopes. 

The changing points are dierent, as is the steepness. During the rst half


of the lifetime both the upward and downward bending stinesses increase. 

During the second half of the lifetime, however, both stinesses decrease. 

Intuitively, the decrease of both stinesses is the most commonly observed 

behaviour and is always observed shortly before failure. Figure 5.8d shows 

an example of a foot for which the upward bending stiness decreases 

throughout the lifetime. The downward bending stiness increases during 

the rst 25%, and then remains constant until 60% through the lifetime at 

which point it starts to decrease and continues to decrease until failure. 

(a)The upward bending stiness decreases 

while the downward bending 

stiness increases. 

(b)The upward bending stiness increases 


stiness decreases. 

(c)During approximately 50% of the 

lifetime both bending stinesses increase 

while in the remaining time 

both decrease. 

(d)The upward bending stiness decreases 


stiness rst increases, then remains 

constant, and nally decreases. 

Figure 5.8 The evolution of the extreme position of the forefoot's actuator shown 

for 4 sample feet. 

The stiness changes were further investigated by performing 100 consecutive 

stiness measurements on a few split-toe feet interspersed with 

30 sec. rest periods. 171 The stiness tests were performed in a MTS


QTest/10LP uniaxial test machine using a crosshead speed of 500 mm/min. 

The foot was loaded until 50 mm extension of the crosshead was reached. 

Both the extension of the crosshead and the load were recorded by the Test- 

Works QT software used to control the test machine. Figure 5.9a shows 

how the split-toe foot was loaded. The evolution of the required load to 

reach 47.3 mm extension of the crosshead is shown in Fig. 5.9b. The initial 

load values of each curve have been subtracted. 

(a)The split-toe foot was loaded until 

47.3 mm extension of the crosshead 

was reached. 

(b)Shows how the load required to 

bend the split-toe foot 47.3 mm 

evolved during 100 consecutive stiness 

measurements of three feet. 

Figure 5.9 

The stiness measurement setup and results for three feet. 

As can be observed from the gure, the load at the 47.3 mm extension 

changes by more than 15 N (approx. 1.2%) during the rst 20 to 

40 measurements. In the remaining measurements the rate of the stiness 

change for all feet decreases to nearly zero and the stiness varies by 

only a few Newtons. Stiness increase during the rst measurements was 

more commonly observed than stiness decrease. Furthermore, it was also 

investigated whether the AE generated during rst time loading and the 

stiness curve could be used to indicate fatigue life. 172 

The results showed 

that this was not possible. This was mainly attributed to the fact that the 

feet failed due to matrix-dominated failure, which was not present initially. 

The position and load of both actuators in a typical fatigue cycle is 

shown in Fig. 5.10. As can be observed, the load curves are asymmetrical 

around the extreme values. The asymmetry is related to several factors, 

including the composite lay-up properties and geometry. The relationship 

between the load and the position of both actuators can also be studied


by plotting the load as a function of the position. Figure 5.11 shows the 

corresponding curves, or hysteresis loops, for both actuators. A comparison 

of the two loops reveals an interesting dierence: one is clockwise and 

the other counter-clockwise. This dierence is due to the geometry of 

the foot and the lay-up, e.g. the unequal displacement of the actuators 

and the energy return. The counter-clockwise loop corresponds to the 

forefoot's actuator. The load measured at actuator, with respect to the 

same position, is higher as it moves down (unloads the forefoot), whereas 

the load measured by the heel's actuator decreases when it moves down. 

The shape of the loops and their area is a function of the load and response 

of the material at the given loading frequency. 

(a)The positions of both actuators 

during one fatigue cycle. 

(b)The loading exerted by the actuators 

on the foot during one fatigue 

cycle. 

Figure 5.10 Shows both the positions of the two actuators during one fatigue 

cycle and the loading on the foot. 


In this section changes in the upward and downward bending stinesses 

of the split-toe foot were estimated by monitoring the maximum and the 

minimum positions of the actuator loading the split-toe foot. The relative 

changes in the upward and downward bending stinesses could be obtained 

because the fatigue testing is performed using a constant amplitude 

loading. It was demonstrated that the evolution of these two stinesses 

provides more information about the material conditions than monitoring 

only the displacement. The stiness increase during the rst cycles is an


Figure 5.11 

The load-position relationship for both actuators. 

interesting behaviour which was observed in a few feet. This behaviour 

was well known by the Össur's personnel and was conrmed after further 

investigation. The behaviour has also been reported in the literature (see 

Sect. 2.3). 

The simplied static nite element analysis presented above showed 

that the maximum tension and compressional stresses are well within the 

limits provided by the manufacturer. But, the shear stresses exceed the 

limits by more than a factor of 5 in both direction. The analysis also 

revealed that the maximum value of the three stresses occurs at the top 

and the bottom layers of the split-toe foot. These results are in agreement 

with the experimental observations. The high stresses in the outer layers 

caused the woven layers in a few of the tested feet to delaminate from 

the unidirectional layers. However, the detrimental delamination cracks 

occurred near the center of the split-toe foot. The formation of these cracks, 

and the splinters, is due to the stress reversal of all the three stresses. The 

stresses change their signs near the center of the material, the exact location 

depends on whether the actuator is loading or unloading, i.e. moving up 

or down, as was demonstrated by the load-position relationship of both 

actuators. Consequently, due to the high shear stress range and the fact


that the three stresses change their signs twice in each fatigue cycle, a shear 

failure, or a matrix dominated failure, is highly probable in fatigue. 

The visual observations presented in the previous section and the results 

presented in this section will be used in the next sections for interpreting 

the AE data. In the next section it will be studied if a timely warning 

about imminent failure can be issued by using the probability distribution 

of an AE feature. 

5.3 Impending Failure Warning 

In the study presented in this section, it is proposed that the probability 

distribution of a suitable AE feature can be used to provide timely warning 

of impending failures in CFRP composites. The results of this study have 

been partially presented in An AE Feature for Issuing Early Failure Warning 

of CFRP Subjected to Cyclic Fatigue 17 

and AE Entropy for Condition 

Monitoring CFRP Subjected to Cyclic Fatigue . 19 

The failure is dened by 

the 10% displacement-based failure criterion. The warnings will be issued 

by comparing the value of the AE feature against its distribution. Hence, 

the distribution as a function of lifetime, e.g. in percents, needs to be 

known or estimated. 

The goal of this study is to nd an AE feature which can be used for this 

purpose. In order to achieve this objective, the experimental data acquired 

during cyclic testing of 75 prosthetic feet is used. The lifetime of each foot 

is normalized to 100% according to the 10% displacement failure criterion. 

The probability distribution, of the feature values at each percentage point 

is estimated by rst computing the feature from all measurements, for each 

foot tested, and then generating a histogram of the feature values at the 

given percentage point of lifetime. The AE features are evaluated by how 

well the two probability histograms at 50% and 95% of the normalized 

lifetime can be separated. 

All gures in this section have a grey area which represents all values 

which lie within one standard deviation from the mean. Also superimposed 

on the gures are histograms in blue and red which show the distributions 

of the feature values at 50% and 95% of the fatigue life respectively. The AE 

features are evaluated by how well the two probability histograms at 50% 

and 95% of the normalized lifetime can be separated using an estimated

5.3 Impending Failure Warning 93 

Bayes optimal decision threshold. Although the Bayes optimal decision 

boundary does not guarantee an error free classication, it gives the lowest 

error rate. 173 

5.3.1 Evolution of Commonly Used AE Features 

Figure 5.12a shows the average evolution of the AE hit count for all feet 

tested. The AE hits are located and determined using the approach described 

in Sect. 3.2. The STFT detection function described in Sect. 3.2.1 

is used, with segment size of k = 128 samples and d = 120 sample 

overlapping. The hits are located by setting the trough-to-peak threshold 

(T tp ) at 304 dB V-s and determined by setting the determination threshold 

(T AE ) at 3 mV. 

(a)The average AE hit count rate. 

(b)The average signal energy. 

Figure 5.12 The average evolution of the AE hit count and the signal's energy 

(per loading cycle). The grey area represents all values which lie within one 

standard deviation from the mean. 

Figure 5.12b shows the average evolution of the signal's energy on a 

decibel scale. The energy of the AE signal, E, is computed using: 

E = 1 R 

N∑ 

x 2 ∆t, (5.1) 

i=1 

where x is a vector of length N, containing the discrete values of the AE 

signal. The sampling interval, ∆t is equal to the reciprocal of the sampling 

rate, or 1/fs. The reference resistance, R, is 10 kΩ. 136 

As a result the 

energy unit is joules (equal to Watts-seconds or volts 2 -seconds per ohm).


Figure 5.13 shows the evolution of six commonly used AE hit features. 

Each curve is generated by averaging the feature evolution curves from 

all feet. The points on the evolution curve for each foot are computed 

by extracting the AE hit features from all hits in a segment and then 

computing their average. By computing the average, extreme AE hit values 

may pass unnoticed because a few high values will not alter the mean by 

much. For this reason it is of interest to study the evolution of the hit 

features extracted from the hit with the largest amplitude. Figure 5.14 

shows the evolution of the amplitude, duration, and the rise time of the hit 

with the largest amplitude from each signal segment. Also depicted in the 

gure is the amplitude ratio of the two hits with the largest amplitudes. 

Elliptical bandpass lters, each with 25 kHz bandwidth, are used to divide 

the original bandwidth into subbands. The power in the subbands is 

computed along with the ratio between the two subbands with the largest 

powers and the ratio between the subbands with the maximum and minimum 

power. The evolution of four selected subbands and the ratios is 

presented in Fig. 5.15. 

The two histograms for each of the features presented in Figs. 5.12 

5.15 have nearly identical shapes and overlap almost completely. For this 

reason they cannot be used to separate the feature values at 50% of the 

lifetime from the values at 95% of the lifetime.


(a)The average evolution curve for the 

amplitude. 

(b)The average evolution curve for the 

RMS. 

(c)The average evolution curve for the 

ring-down counts. 

(d)The average evolution curve for the 

duration. 

(e)The average evolution curve for the 

rise time. 

(f)The average evolution curve for the 

fall time. 

Figure 5.13 The average evolution of six commonly used AE hit features. The 

grey area represents all values which lie within one standard deviation from the 

mean.


(a)The evolution curve for the maximum 

amplitude. 

(b)The evolution curve for the duration 

of the hit with the maximum amplitude. 

(c)The evolution curve for the rise time 

of the hit with the maximum amplitude. 

(d)The evolution curve for the amplitude 

ratio of the two hits with the 

highest amplitude. 

Figure 5.14 The average evolution of AE hit features extracted from the hit with 

the maximum amplitude and the amplitude ratio of the two hits with the largest 

amplitudes. The grey area represents all values which lie within one standard 

deviation from the mean.


(a)The evolution curve for the power in 

the 250275 kHz subband. 

(b)The evolution curve for the power in 


(c)The evolution curve for the power in 


(d)The evolution curve for the power in 


(e)The evolution curve for the ratio of 

the two subbands with the largest 

powers. 

(f)The evolution curve for the ratio of 

the subband with the largest power 

against the subband with the smallest 

power. 

Figure 5.15 The average evolution of AE features in the frequency domain. The 

grey area represents all values which lie within one standard deviation from the 

mean.


5.3.2 Entropy 

Two entropies are estimated in the time domain, one using Shannon's formula 

and one using data compression. In order to apply Shannon's formula 

the probability mass function of the signal's values from each measurement 

is estimated from a normalized histogram using 2 16 bins. In other words, 

the number of bins is set equal to the number of quantized discrete values 

from the 16 bit A/D converter. In order to estimate the entropy using 

data compression, the signed 16-bit integer data is written to a le in 

ASCII form with no spaces in between. The le is then compressed using 

variant H of the PPMd algorithm (PPMdH), as implemented in an open 

source software program called 7-Zip. The resulting le size is then converted 

from bytes to nats (see Eq. 3.8). The model order is determined 

manually. The best compression results are obtained using model order 

k = 5, or when the maximum context length is equal to the maximum 

number of digits used (omitting the sign). In the remaining part of this 

thesis, the entropy computed using Shannon's formula in the time domain 

will be referred to as the signal's entropy, and the entropy estimated using 

the PPMdH compression scheme will be referred to as the PPMdH entropy. 

In the frequency domain Shannon's formula for the entropy is used 

to estimate both the frequency and the spectrum entropies. In order to 

compute the frequency entropy, the probability mass function of the frequencies 

is estimated by rst transforming the signed 16-bit integer data 

to the frequency domain and then normalizing the one sided amplitude 

spectrum to sum to one. Because of the normalization there is no need to 

convert the data values to volts. The transformation is made by applying 

a 221 point discrete Fourier transform (DFT). The number of DFT points 

is set to the next power of two higher than the length of the data series, 

for faster computation. This is done by zero-padding the data to make 

its length a power of two. The computations can also be made faster by 

using fewer points. If fewer points are used, the resolution of the spectrum 

decreases and less information is provided. Consequently, the entropy also 

decreases. If more points are used, the number of frequency bins increases, 

as so does the entropy. This requires zero-padding. Zero-padding the data 

before applying the DFT results in a frequency interpolation, which means 

that the added frequency bins will not contain any new information. As a 

result, the entropy increase will only be a function of the number of added


bins and is the same for all measurements. 

In order to compute the spectrum entropy, the probability mass function 

of the spectral amplitudes is estimated from a histogram of the amplitude 

intensities. Amplitudes below the highest amplitude in the one-sided 

amplitude spectrum of all measurements are quantized with 16 bits. A 

2 16 bin histogram is used to estimate the probability mass function of the 

quantized amplitudes. 

The average evolution of the four entropies for all the feet is shown 

in Fig. 5.16. As can one can observe, the curves are relatively at from 

approximately 20% to 95% of the normalized lifetime, and the standard 

deviation is high. The curves are therefore not suitable for issuing early failure 

alerts. This is veried by the almost perfect overlap of the histograms 

of the entropy values at 50% and 95% of the lifetime. 

It is interesting to note that, of the two entropies computed in the 

time domain, the PPMdH entropy (shown in Fig. 5.16b) is lower than 

the signal's entropy (shown in Fig. 5.16a). In order to apply Shannon's 

formula, the probability mass function of the signal's values is estimated 

using a histogram of the signal's values. This estimates the entropy of 

the signal with respect to a static model. This is by no means the best 

model for the data as can be observed, the PPDdH compression scheme 

produces a better model. Nonetheless, the evolution curve for the PPMdH 

entropy shows no additional information. 

Table 5.2 presents the median Pearson and Spearman correlation coef- 

cients estimated between the AE hit count, the energy and the four entropies. 

Each coecient is estimated by rst computing the corresponding 

coecient between the curves from each fatigue test and then computing 

the median of the coecients obtained from all feet. The results presented 

in the table show that the signal's entropy is highly correlated with the PP- 

MdH entropy and that both these entropies are also highly correlated with 

the AE hit count. The results indicate that the signal's entropy might be 

a better alternative to the AE hit count and the PPMdH entropy. This is 

because it requires less computation and involves no tuning of parameters 

except for choosing the histogram's bin size. 

Furthermore, the calculations also show that there is a signicant correlation 

between the energy and the spectrum entropy. Since the energy 

requires less computation and its interpretation is more intuitive it might


(a)The evolution curve for the signal's 

entropy. 

(b)The evolution curve for the PPMdH 

entropy. 

(c)The evolution curve for the frequency 

entropy. 

(d)The evolution curve for the spectrum 

entropy. 

Figure 5.16 The average evolution of the four entropies computed from the AE 

segments. The grey area represents all values which lie within one standard 

deviation from the mean. 

be a better alternative. The frequency entropy measures the atness of 

the spectrum and can be used to detect the presence of broadband events 

which are not detected in the evolution of the energy. Consequently, the 

frequency entropy can be used to supplement the energy feature. 

5.3.3 Feature Patterns 

In the last part of this study it is investigated whether AE features appear 

in patterns and whether the pattern occurrences can be used to give signs 

about imminent failures. A new feature is proposed for this purpose. The 

new feature is called a trough-to-peak pattern feature. The trough-to-peak


Table 5.2 The median Pearson (left) and Spearman (right) correlation coecients 

between the AE hit count, the energy, and the four entropies. 

AE hit Energy Signal's PPMdH Freq. Spectrum 

count [dB] entropy entropy entropy entropy 

AE Hit Count 1 0,63 / 0,58 0,93 / 0,89 0,92 / 0,89-0,24 /-0,19 0,71 / 0,65 

Energy [dB] 0,63 / 0,58 1 0,74 / 0,72 0,73 / 0,70-0,44 /-0,52 0,92 / 0,91 

Signal's Entropy 0,93 / 0,89 0,74 / 0,72 1 0,99 / 0,99-0,28 /-0,31 0,79 / 0,79 

PPMdH Entropy 0,92 / 0,89 0,73 / 0,70 0,99 / 0,99 1 -0,24 /-0,29 0,78 / 0,79 

Freq. Entropy -0,24 /-0,19-0,44 /-0,52-0,28 /-0,31-0,24 /-0,29 1 -0,23 /-0,20 

Spectrum Entropy 0,71 / 0,65 0,92 / 0,91 0,79 / 0,79 0,78 / 0,79-0,23 /-0,20 1 

pattern feature is made by combining a variant of the ISI feature and the 

hit pattern feature. It is computed by rst determining the time from a 

trough to a peak (and also from a peak to a trough) for each AE hit, then 

coding the results and then counting the occurrences of all patterns found 

in the coded representation. A trough-to-peak interval is a variant of the 

Inter-spike Interval (ISI). It can also be recognized to include variants of 

two commonly used AE hit-based features, namely the rise time and the 

fall time. 

The methodology described in Sect. 3.4 is used to count the pattern 

occurrences. The full bandwidth of the signal (N = 1) and the whole 

segment (K = 1) are used. The AE hits are located using the procedure 

described above, but no determination is performed, i.e. the determination 

threshold (T AE ) is set to 0 mV. Figure 5.17 illustrates how the trough-topeak 

feature is coded into a coding vector. The trough-to-peak intervals, 

in microsecond, are quantized by using a natural logarithm and rounding 

the result to the nearest integer. Figure 5.18 explains how the hit pattern 

feature is computed; by counting how often a certain pattern in the coding 

vector appears. 

The patterns can be of arbitrary integer length containing an arbitrary 

combination of coded trough-to-peak (TTP) and peak-to-trough (PTT) 

intervals from any number of hits. For example, consider the following 

pattern of length 5: [T T P 1 P T T 1 ∗ ∗ T T P 3 ]. In order to match this 

pattern the coded intervals from two hits are required. The asterisk (*) 

is a wildcard symbol which means that any value is accepted; hence, the 

required coded intervals are not required to be from adjacent hits.


Figure 5.17 The rst step in computing the hit pattern feature is the generation 

of the coding vector for the signal segment. 

Figure 5.18 The second step in computing the hit pattern feature is to nd and 

count the number of occurrences for each hit pattern in the coded representation 

of the signal segment.


Figure 5.19 shows the average evolution of four selected trough-to-peak 

patterns of length 2 (see Fig. 3.11 for illustration). These patterns contain 

the coded values of the fall time of one hit and the rise time of the next 

adjacent hit. One can observe that the histograms of the number of occurrences 

at 50% and 95% of the lifetime for these patterns can be separated 

using thresholds. Table 5.3 lists the four patterns and the corresponding 

estimated Bayes optimal decision thresholds. In order to make the patterns 

more intuitive for the reader, the patterns are augmented by placing - and 

+ where the troughs and peaks are located respectively. 

Table 5.3 Four trough-to-peak patterns, of length 2. The patterns have been 

augmented by placing - and + where the troughs and peaks are located respectively. 

The last column contains the estimated Bayes optimal decision threshold. 

The pattern Decision Threshold 

Pattern 87 3 - 3 + 388.6 

Pattern 94 3 - 2 + 562 

Pattern 95 4 - 3 + 64 

Pattern 102 4 - 4 + 11.6


(a)The average evolution of the number 

of occurrences of trough-to-peak pattern 

no. 87. 

(b)The average evolution of the number 


no. 94. 

(c)The average evolution of the number 


no. 95. 

(d)The average evolution of the number 


no. 102. 

Figure 5.19 The average evolution of the number of occurrences of four troughto-peak 

patterns computed from the AE segments. The grey area represents all 

values which lie within one standard deviation from the mean.



In this section several commonly used AE features have been studied for 

the purpose of using them to provide a timely warning of impending failure. 

Furthermore, a trough-to-peak pattern feature was presented, studied 

and compared against the other AE features. The trough-to-peak pattern 

feature is a pattern of an arbitrary length, containing a combination of rise 

times and fall times of one to several AE hits. 

The evolution curves of the trough-to-peak patterns have a slope change 

at around 60% of the lifetime. The slope then remains constant until 

failure. This slope change is not present in the evolution curves for the other 

AE features. This suggests that these trough-to-peak pattern features 

are capturing important information from the AE signal, e.g. the slope 

change may be caused by the formation of a damage which grows until 

failure. Intuitively, the salient slope change can be used to provide an 

early warning about the health of the composite, and the results support 

this. The trough-to-peak patterns are the only features, studied here, which 

probability distributions at 50% and 95% of the lifetime can be reasonably 

well separated using a Bayes optimal decision boundary. 

Patterns made using dierent coding, length, features, or a combination 

of features, can possibly be used to obtain more information. The 

additional information can be combined into a feature vector which can 

be used as an input into classier system for more accurate warnings. For 

this purpose, one-class support vector machines (SVM) are interesting. 174 

Most of the data available for monitoring systems is sampled from healthy 

systems. For this reason the classication task is fundamentally a oneclass 

classication problem and it diers from conventional classication 

problems insofar as the classier is trained only by the healthy data, also 

known as target data, and never sees the unhealthy, or outlier, data. 

In other words, the classier must estimate the boundary that separates 

those two classes, based only on data which lies on one side of it, in order 

to minimize misclassications. 

The evolution curves studied in this section are all normalized according 

to the lifetime determined by a 10% displacement criterion. Half of the 

split-toe foot component for some feet, however, delaminates before the 

criterion is met. This is represented by a minute increase in the standard 

deviation in the last 10% of the lifetime for the energy, amplitude, subband


powers and the entropies except the frequency entropy. The standard deviation 

of the frequency entropy does not increase because the shape of 

the spectrum for these feet does not change. Instead all amplitudes (over 

all frequencies) increase. But, this means that the amplitude distribution 

changes and hence the spectrum entropy. 

It has been suggested that AE from cumulated damage, i.e. friction, 

can provide valuable information about the material health. 89 

This type of 

AE has mainly been regarded as unwanted and many attempts have been 

made to lter it out in order to better detect AE from damage growth, but 

this can be dicult. 8 

The fact that a damage only generates AE once, but 

friction many times, suggests that approaches based on friction will be more 

robust. In this study the energy, the entropies, the subband powers and 

the trough-to-peak patterns were extracted from the AE signals without 

applying any special lters to lter out AE from cumulative damage. 

The exponential increase of the AE hit counts and the signal's entropy 

during the last 3% of the lifetime and their relatively low standard deviation 

suggests that these two features can be used to create an AE-based failure 

criterion which is equivalent to the 10% displacement criterion. 

5.4 AE-Based Failure Criterion 

The aim of the study presented in this section is to determine whether 

an AE-based failure criterion can be designed to be equivalent to the 10% 

displacement failure criterion used in this work. This study was presented 

in Acoustic Emission-Based Fatigue Failure Criterion for CFRP . 14 

Experience 

has shown that when the displacement of the forefoot's actuator 

has changed by some critical percentage (below 10%), the rate of damage 

growth abruptly increases, the 10% displacement failure criterion is exceeded, 

and nal failure normally occurs within relatively few cycles after 

the criterion is met. 

The results presented in the previous section indicate that an AE-based 

early warning system can be designed to give timely warnings about damages 

which will eventually lead to nal failure. This approach, however, 

is based on the estimation of the AE feature's probability distribution. 

Consequently, not all failures will be detected. Hence, an AE-based failure 

criterion equivalent to the 10% displacement criterion can be used to

5.4 AE-Based Failure Criterion 107 

supplement the results presented in the previous section by detecting the 

point at which the damage growth increases abruptly. 

5.4.1 Methodology 

A failure criterion based on the AE signal can be developed in dierent 

ways. The development involves both the processing of data and the design 

of a failure detection algorithm. A threshold-based failure detection 

algorithm is used here. As the name implies, a failure is determined when 

the value of the parameter being monitored exceeds a specied threshold. 

Here three parameters are studied. The rst one is based on the AE hit 

count, the second on the energy, and the third on the signal's entropy. 

A detailed study of the behaviour of the AE signal during the cyclic 

testing of prosthetic feet shows that the signal behaves dierently in dierent 

parts of the fatigue cycle. This can be related to the stresses within the 

split-toe foot (see the static nite element analysis presented in Sect. 5.2). 

Hence, the fatigue cycle is divided into four phases based on the stresses. 

The rst phase starts when the forefoot's actuator is at the minimum loading 

position (50N) and ends when the actuator is located approximately 

at the midpoint of its journey. At the start of this phase, the top layers 

of the split-toe foot are in tension, and the bottom layers are in compression. 

The shear stresses decrease throughout the rst phase, and at the 

end of the phase the stresses change their sign. In the second phase, the 

forefoot's actuator continues its upward movement until full loading is obtained. 

During this time, both the compression stresses in the top layers 

and the tension stresses in the bottom layers increase. Phases 3 and 4 

are the reverses of cases 2 and 1 respectively. The splinters, or tear outs, 

which are commonly observed on the sides on the split-toe foot, can produce 

strong AE during loading. If a splinter is located at the lower half 

of the foot, i.e. below the center line, the splinter pushes out during the 

fourth phase and snaps back in at the start of the rst phase, often producing 

an audible sound. Similar behaviour is observed for splinters located 

above the center line, except they push out in phase 2 and snap back in 

phase 3. 

The procedure for creating a parameter for failure determination will 

now be described. The AE signal from each segment, s, is split into four 

shorter signals, each corresponding to one of the four phases of the fatigue


cycle. The AE feature to be used is then extracted from each of the four AE 

signals, i.e. the AE energy of the signal or the number of hits. The resulting 

four features, denoted by {a i (s)} 4 i=1, are then amplitude-modulated by 

multiplying them together. 

z(s) = 

4∏ 

a i (s) (5.2) 

i=1 

The amplitude modulation, z(s), emphasizes similar behaviour and at 

the same time smoothes out random uctuation and dissimilarities. This 

helps to prevent false failure detection because strong AE signals are generated 

by splinters in only one or two of the loading cases. Furthermore, 

because similar behaviour is emphasized, changes which occur in more than 

one of the phases do not have to be as large to be detected as a change 

which is only present in one of the four phases. 

At the time when the 10% displacement criterion is met damage is 

growing fast; delamination and abrupt changes in the AE activity take 

place in each of the four phases of the fatigue cycle. Consequently, the 

AE-based failure criterion must be designed to detect abrupt changes. The 

test static r(t) is computed by: 

r(s) = 

∣ z(s) − 1 10 

s−15 

∑ 

i=s−6 

z(s) 

∣ 

(5.3) 

By subtracting the mean of recent values, slow changes in z(s) are 

removed. Absolute value is used because any abrupt change large enough 

to exceed the threshold indicates a signicant material change. A failure 

is determined when a change in the test static, r(t), exceeds a specied 

threshold value, T. The units of both the threshold and the test static are 

the fourth power of the units of the AE feature used, e.g. Joules 4 when the 

AE energy is used. The failure detector tests between the two following 

hypotheses: 

H 0 r(s) < T No failure 

H 1 r(s) ≥ T Failure. 

(5.4)


5.4.2 Results 

An AE-based failure criterion which is to give similar detection results to 

the 10% displacement failure criterion must detect failure either before or 

at the same time as the displacement criterion. The dierence between the 

two criteria must also be as small as possible. These design specications 

are used to evaluate the performance of dierent parameter settings. 

Table 5.4 shows how the AE-based failure criterion compares against the 

10% displacement criterion. The rst column species the type of feature 

on which the test static is based. Three types of test statics are used. One 

is based on the AE hit count, the second on the energy, and the third on the 

signal's entropy. The AE hit count is obtained using the approach described 

in Sect. 3.2. The STFT detection function described in Sect. 3.2.1 is used 

with segment size of k = 128 samples and d = 120 sample overlapping. 

In order to locate hits, dierent values of the trough-to-peak threshold, 

T tp , are studied. These values are listed in the second column. Hit are 

determined by setting the determination threshold (T AE ) to 3 mV. The 

AE energy and the signal's entropy are computed as described in Sect. 5.3. 

The threshold, T used for determining failure is shown in column 3. The 

fourth column shows the number of feet for which the AE failure criterion 

did not detect failure. The fth column shows the number of feet for which 

failure is detected after the 10% displacement failure criterion has already 

determined failure. The sixth column shows the number of feet for which 

both criteria detect failure at the same time. The seventh column shows 

the number of feet for which the AE-based criterion detects failure earlier 

than the displacement criterion. The last two columns show the mean and 

the median of the dierence between the two criteria in thousand cycles. 

Negative values are used to represent detections which are made before the 

10% displacement failure criterion is met. The value of the threshold, T, in 

the penultimate row for the energy, entropy and each of the trough-to-peak 

thresholds is the value which gives the best results. This value is found 

manually. The value in the row below this is 10% larger and the two values 

in the rows above are, respectively, 10% and 20% smaller. 

The red rows are the best criterion settings for each test static type. Of 

the three, the best results are obtained using the AE hit count feature and 

setting the trough-to-peak threshold to 304 dB V-s and T = 3.000e10. A 

scatter plot of the failure detections made by using these settings and the


10% displacement failure criterion is depicted in Fig. 5.20. 

Figure 5.20 Scatter plot of failure detections made by the best AE criterion and 

the 10% displacement criterion. 

The points are distributed around a diagonal line, but not symmetrically. 

This is because the detections made by the AE criterion are either 

identical or slightly earlier than those made using the 10% displacement 

failure criterion. One can observe that four detections are signicantly 

dierent. The corresponding points are numbered and indicated by red 

squares. The displacement of the foot associated with point number 1 

abruptly changed to 8% 8,700 cycles before the displacement failure criterion 

was met. During the remaining time in the test, the displacement 

change uctuated around 8%. For the foot associated with point 2, the 

AE-based criterion was met after only 1,200 cycles. This was due to the 

formation of a large splinter and other damage. During the remaining 

6,000 cycles of the test the high energy AE signal was emitted in all of the 

four loading cases. The two remaining feet, corresponding to points 3 and 

4, were picked from scrap. These two feet were discarded due to porosity 

in the surface layers. Several very strong AE hits with enough energy to 

meet the failure criterion were emitted throughout the fatigue life of the 

feet. This produces early failure detections which are correctly detected as


failures; however, they do not correspond to a 10% change in displacement. 

Table 5.4 The results of AE-based failure determination compared to the displacement 

criterion. The values in the three last columns are in thousand cycles 

and negative values represent detections made before the displacement criterion 

is met. 

Feature T tp T 

Energy 

[Joules 4 ] 

Time of detection vs. displ. criterion 

Missed Later Identical Earlier 

Mean 

Median 

8.400e-21 0 0 18 57 -12.6 - 2.1 

9.450e-21 0 0 18 57 -12.5 - 1.2 

1.050e-20 0 0 18 57 -12.0 - 1.2 

1.155e-20 0 1 18 56 -11.8 - 1.2 

Entropy 

[nats 4 ] 

89.6 0 0 15 60 - 7.0 - 0.3 

100.8 0 0 21 54 - 5.5 - 0.3 

112.0 0 0 28 47 - 2.6 0.0 

123.2 2 1 30 42 - 1.6 0.0 

173.7 0.920e11 0 0 4 71 -11.3 - 0.9 

Hits 173.7 1.035e11 0 0 4 71 -10.0 - 0.9 

[counts 4 ] 173.7 1.150e11 0 0 6 69 - 9.1 - 0.6 

173.7 1.265e11 0 1 9 65 - 7.8 - 0.6 

Hits 

Hits 

Hits 

Hits 

260.6 1.920e10 0 0 1 74 -11.8 - 1.2 

260.6 2.160e10 0 0 7 68 -10.2 - 0.9 

260.6 2.400e10 0 0 9 66 -10.2 - 0.9 

260.6 2.640e10 0 2 11 63 - 7.5 - 0.6 

304.0 2.400e10 0 0 27 48 - 3.7 0.0 

304.0 2.700e10 0 0 29 46 - 3.0 0.0 

304.0 3.000e10 0 0 34 41 - 2.3 0.0 

304.0 3.300e10 1 1 33 40 - 2.3 0.0 

347.4 1.080e10 0 0 11 64 -12.1 - 0.9 

347.4 1.215e10 0 0 13 62 - 8.7 - 0.6 

347.4 1.350e10 0 0 17 58 - 7.1 - 0.3 

347.4 1.485e10 0 2 21 52 - 5.5 - 0.3 

434.3 3.120e09 0 0 1 74 -26.3 -26.1 

434.3 3.510e09 0 0 1 74 -24.1 -20.4 

434.3 3.900e09 0 0 2 73 -21.3 -15.9 

434.3 3.290e09 0 1 2 72 -19.7 -13.8



The results show that an AE-based failure criterion can be designed to be 

equivalent to a 10% displacement failure criterion. The failure criterion 

is designed to detect abrupt changes in the test statics, while minimizing 

false detections. If an AE event caused by large splinters is not present 

in all the phases, but is detected as failure, the splinters need to be inspected. 

These results are signicant for three reasons. Firstly, the two 

techniques are based on dierent principles: one measures stress waves generated 

under loading and the other measures displacement. Secondly, this 

is accomplished for an assembled CFRP product subjected to multiaxial 

cyclic loading. Hence, this veries that the AE technique can be applied 

in a practical setting where the AE signal contains mostly emissions from 

cumulative damage. Thirdly, this conrms that a failure criterion using 

more sensitive technique can be designed to obtain nearly identical results 

to those yielded by a stiness-based criterion. 

The favourable results obtained using the test static based on the AE 

hit count can be attributed to both the adjustable trough-to-peak threshold 

and the logarithmic transformation used during the hit determination. The 

logarithmic transformation enhances low energy hits, while compressing 

high energy hits. Consequently, this makes the technique less sensitive to 

the rugged frequency response and placement of the AE transducer. This 

is useful when the transducer cannot be placed at the location of damage 

and the AE signal suers from high attenuation. 

As expected, based on the correlation calculations in Sect. 5.3, the 

entropy-based test static gives results which are close to the results obtained 

using the AE hit count-based test static. The dierence lies in the 

fact that the entropy-based test static has a higher number of early detections. 

The additional early detections are all due to delamination of half of 

the split-toe foot. For these feet, the 10% displacement criterion is not met 

until later, when the delamination has grown larger. Nonetheless, both of 

the AE-based criteria can be used to detect failure at the same time or 

before the 10% displacement failure criterion. The mean dierence for the 

energy-based test static is considered to be too high. In order to improve 

the results a dierent test static, based on the features, or a dierent failure 

detector are required.

5.5 Case Study 113 

5.5 Case Study 

In this section, a case study is presented which is aimed at investigating 

the fatigue evolution of one individual Vari-ex foot. The foot selected for 

the case study has all the main fatigue characteristics observed in the feet 

tested. 

The study is divided into three parts. In the rst part the temporal 

behaviour of the load and displacement are studied. In the second part, the 

evolution of dierent AE features is studied and the results from Sect. 5.3 

and Sect. 5.4 are applied in order to see if they can be used to provide an 

early health warning and to detect failure. In the third and nal part, the 

methodology introduced in Sect. 3.4 is used to investigate whether tracking 

of AE features and AE patterns can provide additional information about 

the fatigue evolution of the foot. It is possible that this information may 

be used to facilitate early damage diagnosis and failure. 

5.5.1 Load and Displacement 

The evolution of the displacement of the forefoot's actuator is presented 

in Fig. 5.21a. As one can observe, the signicant displacement changes 

occur in abrupt steps. The steps, or events, are labelled A to F. Step A is 

due a stiness drop which occurs when splinters of varying sizes form on 

both sides of the split-toe foot (see Sect. 5.1 for a general description of the 

splinters). After the formation of the splinters, in the interval between step 

A and step B, the displacement remains fairly constant. Then, at step B, 

half of the split-toe foot delaminates and the downward bending stiness 

drops (see Fig. 5.21b). The delamination was veried by visual inspection. 

After step B, the downward bending stiness starts to decrease gradually 

between the abrupt steps. This gradual decrease is due to delamination 

growth. The upward bending stiness (the black curve in Fig. 5.21b) remains 

constant until step E, or when considerable damage has accumulated 

in the split-toe foot. After spike number 4, at step E, both the upward and 

downward bending stinesses decrease rapidly until failure, at step F. 

The extreme load values applied by the heel's actuator, shown in Fig. 5.21c, 

are relatively constant throughout the fatigue test. Hence, the spikes in 

the displacement numbered 1,2,3 and 4 in Fig. 5.21a are due to the loading


applied by the forefoot's actuator, which can be traced to the PID control 

algorithm used to control the loading (see Figs. 5.21b and 5.21d). 

The evolution of the load and displacement parameters does not provide 

any early warnings before the delamination of half of the split-toe foot 

at step B. After the delamination, visual inspection can be performed to 

detect and verify the type of damage. However, if visual inspection is 

not possible, then it can be dicult to estimate the severity of the damage 

which causes the stiness change at each step from these parameters alone. 

Consequently, warnings about detrimental damage growth will be issued 

after step B. 

(a)The evolution of the displacement 

of the forefoot's actuator. 

(b)The evolution of the maximum and 

minimum positions of the forefoot's 

actuator. 

(c)The evolution of the maximum and 

minimum load exerted by the heel's 

actuator. 

(d)The evolution of the maximum and 

minimum load exerted by the forefoot's 

actuator. 

Figure 5.21 The evolution of the displacement, extreme positions of the forefoot 

actuator, and both extreme load values of the heel and forefoot's actuators.


5.5.2 AE Features 

Based on the results of visual and acoustic inspection performed by the 

author, i.e. watching and listening, during the cyclic testing of the foot, 

the temporal behaviour of the AE features presented in Fig. 5.23 can be 

interpreted. These features were studied in Sect. 5.3 and are extracted here 

using the same settings. Each feature is overlaid onto its corresponding 

mean and standard deviation. The mean is computed by averaging the 

evolution curves of all the other feet. 

Shortly after the cyclic test is initiated, or after 6k cycles, small splinters 

start to form on both sides of the split-toe foot. During the next 4.2k cycles 

the splinters grow larger and rub against the sides. This results in a very 

steep increase in the AE energy, but only a slight increase in the number 

of AE hits. Two spikes are observed in the AE energy when 12.3k and 

13.2k cycles have elapsed. At this time a medium-sized splinter forms on 

the right side of the split-toe foot. The two measurements corresponding 

to the spikes in AE energy are taken at points when there is growth in 

the splinters. This means that the readings are composed of AE from 

both rubbing and damage growth. Thus, spikes are observed rather than 

a permanent increase. The reader is reminded that measurements are 

made at 5-minute intervals, or every 300 cycles; hence, the probability of 

recording AE from damage growth is low. 

In the interval between cycles 15k to 18.6k cycles, a large splinter 

on the right side of the split-toe foot forms. The splinter, depicted in 

Fig. 5.22a, causes both the upward and downward bending stinesses to 

drop. As a consequence, the displacement of the forefoot's actuator increases 

abruptly. The abrupt displacement increase is labelled as step (or 

event) A in Fig. 5.21. The formation of the splinter is accompanied by an 

increase in the AE energy and an abrupt jump in the AE hit count. 

Within a few cycles after the formation of the splinter, or when 21.6k 

fatigue cycles have been applied, the outer woven layers on the left side 

delaminate from the unidirectional layers. The delamination crack begins 

from the splinter crack and grows for undetermined number of cycles. The 

number of cycles is undetermined because it is not possible to establish if 

and when the crack growth stops using visual inspection. In each cycle, 

when the crack opens an audible AE is produced. Due to this and also 

because the crack grows over time, the AE energy increases. From 21.6k to


(a)Right side of the split-toe foot under 

static loading. 

(b)Left side of the split-toe foot under 

static loading. 

Figure 5.22 

The left and right sides of the split-toe foot after cyclic testing. 

28.5k cycles the AE energy increases at a relatively steady high rate, but 

then it becomes constant. At 28.5k cycles a medium-sized splinter forms on 

the left side. The splinter, shown in Fig. 5.22b, does not aect the bending 

stinesses and is not detectable in the evolution of any of the AE features. 

At 33.9k cycles there is an abrupt jump in the AE energy and over the 

next 4.1k cycles the energy falls by 50% of the jump. Shortly after that, 

or at 40.2k cycles, another abrupt jump in the AE energy occurs. From 

this point the energy reduces initially at a high rate, but the rate decreases 

temporarily at 41.7k cycles, and increases again at 55.2k cycles for 900 

cycles. After this, the energy reduces at a low rate until the reduction 

ceases, at 64.8k cycles The two abrupt jumps in the energy, at 33.9k and 

40.2k cycles, are not accompanied by any changes in the bending stinesses. 

Subtle changes, however, can be detected in the slope of the AE hit count, 

duration, and the signal's entropy at 40.2k cycles. 

At 72k cycles, the left half of the split-toe foot delaminates. This results 

in a drop in the bending stinesses. The corresponding abrupt displacement 

increase is labelled as event B in Fig. 5.21. Abrupt jumps in the 

AE energy, AE hit count and the signal's entropy are also observed. The 

average duration, however, does not jump abruptly, but instead increases 

at a higher rate. 

The average duration of each measurement does not provide much information; 

in fact, the curve looks similar to the evolution of the AE hit 

counts with the abrupt jumps removed. As expected, based on the cor-


(a)The evolution of the AE hit count. 

(b)The evolution of the cumulative AE 

hit count. 

(c)The evolution of the energy 

(d)The evolution of the average duration 

(e)The evolution of the average amplitude 

(f)The evolution of the signal's entropy 

Figure 5.23 The evolution of selected AE features throughout one fatigue test. 

The grey area for each feature represents all values which lie within one standard 

deviation from the mean (black curve). The mean is computed by averaging the 

evolution curves from all other feet.


relation calculations in Sect. 5.3, the curve showing the evolution of the 

signal's entropy is nearly identical to the one showing the evolution of the 

AE hit counts, except it has fewer uctuations. The cumulative AE hit 

count, presented in Fig. 5.23b, is a commonly used parameter for the study 

of acoustic emission. Although the cumulative sum contains the same information 

as the AE hit counts, the information provided by subtle slope 

changes, small jumps, and uctuations is harder to detect. One can observe 

from the gure that the curve can be divided into three segments, 

each with a dierent slope. The slope changes occur at events A and B. 

However, the AE hit count, shown in Fig. 5.23a, is the slope of the curve 

in Fig. 5.23b at every measurement. The AE hit count is absolute in that 

it does not depend on prior values, but each value of the cumulative curve 

depends on all prior values. This means that missing or late measurements 

do not aect the results when monitoring the AE hit count, but the slope 

of the cumulative curve is a function of the frequency of the measurements, 

i.e. dierent curves are obtained by summing up the AE hit counts from 

measurements made at dierent or irregular intervals. Hence, the cumulative 

AE hit count works best when the interval between the measurements 

can be xed. 

The evolution of the average amplitude, depicted in Fig. 5.23e, is strongly 

correlated with the AE energy on a decibel scale, shown in Fig. 5.23e. The 

Pearson and Spearman correlation coecients for the two curves are 0.88 

and 0.92 respectively. 

Figure 5.24 shows the evolution of the total number of observations for 

the same four patterns as those studied in Sect. 5.3. The histograms at 

50% and 95% of the normalized lifetime (see Fig. 5.19) overlap slightly 

for each pattern. As a result there is a small probability of error, but the 

Bayes optimal decision boundary gives the lowest probability of error. The 

green line is the Bayes optimal decision boundary between the histograms 

at 50% and 95% of the normalized lifetime. 

By classifying between the histograms at 50% and 95% of the normalized 

lifetime, three out of four patterns can be used to issue a timely 

warning before the 10% displacement failure criterion is met. The classi- 

er, however, is not able to issue an early warning before the delamination 

which occurs after 72k cycles, or at step B. 

Figure 5.25 shows the evolution of the test static used for AE-based


(a)The evolution of the number of occurrences 

of trough-to-peak pattern 

no. 87. 

(b)The evolution of the number of occurrences 


no. 94. 

(c)The evolution of the number of occurrences 


no. 95. 

(d)The evolution of the number of occurrences 


no. 102. 

Figure 5.24 The evolution of the number of occurrences for four trough-to-peak 

(ISI) patterns computed from the AE segments. The grey area for each pattern 

represents all values which lie within one standard deviation from the mean (black 

curve). The mean is computed by averaging the evolution curves from all other 

feet. 

failure detection. The test static is based on the AE hit count and the 

threshold for failure is T = 3.000e10 (see Sect. 5.4). The failure criterion 

correctly detects when the displacement of the forefoot's actuator has 

changed by more than 10% from the initial value.


Figure 5.25 

The evolution of the AE hit count-based test static.


5.5.3 AE Feature Tracking 

The approach used in the above study to extract the AE features and visualize 

their evolution can be formulated as a special case of the methodology 

described in Sect. 3.4, i.e. using one interval (K = 1) and full bandwidth 

(N = 1). This produces the results presented above. By dividing the measurement 

segments into shorter intervals, the dimension of time within a 

segment is added to the analysis. Furthermore, by bandpass ltering the 

signal and studying each subband separately the results are divided into 

N dierent subresults, one for each subband. This dierent approach for 

quantifying the AE features requires a dierent visualization method to 

interpret the results. In Sect. 3.4 a 2D intensity image for each subband is 

proposed. 

In this study, which was presented in Monitoring The Evolution of Individual 

AE Sources in Cyclically loaded FRP Composites , the reference 

16, 20 

signal is the phase of the position of the forefoot's actuator. Because the 

position is at constant angular velocity it is converted to cycle time. The 

cycle time starts at the lowest position of the actuator, or at 0 ◦ phase angle. 

The AE signal is bandpass ltered into N = 19 subbands, each with 33 kHz 

bandwidth. A phaseless ltering is used in order to avoid phase delay. 167 

The removal of phase delay is important in interpreting and comparing the 

results from one subband against the results from another. Each subband 

segment is divided into K = 200 equally-sized intervals before extracting 

the spectrum entropy from each interval. The maximum amplitude of the 

rectied signal in each interval is used to generate the feature vector. The 

procedure is explained in Fig. 3.15. 

Figure 5.26 shows the resulting intensity image for the 133166 kHz 

subband and also the evolution of the AE energy and the AE hit count 

from each segment. The AE energy and the hit count are computed as 

before, i.e. using the full signal's bandwidth. Figure 5.27 shows four more 

intensity images corresponding to the 266300 kHz, 366400 kHz, 466 

500 kHz and 566600 kHz subbands. By comparing the evolution of the 

AE energy and the AE hit count in Fig. 5.26 against the intensity images 

depicted in Fig. 5.26 and Fig. 5.27, one can see that the intensity images 

facilitate a better understanding of the changes which are occurring in the 

material. 

The steep increase in the AE energy early in the fatigue test is at-


Figure 5.26 The resulting intensity image for the 133166 kHz subband. Each 

value in the image is the maximum amplitude in the corresponding interval. Also 

depicted is the evolution of the total AE energy and AE hit count from each 

segment (computed using the signal's full bandwidth). 

tributed to formation of small splinters on the side of the split-toe foot. In 

each fatigue cycle these splinters rub against the toe-foot component and 

occasionally grow. The AE from these splinters is presented as a growing 

cluster in the upper left corner of the intensity image depicted in Fig. 5.26. 

The cluster is circled and labelled a. 

At 12.3k and 13.2k cycles two spikes are observed in the evolution of 

the AE energy. These spikes are due to the formation of a medium-sized 

splinter on the right side of the split-toe foot. Although the AE energy 

only shows two spikes, one can see, from the intensity images, two new 

paths initiate at this time from within the cluster labelled a (Fig. 5.26). 

The paths are circled and labelled b (Fig. 5.27d). 

A large splinter on the left side of the split-toe foot forms during the 

period from 15k to 18.6k cycles. The splinter causes a drop in both bending 

stinesses and can be detected as a subtle change in the evolution of the AE 

energy, but as an abrupt jump in the AE hit count (labeled A in Fig. 5.26. 

In the intensity images, this event can be detected by the formation of new 

paths and a sudden change in the left path of the two circled and labelled 

b (Fig. 5.27d). The left path changes its course, shifts to the left and 

disappears. Within a few hundred cycles after the formation of the splinter,


the woven layers at the left bottom of the split-toe foot delaminate from 

the unidirectional layers. The delamination crack opens every time that 

the heel's actuator is nearly fully loaded and an audible AE is generated. 

The crack grows and the AE energy increases at a steady high rate. The 

AE from the delamination crack resides in the lower frequency bands and 

can be observed in the boxed area labelled c (Fig. 5.26). In the 133 

166 kHz subband, the AE from the delamination crack masks out other 

AE. However, the AE is bandlimited; hence, dierent frequency bands can 

be used to monitor some of the masked-out damages, e.g. the circled paths 

labelled b and d (Fig. 5.27d). 

At 28.5k cycles a medium-sized splinter forms on the left side of the 

split-toe foot. The formation cannot be detected from the the evolution of 

the AE energy, AE hit count nor the bending stinesses. The AE emitted 

from the splinter is masked out in the 133166 kHz subband, but can be 

detected and monitored in intensity images for the higher frequency bands. 

The corresponding evolution path is circled and labelled d in Fig. 5.27d. 

By studying dierent subbands, one can in some cases detect and distinguish 

between damages that emit bandlimited AE signals at the same 

time, but are evolving in dierent directions, as can be seen by comparing 

the circled paths labelled e in Fig. 5.27b and Fig. 5.27c. Most of the energy 

from the frictional AE caused by the rubbing of the splinters is located 

in the lower frequencies. The boxed region labelled f ( Fig. 5.27a) shows 

where the frictional AE is located within the fatigue cycles. In addition to 

the frictional AE, the splinters also, for a limited time, produce strong AE 

at the end of their push-out movement (the circled paths labelled b and d 

in Fig. 5.27d) and also when they snap back in (the boxed area labelled g 

in Fig. 5.27d). 

The two abrupt jumps in the AE energy and amplitude at 33.9k and 

40.2k cycles are accompanied only by subtle changes in the slope of the 

other AE features, but no changes in the bending stinesses. The intensity 

images, however, show the initiation of two paths originating from 

within the area where the frictional AE from the splinters is located. The 

beginnings of the paths are circled and labelled h and i in Fig. 5.27b. 

In the rst half of the segment in which the rst path starts (labelled 

h in Fig. 5.27b), a high amplitude AE can be observed in the intensity 

image for the 133166 kHz subband (Fig. 5.26). This portion is circled


(a)Intensity image for the 266300 kHz 

subband. 

(b)Intensity image for the 366400 kHz 

subband. 

(c)Intensity image for the 466500 kHz 

subband. 

(d)Intensity image for the 566600 kHz 

subband. 

Figure 5.27 The resulting intensity images for four selected subbands. The 

brightness of each pixel is based on the amplitude in the corresponding interval. 

and labelled j. Furthermore, two evolving high amplitude paths end in 

this portion. Simultaneously with the initiation of the second path, labelled 

i (Fig. 5.27b), another high amplitude AE path initiates in the rst half of 

the loading cycle. The path can be seen in all subbands. The beginning 

of the path is circled and labelled k in Fig. 5.26. The two paths, labelled 

h and i (Fig. 5.27b), evolve asymptotically towards a line close to and 

parallel to the 750 ms line, labelled n in Fig. 5.26. Initially the paths 

evolve at a high rate but as they approach the line the rate decreases. The


vertical asymptote line is located where the tensional, compressional and 

shear stresses change their signs. This location in the fatigue cycle acts as 

an attractor for most evolving AE sources in the left half of the intensity 

images, i.e. during the downward movement of the forefoot's actuator. 

Conversely, during the upward movement of the actuator, the so-called 

attractor is around 250 ms, shown by a line labelled m in Fig. 5.26. As can 

be observed in the gure, the attractor is oset to the right. This is because 

the the loading is not symmetrical around the 500 ms (see Fig. 5.11). 

The left half of the split-toe foot delaminates at 72k cycles. This event 

(labelled B in Fig. 5.26) can be observed in the evolution of all AE features 

and also in the downward bending stiness. After the delamination, 

a high amplitude AE is generated in a large portion of each cycle and in 

all subbands. During the 12k cycles leading up to the delamination the 

AE activity, as indicated by the evolution of the AE features in Fig. 5.23, 

remains at a relatively steady level. However, the intensity images show 

few changes which can be interpreted as warnings. First, several new highamplitude 

paths start during this period. These paths are circled and 

labelled l, o and p in Figs. 5.26, 5.27c and 5.27d. Second, during this period 

one can observe that the path which began in the circled area labelled 

h moves one step closer to the 750 ms line. 

The AE energy feature produces nearly identical results to those presented 

here. Both the maximum amplitude and the AE energy are computed 

without any adjusting parameters. Figure 5.28a and Fig.5.28b show 

results computed using the ring-down counts and the duration of the hit 

with the maximum amplitude in each interval respectively. In order to 

compute the features, the determination threshold, T AE , is set to 3 mV. 

These images do not have as well dened paths as the images presented 

above, but dierent features can reveal new patterns (e.g. the circled path 

labelled q in Fig. 5.28a). The main challenge in using this approach for 

threshold-based features is the task of adjusting, for each subband, the 

trough-to-peak threshold, T tp , used for locating hits from the detection 

function, and the determination threshold, T AE , used both for determining 

hits and for extracting the threshold-based features.


(a)Intensity image computed using the 

ring-down counts of the hit with the 

maximum amplitude in each interval. 

(b)Intensity image computed using the 

duration of the hit with the maximum 

amplitude in each interval. 

Figure 5.28 Two intensity images, for the 133166 kHz subband, made using 

threshold-based AE features. The brightness of each pixel is based on the value 

of the AE feature in the corresponding interval. 

5.5.4 AE Pattern Tracking 

This case study ends with an investigation into whether AE-hit patterns 

can be used to improve the tracking results presented above. This investigation 

was presented in On Using AE Hit Patterns for Monitoring Cyclically 

15, 18 

Loaded CFRP. The segmentation and subband ltering are performed 

as above with N = 19 subbands. The AE hits are located and determined 

using the time domain detection function described in Sect. 3.2.1. The 

trough-to-peak threshold, T tp , is adjusted for each subband so that the 

average number of hits in the rst 5 measurements is around 10.000. In 

other words, the average pulse duration in each subband is 0.1 ms. By using 

these settings small pulsations in the AE signal's amplitude are detected 

as hits. In order to determine hits, the determination threshold, T AE , is 

set to 3 mV. Two dierent coding representations are studied: one using 

only ISI information, and another using both ISI and the peak amplitude 

of the hits. The values of N ISI and N AMP are both set to 10, and K = 200 

intervals are used when computing the feature vectors. The resulting feature 

vector for each pattern contains the total number of observations in 

each interval. In order to ght the curse of dimensionality only two pattern


lengths are used for both coding representations: L = 2 and L = 4. 

ISI coding 

Approximately 60 patterns are obtained for each subband using ISI coding. 

However, only a handful of them produce intensity images with detectable 

paths, which can be used to track the locations of the AE sources. Figure 

5.29 shows an example of two such images. 

(a)An intensity image for an ISI pattern 

which does not show any paths. 

(b)An intensity image for an ISI pattern 

which does not show any paths. 

Figure 5.29 Two intensity images which have no detectable paths. The brightness 

of each pixel is based on how often a pattern is observed in the corresponding 

interval. 

Figure 5.30 shows intensity images for four handpicked patterns. As one 

can observe, the circled paths labelled 1, 2, 3 and 6 in the gure are the 

same paths as those depicted in Fig. 5.26 and Fig. 5.27. However, further 

comparison of the images, in these three gures, shows that only small 

portions of the circled paths labelled 4 and 5 in Fig. 5.30 can be detected 

in the other two gures. Consequently, by using AE patterns based on 

the ISI, more dened and more visually detectable paths can be detected. 

These paths can be used to locate AE sources for tracking and for detailed 

analysis of their AE signals. 

Figure 5.30b and Fig. 5.30c show that dierent patterns may be used 

to monitor the same AE source. This is because the ISI, as used here, is


the based on the time between the small pulsations in the AE amplitude; 

hence, the AE emitted from a source may contain several patterns. 

The intensity images for some patterns do not have any prominent 

paths, but instead clusters. An example of such an image is shown in 

Fig. 5.30d. The high values in this image are clustered where the frictional 

AE is emitted; hence, some patterns may be used to monitor the frictional 

AE. 

(a)Intensity image for a pattern in the 

333366 kHz subband. 

(b)Intensity image for a pattern in the 


(c)Intensity image for a pattern in the 


(d)Intensity image for a pattern in the 


Figure 5.30 Intensity images corresponding to four selected ISI patterns. The 

brightness of each pixel is based on how often a pattern is observed in the corresponding 

interval.


ISI/Peak Amplitude Coding 

By combining the ISI coding with the peak amplitude and searching for 

patterns of length L = 2 and L = 4, the total number of patterns increases 

up to approximately 600 patterns for each subband. The increase is a 

function of the number of quantization levels used for the amplitude,N AMP . 

Figure 5.31 shows intensity images corresponding to four handpicked 

patterns. The circled paths labelled I, III and IV can also be detected in 

the images obtained using only ISI coding (see Fig. 5.30b). However, these 

paths are more prominent in Fig. 5.31. This is because the addition of 

the peak amplitude works like a lter. The observations of patterns with 

certain ISI coding are divided between patterns with the same ISI coding, 

but dierent amplitude coding. As a result, the number of AE patterns is 

higher. This ltering also helps to detect patterns which would otherwise 

pass undetected, e.g. the circled paths labelled II in Fig. 5.31b. 

By visually inspecting the intensity images for dierent patterns and 

extracting prominent paths, e.g. those circled in Fig. 5.31, a composite 

image can be made by piecing together the individual paths. Figure 5.32 

shows a composite image, made by picking out, overlaying and enhancing 

paths extracted from 32 handpicked intensity images. The images are from 

all subbands. On the right side the composite image is the evolution of the 

AE energy in each segment. 

A comparison of the intensity images in Fig. 5.30 with the intensity 

image in Fig. 5.32 reveals that the addition of the peak amplitude makes 

it possible to track the evolution of several AE sources after the left half 

of the split-toe foot delaminates at 72k cycles. The tracking improvement 

can also be observed by comparing the 750-1000 ms region of the images 

(where the frictional AE due to the rubbing of the splinters is located). In 

this region of the fatigue cycle, the initiation of 3 paths can be observed 

(indicated by arrows). Furthermore, the rst path, which starts at event 

A, can now be tracked until shortly before the delamination of the left 

half. Based on these results, it can be deduced that the splinters initiate 

damages which grow until delamination occurs.


(a)Intensity image for a pattern in the 


(b)Intensity image for a pattern in the 


(c)Intensity image for a pattern in the 


(d)Intensity image for a pattern in the 


Figure 5.31 Intensity images corresponding to four handpicked patterns. The 

brightness of each pixel is based on how often a pattern is observed in the corresponding 

interval. 


The results of the case study show that the AE hit patterns can be used 

to provide an early warning before the 10% displacement criterion is met, 

and that the AE failure criterion, presented in Sect. 5.4, successfully detects 

failure at the same time as the 10% displacement failure criterion.


Figure 5.32 A composite image made by overlaying and enhancing the results 

from 32 patterns (left) and the evolution of the AE energy (right) 

The results also show that none of the AE features studied here can be 

used to give timely warnings about the delamination which occurs at step 

B when the method of extracting one AE feature from each segment and 

studying its evolution is used. The abrupt jumps in the AE energy (and the 

average amplitude) at 33.9k and 40.2k cycles may perhaps be considered 

as early warning signs. However, because the AE energy decreases rapidly 

after the jumps and no signicant changes are observed in the evolution of 

the other AE features, nor in either of the bending stinesses, nor from the 

visual tests, the potential warning signs cannot be interpreted or veried. 

In order to extract more information from the AE signal using these same 

features, it was concluded that they must be quantied and presented 

dierently, e.g. using the methodology for tracking AE sources, described 

in Sect. 3.4. 

The nal part of the case study presents the results from an investigation 

into whether this methodology could be used to provide information 

for the interpretation of the potential warning signs mentioned above. In 

other words, the aim was to investigate if the results could be used to answer 

questions such as whether a growing, steady or decreasing feature size 

is due to friction, damage growth, or both? 

The results obtained by using either the AE energy, or the maximum


amplitude, in each interval show that valuable information about the location 

and the evolution of multiple AE sources can be obtained. The sources 

are identied and monitored using the paths in the resulting intensity images. 

Furthermore, by bandpass ltering the AE signal and studying each 

subband separately, band-limited AE sources can be identied and monitored. 

These sources may otherwise pass unnoticed. 

From the resulting intensity images, the initiation of two AE sources was 

identied and tracked until delamination of the foot. Visual inspection of 

the intensity images revealed that the corresponding paths initiated from 

where the AE from the splinters was located. This suggested that the 

corresponding damages were caused by the splinters. Hence, the paths can 

be used to signicantly improve our understanding of the changes occurring 

in the material, and lead to more focused analysis of the AE signal. The 

analysis becomes more focused and detailed because it is possible to locate 

the AE from one particular AE source in the subband of interest. This 

means that the detection of paths is important for all further analysis and 

interpretation of the AE signal. In addition, because the intensity images 

obtained using one type of AE feature do not reveal all existing patterns, 

other features must also be used. 

Consequently, as a part of the investigation, hit-based AE features and 

AE pattern features were studied for the purpose of identifying new paths. 

The results obtained using hit-based features indicate that they are not 

good for this task. However, the results show that the AE patterns made 

from inter-spike intervals (ISI) can be used to track the locations of AE 

sources. The paths obtained using the patterns are nearly the same as the 

those obtained using the AE energy. These results are especially interesting 

since the study of the ISI as a feature to track AE sources has, to the best 

of the authors' knowledge, not previously been reported. 

A signicant improvement in the source tracking using a AE pattern 

features is accomplished by combining the ISI information with the peak 

amplitude of each hit. This is because the addition of the amplitude acts 

like a lter on the results obtained using ISI patterns. Hence, by adding 

the peak amplitude it is possible to track sources when there is very high 

AE activity, for example when delamination or rubbing have occurred.

"All great truths are simple in nal analysis, 

and easily understood; if they are not, they 

are not great truths." 

Napoleon Hill 

6 Conclusion 

This thesis investigated the acquisition, processing and presentation of 

acoustic emissions generated during cyclic loading CFRP composites with 

the aim of using them to identify early signs of impending failure. 

In order to achieve the objective of the thesis, an experimental setup was 

designed and implemented to acquire the acoustic emissions during multiaxial 

cyclic loading of 75 nominally identical samples of the prosthetic foot 

Vari-ex. The Vari-ex is a bolted assembly of three CFRP components 

which are curved with both varying thickness and width. Two pneumatic 

actuators were used to ex the feet, which were slightly rotated out of the 

plane dened by the movement of the actuators. Consequently, the feet 

were simultaneously subjected to compression, tension, shear and torsion 

stresses which changed their signs in each cycle. The positions and loading 

applied by the actuators were acquired synchronously with the acoustic 

emissions. 

Five research steps were carried out on the acquired experimental data. 

The results obtained from these steps are the main contributions of this 

thesis, and will be discussed in the next section. The chapter, and this 

thesis, ends with a section in which directions for future research are outlined.

134 Chapter 6. Conclusion 

6.1 Contributions 

The rst contribution of this thesis, presented in Sect. 3.2, is the formulation 

of an approach for locating and determining AE hits in the acquired 

AE signal. A new approach was necessary because threshold-based hit 

detection, with a xed or a oating threshold, was not suitable. Fixed 

thresholds are set at the start of the monitoring, i.e. tuned to the noise 

level of the AE signal. As the material degrades and AE is generated by 

the cumulative damage, the AE signal level increases and the threshold 

cannot be used to pick out individual hits. Furthermore, the xed threshold 

cannot be used to distinguish between hits when a burst of strong, 

slightly overlapping AE is encountered. This type of burst was commonly 

observed in the AE measurements and was generated by the rubbing of the 

splinters. The increase in AE signal strength over time was due to cumulated 

damage, but not noise. For this reason, a oating threshold was not 

suitable. Furthermore, because the strength of the AE emissions varied 

within each cycle, it was dicult to set the appropriate response time of 

the oating threshold. If the response was set too fast the threshold was 

aected by strong transients. The approach presented in this thesis was designed 

to overcome the abovementioned limitations of the threshold-based 

approaches. However, the approach has, intuitively, its own limitations. 

These include the tuning of the parameters used and the required computational 

load. The hit determination in the time domain, which is based on 

the signal's energy, has a signicantly lower computational load than the 

STFT-based determination in the time-frequency domain. Furthermore, 

it does not suer from the time-frequency trade-o associated with the 

STFT. 

The second contribution is the proposition and formulation of two new 

AE features: the inter-spike intervals (ISI) and the AE hit patterns. These 

features were used in two studies presented in Chapter 5 (Sect. 5.3 and 

Sect. 5.5). The favourable results show that there is valuable information 

contained within these features. Although the results were based on a 

combination of these features, i.e. the patterns made by the ISI were 

investigated, this does not in any way undermine the information provided 

by the ISI feature alone and its variant, the trough-to-peak interval. This 

is because the AE hit pattern feature does not add any information; it 

is a technique for: a) fusing the features extracted from each AE hit, b)

6.1 Contributions 135 

combining the fused data from all hits, and c) nding and locating patterns 

which appear within the fused data representation. 

The third contribution is the results of the study presented in Sect. 5.3. 

In this study, the average evolution of several AE features was computed 

for the purpose of estimating the feature's probability distribution, at each 

percent of the lifetime. The probability distribution was then evaluated 

to determine whether it could be used to provide timely warning of impending 

failures in CFRP composites. The failure was dened by the 10% 

displacement-based failure criterion. The results show that, of all the AE 

features studied, only a few trough-to-peak patterns can be used to issue 

early failure warnings. The evolution curves of these patterns have 

a salient slope change at around 60% of the lifetime, but the curves of 

other AE features have only a signicant change in the last 10-5% of the 

fatigue life. The meaning of the patterns was not explored. The results 

also revealed a strong correlation between the AE hit count and the signal's 

entropy. These results are interesting, because in order to compute 

the signal's entropy only one parameter needed to be set: the number of 

bins in the histogram, whereas in order to locate and determine the hits 

using the STFT approach, several parameters needed to be set. In addition, 

the computational cost required to compute the signal's entropy is 

substantially less than that needed to determine and count the AE hits. 

Although the results showed that early warning of impending failure 

could be issued, it was recognized that the approach was based on an 

estimated probability distribution; hence, not all imminent failures were 

detected in advance of their occurrence. For this reason it was deemed 

necessary to design a failure criterion for the detection of all failures. From 

the study of the evolution of the dierent AE features it was observed that 

the AE hit counts, energy and the signal's entropy increased exponentially 

during the last 3% of the lifetime. The exponential increase was associated 

with rapid damage growth. A further study revealed that the signal's 

behaviour within each fatigue cycle could be associated with four dierent 

phases of the cycle. Subsequent, nite element analysis showed that the 

four phases were directly related to the evolution of the stresses within 

the material. Based on these results, an AE-based failure criterion was 

designed to be equivalent to the 10% displacement failure criterion used 

in this work. The AE-based failure criterion, presented in Sect. 5.4, is the 

fourth contribution of this thesis.

136 Chapter 6. Conclusion 

The fth and nal, and perhaps the most signicant contribution of 

this thesis is the methodology presented and formulated in Sect. 3.4. The 

methodology is designed for processing, presenting and quantifying AE 

data so that it can be used to identify multiple AE sources and track 

their locations relative to the phase of a reference signal. A study was 

conducted to investigate the hypothesis that the methodology could be 

used to improve the method for issuing early warnings by facilitating early 

damage diagnosis and failure prognosis. The results showed that, by using 

this methodology, both frictional AE and AE from evolving damage growth 

could be identied, located and tracked. Furthermore, because AE from 

specic AE sources can be identied and isolated, further analysis of the AE 

can be made more eective. Hence, the results conrmed the hypothesis. 

6.2 Directions for Future Research 

The use of the methodology designed for tracking AE sources is limited 

neither to AE signals nor to periodic reference signals. It can be used to 

study changes, or artifacts, in other signals using either periodic or aperiodic 

reference signals. Examples of signals which can be studied include 

AE from relays and valves (aperiodic), vibrational data, ECG, EEG, etc. 

The methodology, however, was not fully developed in this thesis. It is 

recommended that future research and development should address the 

following issues. 

First, the methodology does not currently address the problem that 

arises when either (or both) the upper or the lower limit of the dynamic 

range of the reference signal changes. Furthermore, if one wishes to use a 

reference signal other than relative time, e.g. load or displacement, then 

the methodology must also be to deal with a variable rate in the reference 

signal. 

Second, all further analysis of the AE signal strongly depends on the 

detection of evolving paths in the intensity images. For this reason, different 

signal and image processing techniques should be investigated at 

each step of the methodology, from subband ltering to feature extraction, 

and from feature extraction to the generation of the nal intensity images. 

The investigation should also include a further in-depth study of AE features, 

e.g. the eect of using dierent coding for the hit pattern feature or

6.2 Directions for Future Research 137 

dierent pattern lengths. 

Third, there is much room for automation. For example, in this thesis 

useful hit patterns for AE tracking were identied and selected manually 

through visual inspection of the intensity images. It is unlikely that the 

same patterns will be useful for other test specimens. Furthermore, evolving 

paths only appear in certain intensity images, depending both on the 

type of feature and on the subband. Hence, for a successful application of 

the methodology one may be required to visually inspect a large number 

of intensity images within a limited amount of time, and perform an analysis. 

It would therefore be useful to develop a technique for automatically 

detecting paths and patterns in the intensity images.


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List of Tables 

4.1 The measurement equipment used for acquiring AE and the position 

of the forefoot's actuator during fatigue testing. . . . . . 71 

5.1 The maximum stresses found by the nite element analysis of the 

Vari-Flex foot. . . . . . . . . . . . . . . . . . . . . . . . . . 86 

5.2 The median Pearson (left) and Spearman (right) correlation coef- 

cients between the AE hit count, the energy, and the four entropies.101 

5.3 Four trough-to-peak patterns, of length 2. The patterns have been 

augmented by placing - and + where the troughs and peaks are located 

respectively. The last column contains the estimated Bayes 

optimal decision threshold. . . . . . . . . . . . . . . . . . . . 103 

5.4 The results of AE-based failure determination compared to the 

displacement criterion. The values in the three last columns are 

in thousand cycles and negative values represent detections made 

before the displacement criterion is met. . . . . . . . . . . . . 111


List of Figures 

2.1 Shows matrix cracks, broken bres, debonding and delamination. 11 

2.2 Shows what happens when air gets trapped between layers. . . . 12 

2.3 Shows foreign inclusion and a wrinkle. . . . . . . . . . . . . . 13 

2.4 Schematic progression of fatigue damage in composites. . . . . 17 

3.1 An illustration of a typical resonant AE transducer and how an 

AE is converted into an electric representation. . . . . . . . . 27 

3.2 Two calibration curves for the same resonant AE transducer. The 

red curve is the result of a pressure calibration and the green is the 

result of a displacement calibration (reproduced with permission 

from Vallen GmbH). . . . . . . . . . . . . . . . . . . . . . . 28 

3.3 Illustration of conventionally used AE hit-based features. . . . . 32 

3.4 Flow chart of the AE hit determination procedure. . . . . . . . 40 

3.5 Illustration of how the STFT-based detection function is generated. 42 

3.6 Illustration of the incremental peak picking procedure. . . . . . 44 

3.7 Illustration of how the hit determination approach presented here 

is able to detect and separate overlapping transients which the 

threshold-based procedure cannot. . . . . . . . . . . . . . . . . 47 

3.8 The left gure shows an AE signal which consists of weak (0-5 

ms), intermediate (5-10 ms) and strong transients (10-15 ms). 

Above the AE signal is the STFT-based detection function. The 

right gure shows the weak transients in more detail, the detection 

function, and the detected troughs and peaks. . . . . . . . . . 48 

3.9 The intermediate and strong transients of the signal shown in 

Fig. 3.8a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

160 LIST OF FIGURES 

3.10 The generation of the coding vector illustrated using two element 

subvectors for each hit. The two elements are coded maximum 

amplitude and coded ISI respectively. . . . . . . . . . . . . . . 56 

3.11 The procedure for nding hit patterns in the coded representation. 57 

3.12 Schematic overview of the proposed experimental methodology. . 58 

3.13 The AE signal is segmented and each segment is split into N 

subbands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 

3.14 The left image shows a wavelet packet tree corresponding to conventional 

DWT and the packet numbers. The right image shows 

a full 4 level wavelet packet tree and the packet numbers. . . . . 60 

3.15 For each subband segment, the new feature vector is computed 

by rst rectifying the signal, then computing a piecewise constant 

envelope, and nally down-sampling the envelope. . . . . . . . 61 

3.16 For each subband, new feature vectors are appended to previous 

vectors and an intensity image is generated. . . . . . . . . . . 62 

4.1 The assembled Vari-Flex. The Vari-Flex is made up of two heel 

parts and one toe part. . . . . . . . . . . . . . . . . . . . . . 66 

4.2 A mould for the toe components and the resulting panel after the 

components have been cut out. . . . . . . . . . . . . . . . . . 67 

4.3 Schematic representation of the experimental setup for both the 

AE and the position measurements. . . . . . . . . . . . . . . 68 

4.4 Shows both the maximum loading as a function of stiness category 

and the Vari-Flex with a wedge. . . . . . . . . . . . . . . 69 

4.5 The shape of the Vari-ex at the two extreme loading conditions 

in each fatigue cycle, i.e. forefoot loaded (left) and heel loaded 

(right). The images are made by tracing video frames of a foot 

in a test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

4.6 The frequency response of the VS375-M transducer. . . . . . . 72 

4.7 Schematic illustration of the bending of the transducer's contact 

surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

4.8 The shim (left) and the isolated AE transducer (right). . . . . . 73 

4.9 The c-clamp used to hold the transducer during the fatigue testing 

(left) and the resulting supercial damage due to sticking of the 

split-toe component and the heel. . . . . . . . . . . . . . . . . 74

LIST OF FIGURES 161 

4.10 The resolution of the L-Gage Q50A sensor. A fast response speed 

is used. The gure is taken from a specications sheet provided 

by the manufacturer. . . . . . . . . . . . . . . . . . . . . . . 75 

5.1 The fatigue life distribution of the feet according to the 10% displacement 

criterion. A two-parameter Weibull distribution t is 

superimposed. . . . . . . . . . . . . . . . . . . . . . . . . . . 79 

5.2 The side of ve split-toe feet components after failure. The components 

are statically loaded. . . . . . . . . . . . . . . . . . . 80 

5.3 Shows both the positions of the two actuators during one fatigue 

cycle and the loading on the foot. . . . . . . . . . . . . . . . . 81 

5.4 The area model and the element model used for studying the 

stresses in the foot. . . . . . . . . . . . . . . . . . . . . . . . 83 

5.5 Shows the compressional and tensional stresses at the two extreme 

positions of the forefoot's actuator. . . . . . . . . . . . . 84 

5.6 Shows the shear stresses at the two extreme positions of the forefoot's 

actuator. . . . . . . . . . . . . . . . . . . . . . . . . . 85 

5.7 The solid curve shows the mean displacement change and all values 

within one standard deviation from the mean. The dashed 

curve is a log 10 transformation of the solid curve. . . . . . . . 87 

5.8 The evolution of the extreme position of the forefoot's actuator 

shown for 4 sample feet. . . . . . . . . . . . . . . . . . . . . 88 

5.9 The stiness measurement setup and results for three feet. . . . 89 

5.10 Shows both the positions of the two actuators during one fatigue 

cycle and the loading on the foot. . . . . . . . . . . . . . . . . 90 

5.11 The load-position relationship for both actuators. . . . . . . . . 91 

5.12 The average evolution of the AE hit count and the signal's energy 

(per loading cycle). The grey area represents all values which lie 

within one standard deviation from the mean. . . . . . . . . . 93 

5.13 The average evolution of six commonly used AE hit features. The 

grey area represents all values which lie within one standard deviation 

from the mean. . . . . . . . . . . . . . . . . . . . . . 95

162 LIST OF FIGURES 

5.14 The average evolution of AE hit features extracted from the hit 

with the maximum amplitude and the amplitude ratio of the two 

hits with the largest amplitudes. The grey area represents all 

values which lie within one standard deviation from the mean. . 96 

5.15 The average evolution of AE features in the frequency domain. 

The grey area represents all values which lie within one standard 

deviation from the mean. . . . . . . . . . . . . . . . . . . . . 97 

5.16 The average evolution of the four entropies computed from the 

AE segments. The grey area represents all values which lie within 

one standard deviation from the mean. . . . . . . . . . . . . . 100 

5.17 The rst step in computing the hit pattern feature is the generation 

of the coding vector for the signal segment. . . . . . . . . 102 

5.18 The second step in computing the hit pattern feature is to nd 

and count the number of occurrences for each hit pattern in the 

coded representation of the signal segment. . . . . . . . . . . . 102 

5.19 The average evolution of the number of occurrences of four troughto-peak 

patterns computed from the AE segments. The grey area 

represents all values which lie within one standard deviation from 

the mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 

5.20 Scatter plot of failure detections made by the best AE criterion 

and the 10% displacement criterion. . . . . . . . . . . . . . . 110 

5.21 The evolution of the displacement, extreme positions of the forefoot 

actuator, and both extreme load values of the heel and forefoot's 

actuators. . . . . . . . . . . . . . . . . . . . . . . . . 114 

5.22 The left and right sides of the split-toe foot after cyclic testing. 116 

5.23 The evolution of selected AE features throughout one fatigue test. 

The grey area for each feature represents all values which lie 

within one standard deviation from the mean (black curve). The 

mean is computed by averaging the evolution curves from all other 

feet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

5.24 The evolution of the number of occurrences for four trough-topeak 

(ISI) patterns computed from the AE segments. The grey 

area for each pattern represents all values which lie within one 

standard deviation from the mean (black curve). The mean is 

computed by averaging the evolution curves from all other feet. . 119

LIST OF FIGURES 163 

5.25 The evolution of the AE hit count-based test static. . . . . . . 120 

5.26 The resulting intensity image for the 133166 kHz subband. Each 

value in the image is the maximum amplitude in the corresponding 

interval. Also depicted is the evolution of the total AE energy 

and AE hit count from each segment (computed using the signal's 

full bandwidth). . . . . . . . . . . . . . . . . . . . . . . . . . 122 

5.27 The resulting intensity images for four selected subbands. The 

brightness of each pixel is based on the amplitude in the corresponding 

interval. . . . . . . . . . . . . . . . . . . . . . . . . 124 

5.28 Two intensity images, for the 133166 kHz subband, made using 

threshold-based AE features. The brightness of each pixel is based 

on the value of the AE feature in the corresponding interval. . 126 

5.29 Two intensity images which have no detectable paths. The brightness 

of each pixel is based on how often a pattern is observed in 

the corresponding interval. . . . . . . . . . . . . . . . . . . . 127 

5.30 Intensity images corresponding to four selected ISI patterns. The 

brightness of each pixel is based on how often a pattern is observed 

in the corresponding interval. . . . . . . . . . . . . . . . . . 128 

5.31 Intensity images corresponding to four handpicked patterns. The 

brightness of each pixel is based on how often a pattern is observed 

in the corresponding interval. . . . . . . . . . . . . . . . . . 130 

5.32 A composite image made by overlaying and enhancing the results 

from 32 patterns (left) and the evolution of the AE energy (right) 131


List of Algorithms 

1 STFT-based detection function . . . . . . . . . . . . . . . . . . 43 

2 Trough- and Peak-Picking Algorithm . . . . . . . . . . . . . . 45 

3 Trough- and Peak-Removal Algorithm . . . . . . . . . . . . . . 45

Acoustic Emission Monitoring of CFRP Laminated Composites ...

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