Robust Design - Dynardo GmbH

dynardo

Robust Design - Dynardo GmbH

DYNARDO • © Dynardo GmbH 2012

Robustness & Reliability Analysis

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DYNARDO • © Dynardo GmbH 2012

Robust Design Optimization

Robust Design

Variance based

Robustness Evaluation

Probability based

Robustness Evaluation,

(Reliability analysis)

Optimization

Sensitivity Study

CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)

Robust Design Optimization Methodology

Start

Single & Multi objective

(Pareto) optimization

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DYNARDO • © Dynardo GmbH 2012

How to define Robustness of a Design

• Intuitively: The performance of a robust design is largely

unaffected by random perturbations

• Variance indicator: The coefficient of variation (CV)

of the objective function and/or constraint values is smaller than

the CV of the input variables

• Sigma level: The interval mean+/- sigma level does not reach an

undesired performance

(e.g. design for six-sigma)

• Probability indicator: The probability of reaching undesired

performance is smaller than an acceptable value

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DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation / Reliability Analysis

• Variance-based robustness evaluation

measure product serviceability

– Safety and reliability for 1 & 2 (3)

Sigma levels and identifies the most

sensitive stochastic variables

– Possible with high number of

stochastic variables

• Probability-based robustness evaluation

(reliability analysis) measure product

serviceability

– Safety and reliability for high

reliability levels (3,4,5,6-Sigma) with

small number of variables

– Possible with a limited number of

stochastic variables

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DYNARDO • © Dynardo GmbH 2012

Definition of Uncertainties

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DYNARDO • © Dynardo GmbH 2012

Uncertainties and Tolerances

Design variables

• Material, geometry, loads,

constrains,…

• Manufacturing

• Operating processes (misuse)

• Resulting from Deterioration

• …

Property SD/Mean

%

Metallic materiales, yield 15

Carbon fiber rupture 17

Metallic shells, buckling

strength

6

14

Bond insert, axial load 12

Honeycomb, tension 16

Honeycomb, shear, compression 10

Honeycomb, face wrinkling 8

Launch vehicle , thrust 5

Transient loads 50

Thermal loads 7.5

Deployment shock 10

Acoustic loads 40

Vibration loads 20

Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace.

Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris 1994


DYNARDO • ECCOMAS 2012 congress• © Dynardo GmbH 2012

Definition of Uncertainties

Translate know how about uncertainties into proper scatter definition

Distribution functions define

variable scatter

Correlation is an important

characteristic of stochastic

variables.

Yield stress

Tensile strength

Correlation of single uncertain values

spatial correlated

thickness distribution

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DYNARDO • © Dynardo GmbH 2012

Design “single” scatter shapes

• Use of CAD-parameter or mesh morphing functions to

design “single” scatter shapes

Measured ed imperf imperfection modelled imperfection

Imperfection of cylindricity of truck wheel component

by courtesy of

Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light

truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, www.dynardo.de]

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DYNARDO • © Dynardo GmbH 2012

Random Field Parametric

• Introduction of scatter of spatially correlated scatters need parametric of

scatter shapes using random field theory.

The correlation function represents the

measure of “waviness” of random fields.

The infinite correlation length reduced the

random field to a simple random variable.

Usually, there exist multiple scatter shapes

representing different scatter sources.

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DYNARDO • RDO forming simulation • © Dynardo GmbH 2012

Use forming simulation to generate scatter fields

4. Mapping to crash mesh

3. Generation of n-imperfect formed

parts using scatter field parametric

2. Identification of most important

scatter fields for scattering forming

result values (thickness,

hardening)

5. Run Robustness Evaluation of

assembly including scatter from forming

1. Running Robustness

evaluation of forming simulation

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DYNARDO • © Dynardo GmbH 2012

Use measurements to generate Random Fields

3. Identification of most

important random fields for

measured quantity (geometry)

4. Generate imperfect geometries using

Random Field parametric

2. Trimming of initial FE-mesh regarding

measurement or realization

5. Run Robustness Evaluation to identify

the most sensitive random fields



• •




••






1. Multiple Measurements

from Manufacturing

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DYNARDO • © Dynardo GmbH 2012

Implementation of Random Field Parametric

Introduction of spatial correlated scatter to CAE-Parameter (geometry,

thickness, plastic astic values)

3. Generation of multiple imperfect

structures using Random Field parametric

2. Generation of scatter shapes using

Random field parametric, quantify scatter

shape importance

4. Running Robustness Evaluation

including Random Field effects

1. Input: process simulation or

measurements

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DYNARDO • © Dynardo GmbH 2012

Variance-based Robustness Analysis

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DYNARDO • © Dynardo GmbH 2012

Which Robustness do You Mean?

Robustness evaluation due to naturally given scatter

Goal: measurement of variation and correlation

Methodology: variance-based robustness evaluation

Positive side effect of robustness evaluation: The measurement of

prognosis quality of the response variation answer the question - Does

numerical scatter significantly influence the results?

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DYNARDO • © Dynardo GmbH 2012

Statistic Measurements

• Evaluation of robustness with statistical

measurements

– Variation analysis (histogram,

coefficient of variation, standard

variation, distribution fit,

probabilities)

– Correlation analysis (linear,

quadratic, nonlinear) including

principal component analysis

– Forecast quality: Evaluation of

Coefficient of Prognosis (CoP)

including coefficients of

determination (CoD)and coefficient

of importance (CoI)

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DYNARDO • © Dynardo GmbH 2012

Advanced Statistic Measurements

• Advanced histogram options

– PDF fit (automatic/manual)

– Number of histogram classes

– PDF values ready for optiSLang

input

– Limits with probabilities

– Probabilities with limit

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DYNARDO • © Dynardo GmbH 2012

Standardized and Automated Post Processing

Example how the post

processing is

automated for passive

safety at BMW

The maximum from

the time signal was

taken.

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DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation using optiSLang

1) Define the robustness space using

scatter range, distribution and

correlation

5) Identify the most

important scattering

variables

4) Check the CoI/CoP CoI

2) Scan the robustness space by

producing and evaluating n

(100) Designs

3) 3) Check the variation interval

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DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation of NVH Performance

Start in 2002, since 2003 used for Production Level

How does body and suspension system scatter influence the NVH

performance?

• Consideration of scatter of body in

white, suspension system

• Prognosis of response value scatter

• Identify correlations due to the input

scatter

• CAE-Solver: NASTRAN

• Up-to-date robustness evaluation of

body in white have 300 .. 600

scattering variables

• Using filter technology to optimize the

number of samples

by courtesy of

Will, J.; Möller, J-St.; Bauer, E.: Robustness evaluations of the NVH comfort using full vehicle models

by means of stochastic analysis, VDI-Berichte Nr.1846, 2004, S.505-527, www.dynardo.de

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DYNARDO • ECCOMAS 2012 congress• © Dynardo GmbH 2012

Robustness Evaluation of break systems

Start in 2007, since 2008 used for Production Level

How does material and geometric scatter influence the break noise

performance ?

• Consideration of material

and geometry scatter

• Break noise is a instability

problem

• Identify correlations due to

the input scatter

• CAE-Solver: NASTRAN,

ABAQUS, ANSYS

• Up-to-date robustness

evaluation have 20 ..30

scattering variables

• Integration of geometric

scatter via random fields

1. Define the

Uncertainties

4. Post

processing

2. Simulate random m parameters

p

3. Generate set of random

specimen, replace in FE assembly

to compute

by courtesy of

Will, J.; Nunes, R.: Robustness evaluations of the break system concerning squeal noise

problem, Weimarer Optimierungs- und Stochastiktage 2009, www.dynardo.de

X2

20

X1


DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation of Forming Simulations

• Consideration of process

and material scatter

• Determination of process

robustness based on 3-

Sigma-values of quality

criteria

• Projection and

determination of

statistical values on

FE-structure

necessary

CAE-Solver: LS-DYNA,

AUTOFORM and others

Start in 2004 - since 2006 used for production level

1. Variation der Eingangsstreuungen

mittels geeigneter

Samplingverfahren

3. statistische Auswertung

und Robustheitsbewertung

Will, J.; Bucher, C.; Ganser, M.; Grossenbacher, K.: Computation and visualization of

statistical measures on Finite Element structures for forming simulations; Proceedings

Weimarer Optimierung- und Stochastiktage 2.0, 2005, Weimar, Germany

2. Simulation inkl.

Mapping

auf einheitliches

Netz

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Why SoS and What is SoS ?

Why: Engineers need to evaluate statistical Das Bild kann zurzeit nicht angezeigt werden. data on the structure to locate

„hot spots“ of variation as well as investigate correlations

What: A post processor for Statistics on finite element Structures

• Visualization of descriptive statistics on the structure

• Visualization of correlations between random input

and structural results

• Visualization of quality performance (QCS)

• Identification of scatter shapes using Random Fields

Key features:

• locale „hot spots“ of variation

• Data reduction and smoothing by mesh coarsening

• Identification of relevant scatter shapes

• Vizualisation statistics of eroded (failed) elements

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DYNARDO • © Dynardo GmbH 2012

Statistical post-processing on FE-meshes

Motivation: - Visualization of statistical measurements

- Identification of hot spots,

- Identification of correlation structure (random fields)

1. Import data

(multiple simulation on runs

or measurements) ments)

3. Export local statistics

and imperfection

amplitudes to

optiSLang for further ther

post-processing

2. Visualize variation, v correlation,

identify ify random fi field shapes

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DYNARDO • © Dynardo GmbH 2012

Statistical post-processing on FE-meshes

SoS is the tool to answer the questions:

Where? Locate hot spots of highest variation and/or extreme values, which

may cause lack of performance or quality.

Why? Find the input parameters which cause scatter of the results, by

analysing correlation/CoD between random inputs and spatially distributed

results, export to optiSLang p g for MoP/CoP / analysis. y

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DYNARDO • © Dynardo GmbH 2012

SoS application crash simulation

• Stringer in a car body subject to crash simulation

• 55 random inputs: sheet thickness and material parameters (also of

other parts), load parameters (velocity, barrier angle etc.)

• Observed result: remaining effective plastic strain

[Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts.

SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.]

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DYNARDO • © Dynardo GmbH 2012

SoS application crash simulation

• Analysis of a car structure subject to

random crash load case

• Decomposition of plastic strain

random field

• Analysis of largest influence by

MoP/CoP in optiSLang

[Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts.

SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.]

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DYNARDO • © Dynardo GmbH 2012

SoS - Eroding elements

General eroding information.

Green area: no elements eroded.

Red area: there were eroded elements.

Eroding percent plot shows the

percentage of eroded elements.

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DYNARDO • © Dynardo GmbH 2012

SoS – Validated Global and Local Statistics

Variation, mean value, correlation, Histogram, linear & quadratic

QCS using SoS on FE-structure correlation, CoD, CoI, CoP and

Anthill plots using optiSLang at local

nodal or element values

Selection of nodal/element results in

SoS and export to optiSLang *.bin

CoD linear base

Correlation

R-value

Cotrrelation

Y-tolerance

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DYNARDO • © Dynardo GmbH 2012

SoS - Applications

- use SoS for robustness evaluation of forming processes

- use SoS for visualization and hot spot investigation at robustness

evaluations in crashworthiness or drop test applications

- use SoS for the identification of random fields from simulation or

measurements

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Standardized and Automated Post Processing

Productive Level needs standardized and automated post processing!

1. Check variation of

plasticity, failure,

intrusions.

3. Summarize variation

and correlation

2. Identify the beginning of the

phenomena in time and use SoS to

identify the source of variation

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DYNARDO • © Dynardo GmbH 2012

Summary SoS – Statistic on Structure

The post processor for Statistics on finite element Structures

- Statistic Measurements

- Single Designs

- Differences between Designs

- Variation interval

- Minimum/Maximum

- Mean Value

- Standard deviation

- Coefficient of variation

- Quantile (± ����

- Correlation & CoD

- Linear correlation & CoD

- At nodal/element level

- Process quality criteria Cp, Cpk

process indices

- Random field generation

- Scatter shape extraction and

visualisation

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DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation of Passive Safety

• Consideration of scatter of material

and load parameters as well as test

conditions

• Prognosis of response value

variation = is the design robust!

• Identify correlations due to the input

scatter

• Quantify the amount of numerical

noise

• CAE-Solver: MADYMO, ABAQUS

Start in 2004, since 2005 used

for productive level

Goal: Ensuring Consumer

Ratings and Regulations &

Improving the Robustness of a

System

Will, J.; Baldauf, H.: Integration of Computational Robustness Evaluations in Virtual

Dimensioning of Passive Passenger Safety at the BMW AG , VDI-Berichte Nr. 1976, 2006,

Seite 851-873, www.dynardo.de

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Robustness Evaluation Crashworthiness

Start in 2004 – since 2007 use for Production Level

• Consideration of scatter of thickness,

strength, geometry, friction and test

condition

• CAE-Solver: LS-DYNA, Abaqus

• Prognosis of intrusions, failure and

plastic behavior

• Identify Coefficient of Prognosis and

nonlinear correlations

• Check model robustness

• 100 .. 200 scattering variables

• Introduction of forming scatter via

Random Fields

by courtesy of the Daimler AG

In comparison to robustness evaluations for NVH, forming or passive

safety, crashworthiness has very high demands on methodology and

software!

by courtesy of

Will, J.; Frank, T.: Robustness Evaluation of crashworthiness load cases at Daimler AG;

Proceedings Weimarer Optimierung- und Stochastiktage 5.0, 2008, Weimar, Germany,

www.dynardo.de

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DYNARDO • © Dynardo GmbH 2012

Summary Robustness Evaluation

• optiSLang + SoS have completed the necessary methodology to run

robustness evaluation for NVH, passive safety, forming simulation or

crashworthiness

Success Key:

• Necessary distribution types and correlation definitions

available

• Optimized LHS sampling

• Reliable measurements of variation, correlation and determination

including filter technology

• Projection of statistic onto the FE-structure

Main customer benefit:

• Identification of problems early in the virtual prototyping stage

• Measure, verify and finally significantly improve the modeling quality

(reduce numerical scatter and modeling errors)

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DYNARDO • © Dynardo GmbH 2012

What is necessary for successful implementation?

1. Introduction of realistic

scatter definitions

� Distribution function

� Correlations

� Random fields

2. Using of reliable stochastic methodology

methodology

� Variance-based robustness

evaluation using optimized LHS

3. Development of reliable robustness

measurements

� Standardized post processing

� Significance filter

� Reliable variation and correlation

measurements

Acceptance of method/result documentation/communication!

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DYNARDO • © Dynardo GmbH 2012

Robustness and Stability of the Model

Which quantity of „numerical noise“ is acceptable?

� Quantification via coefficients of prognosis (CoP)

� Estimation of numerical noise: 100% - CoP

Experience in passive safety, CFD or

crashworthiness tells that result values

with lower CoP than 80% show:

- High amount of numerical noise

resulting from numerical approximation

method (meshing, material, contact,..)

- Problems of result extractions

- Physically instable behavior

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DYNARDO • © Dynardo GmbH 2012

Robustness Insurance Crash Loading

Response CoV

CoD

lin[%]

CoD lin

adj [%]

CoD

quad [%]

CoD

quad adj

[%]

max_int_energy 0.036 99.0 99.0 100.0 99.0

max_hourglass_energy 0.066 91.0 87.0 98.0 94.0

x_1129403_1129404 0.217 54.0 31.0 93.0 79.0

x_4000558_1129403 1.383 86.0 79.0 93.0 80.0

x_4139132 0.123 89.0 83.0 97.0 91.0

x_4144932 0.131 88.0 82.0 97.0 90.0

y_4139132 0.224 92.0 89.0 98.0 93.0

y_4144932 0.252 95.0 93.0 98.0 95.0

z_4139132 0.348 33.0 0.015 90.0 71.0

z_4144932 1.035 49.0 24.0 91.0 74.0

max_sec29_rforce 0.032 87.0 80.0 96.0 88.0

max_sec29_xforce 0.032 86.0 78.0 96.0 87.0

max_sec33_rforce 0.034 89.0 84.0 97.0 90.0

max_sec33_xforce 0.034 90.0 84.0 97.0 90.0

max_plast 0.211 88.0 82.0 95.0 86.0

summ_plast 0.26 91.0 87.0 97.0 92.0

In qualified FE-models numerical scatter is not

dominating important response values!

Model guidelines, model verification and robustness

evaluation ensure a reasonable model quality.

LS-DYNA low speed structural

crash case

Robustness evaluation against

structure and loading scatter

show coefficients between 71

and 99 %

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DYNARDO • © Dynardo GmbH 2012

Robustness check of optimized designs

• With the availability of parametric modeling environments like

ANSYS workbench an robustness check becomes very easy!

• Menck see hammer for oil and gas exploration (up to 400m deep)

Robustness evaluation against tolerances, material scatter and working

and environmental conditions

• 60 scattering parameter

Design Evaluations: 100

Process chain: ProE-ANSYS workbench- optiSLang

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DYNARDO • © Dynardo GmbH 2012

Robustness evaluation as early as possible

Goal: Tolerance check before any

hardware exist!

Classical tolerance analysis tend to be very

conservative

Robustness evaluation against production

tolerances and material scatter (43

scattering parameter) shows:

- Press fit scatter is o.k.

- only single tolerances are important (high

cost saving potentials)

Production shows good agreement!

Design Evaluations: 150

solver:

ANSYS/optiSLang

by courtesy of

Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light

truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, www.dynardo.de

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DYNARDO • © Dynardo GmbH 2012

Reliability Analysis

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© Dynardo GmbH 2012

Reliability analysis

• Limit state function g(x) divides random variable space X

in safe domain g(x)>0 and failure domain g(x) ��

• Multiple failure criteria (limit state functions) are possible

• Failure probability is the probability that at least one failure criteria is

violated (at least one limit state function is negative)

• Integration of joint probability density function over failure domain

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DYNARDO • © Dynardo GmbH 2012

Definition of limit state functions

Dynardo • optiSlang Seminar

Example damped oscillator

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DYNARDO • © Dynardo GmbH 2012

Reliability Analysis Algorithms

Gradient-based

algorithms = First

Order Reliability

algorithm (FORM)

ISPUD Importance

Sampling using Design

Point

Adaptive Response

Surface Method

Monte Carlo Sampling Latin Hypercube Sampling Directional Sampling

X2

X1

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DYNARDO • © Dynardo GmbH 2012

How choosing the right algorithm?

Robustness Analysis provide the

knowledge to choose the

appropriate algorithm

Robustness & Reliability Algorithms

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DYNARDO • © Dynardo GmbH 2012

Application Example ARSM for Reliability

• Fatigue life analysis of Pinion shaft

• Random variables

• Surface roughness

• Boundary residual stress

• Prestress of the shaft nut

• Target: calculate the probability of

failure

• Probability of Failure:

• Prestress I: P(f)=2.3 10 -4 (230

ppm)

• Prestress II: P(f)=1.3 10 -7 (0.13

ppm)

by courtesy of

Solver: Permas

Method: ARSM

75 Solver evaluations

sigma = +/-5kN

sigma = +/-10kN

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DYNARDO • © Dynardo GmbH 2012

Probability Assessment of Railways

• Goal: investigate the crosswind stability of Railway

systems

• Sensitivity analysis against stochastic loading

parameters followed by probability analysis

• Random variables

• crosswind amplitude, duration

• aerodynamic coefficients

Solver: ADAMS + Matlab

Methods: LHS, FORM, ISPUD

Proppe, C.Wetzel, C.; Probabilitic Assessment of the Crossswind Stability of Railway

Systems; Proceedings Weimarer Optimierung- und Stochastiktage 4.0, 2007, Weimar,

Germany, www.dynardo.de

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DYNARDO • © Dynardo GmbH 2012

Robust Design Optimization

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DYNARDO • © Dynardo GmbH 2012

Design for Six Sigma

• Six Sigma is a concept to optimize the manufacturing processes such

that automatically parts conforming to six sigma quality are

produced

Design for Six Sigma is a concept to optimize the design such that

the parts conform to six sigma quality, i.e. quality and reliability are

explicit optimization goals

• Because not only 6 Sigma values have to be used as measurement

for a robust design, we use the more general classification Robust

Design Optimization

48


© Dynardo GmbH 2012

© Dynardo GmbH

Sigma level vs. failure probability

• The sigma level can be used to calculate the probability of exceeding

a certain response value

• Since the distribution type is often unknown, this estimate may be

very inaccurate for small probabilities

• The sigma level deals with single limit values, whereas the failure

probability quantifies the event, that any of several limits is exceeded

� Reliability analysis should be applied to proof the required safety level

Distribution Required sigma level (CV=20%)

p F = 10 -2 p F = 10 -3 p F = 10 -6

Normal 2.32 3.09 4.75

Log-normal 2.77 4.04 7.57

Rayleigh 2.72 3.76 6.11

Weibull 2.03 2.54 3.49

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DYNARDO • © Dynardo GmbH 2012

Robust Design Optimization

Robust Design

Variance based

Robustness Evaluation

Probability based

Robustness Evaluation,

(Reliability analysis)

Optimization

Sensitivity Study

CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)

Robust Design Optimization Methodology

Start

Single & Multi objective

(Pareto) optimization

50


Robust Design

Robust Design Optimization (RDO) optimize the design performance

with consideration of scatter of design (optimization) variables as

well as other tolerances or uncertainties.

As a consequence of uncertainties the location of the optima as well as

the contour lines of constraints scatters.

To proof Robust Designs safety distances are quantified with variance

or probability measurements using stochastic analysis.

51


Methods for Robust Design Optimization

Variance-based RDO

• Safety margins of all critical responses

are larger than a specified sigma level

(e.g. Design for Six Sigma)

Reliability-based RDO

• Failure probability with respect to given

limit states is smaller as required value

Taguchi-based RDO

• Taguchi loss functions

• Modified objective function

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DYNARDO • © Dynardo GmbH 2012

Robust Design Optimization - RDO

Robust Design Optimization combines optimization and Robustness

Evaluation. From our experience it is often necessary to investigate both

domains separately to be able to formulate a RDO problem. optiSLang

offers you either iterative or automatic RDO flows.

Robustness Robustne evaluation

SSensitivity it analysis

Define safety factors

Robust design optimization

Robustness proof!

53


DYNARDO • © Dynardo GmbH 2012

Iterative RDO Application Connector

2) The DX Six Sigma design was checked in

the space of 36 scattering variables using

optiSLang Robustness evaluation. Some

Criteria show high failure probabilities!

1) From the 31 optimization

parameter the most effective

one are selected with

optiSLang Sensitivity

analysis.

3) From optiSLang Robustness

Evaluation safety margins are

derived.

4) Three steps of optimization

using optiSLang ARSM and EA

optimizer optimizer improve the design to

an optiSLang Six sigma design.

5) Reliability proof using ARSM

to account the failure probability

did proof six sigma quality.

Start: Optimization using 5 Parameter using DX Six Sigma, then customer

asked: How save is the design?

by courtesy of

54


Robust Design Optimization of a rubber seal

Using DesignModeler parametric

was rebuild with 11 Parameter.

Using optiSLang sensitivity

analysis 7 effective parameter

are identified. Using ARSM

design was optimized to have

minimal volume and sufficient

pressure at all contact points.

Initial design

Including Uncertainty of

loading and material 6

Sigma quality was violated.

Therefore iterative RDO

increasing safety margins

was performed to reach 3

Sigma design level.

Robust design

Using optiSLang Reliability

Analysis 3 sigma quality was

proven.

Customer started optimization with two parameter and found minimal improvement

potential.

55


DYNARDO • NAFEMS conference 2012 • © Dynardo GmbH 2012

Summary

• Stochastic analysis needs a balance between input definitions,

stochastic analysis method and post processing

• Use specific/concrete robustness/reliability measurements

• RDO using one global response surface approximation for

optimization and robustness space usually underrepresents the

influence of scattering variables

• Because all RDO strategies will try to minimize solver runs for

robustness measures, a final proof of robustness/reliability is

mandatory

• Carefully translation and introduction of material scatter is crucial

• Start with robustness evaluation of start/optimal candidate design

• Continue with iterative RDO approach using safety distances

• If safety distances in optimization space vary significant automatic

RDO is necessary

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DYNARDO • © Dynardo GmbH 2012

Part 7

Applications

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DYNARDO • © Dynardo GmbH 2012

Application Crashworthiness

AZT Insurance Crash Load Case

• Scatter definition (40..60 scattering

parameter)

– Velocity, barrier angle and position

– Friction (Road to Car, Car to

Barrier)

– Yield strength

– Spatially correlated sheet metal

thickness

• Main result: Prognosis of plastic

behavior

• CAE-Solver: LS-DYNA

Deterministic analysis show no problems with an AZT load case. Tests

frequently show plastic phenomena which Daimler would like to minimize.

Motivation for the robustness evaluation was to find the test phenomena

in the scatter bands of robustness evaluations, to understand the sources

and to improve the robustness of the design.

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DYNARDO • © Dynardo GmbH 2012

Did You Include All Important Scatter?

Scatter of uniform sheet

thickness thickness (cov=0.05),

yield strength, friction, test est

conditions

We could not find

or explain the test

results!

Introduction of sheet metal

thickness scatter per part

- 100 LS-DYNA simulation

- Extraction via LS-PREPOST

SoS - post processing

Statistics_on_Structure

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DYNARDO • © Dynardo GmbH 2012

Definition of Scatter is the Essential Input!

Which degree of forming scatter discretization is becomes necessary?

Level 1 - No distribution information: - increase uniform coil thickness

scatter cov=0.02 to cov=0.03..0.05

Level 2 - Use deterministic distribution information: - use thickness

reduction shape from deterministic forming simulation and superpose coil

(cov=0.02) and forming process scatter (cov=0.01..0.03)

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DYNARDO • © Dynardo GmbH 2012

Did You Include All Important Scatter?

Scatter of sheet

thickness, forming

process scatter

covmax=0.05

yield strength, friction,

n,

test conditions

We could find and

explain the test results!

+

Introduction of spatial correlated

forming process scatter

- 100 LS-DYNA simulation

- Extraction via LS-PREPOST

SoS

- post prozessing

Statistics_on_Structure

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DYNARDO • © Dynardo GmbH 2012

Iterative Robust Design Optimization

Design optimization task

• 4 continuous, 2 binary design

variables

• Single objective formulations

(maximal removal power)

• 2 optimization restrictions

Robustness of performance should

be preserved

by courtesy of

Könning, M; Plotzitza, A.: Optimierung und Robustheitsbewertung mit optiSLang bei der

Robert Bosch GmbH, Proceeding Weimarer Optimierung- und Stochastiktage 1.0, 2004,

www.dynardo.de

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DYNARDO • © Dynardo GmbH 2012

Iterative Robust Design Optimization

• With help of the sensitivity analysis,

the optimization task was

formulated.

• With help of genetic algorithms, the

optimization was performed.

• With robustness evaluation,

robustness and reliability were

checked.

• The performance was increased by

25 %!

• The results of the digital product

development were proven by

testing!

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DYNARDO • © Dynardo GmbH 2012

RDO Centrifugal Compressor

Parameterization

Parametric geometry definition using ANSYS BladeModeler

(17 geometric parameter)

Model completion and meshing using ANSYS Workbench

by courtesy of

64


DYNARDO • © Dynardo GmbH 2012

RDO Centrifugal Compressor

Fluid Structure Interaction (FSI) coupling

Parametric fluid simulation setup using ANSYS CFX

Parametric mechanical setup using ANSYS Workbench

by courtesy of

65


DYNARDO • © Dynardo GmbH 2012

RDO Centrifugal Compressor

Optimization goal: increase efficiency

Constraints: 2 pressure ratio’s, 66 frequency constraints, Robustness

Initial SA ARSM I EA I ARSM II ARSM III

Total Pressure Ratio 1.3456 1.3497 1.3479 1.3485 1.356 1.351

Efficiency [%] 86.72 89.15 90.62 90.67 90.76 90.73

#Designs - 100 105 84 62 40

by courtesy of

Input Parameter 21

Output Parameter 43

Constraints 68

Tolerance

limit

1.34


DYNARDO • © Dynardo GmbH 2012

RDO Centrifugal Compressor

Robust Design Optimization with respect to 21 design parameters and 20

random geometry parameters, including manufacturing tolerances. Robust

Design was reached after 400+250=650 design evaluations consuming.

Robustness evaluation

Sensi + first optimization step

by courtesy of

RDO optimization

Robustness proof using Reliability

Analysis

67


Robust Design Optimization of a rubber seal

Parametric model and Sensitivity Study

• Customer investigated Seal optimization using only 2 parameter

• Using DesignModeler parametric was rebuild with 11 parameter

Initial design

Sensitivity study

• Using optiSLang sensitivity approach 7 effective optimization

parameter are identified

68


Robust Design Optimization of a rubber seal

Deterministic optimization

Using optiSLang ARSM algorithm

design was optimized to have minimal

volume and sufficient pressure at all

contact points.

Initial design

Including Uncertainty of loading and

material 6 Sigma quality was violated.

Therefore iterative RDO increasing safety

margins of contact forces was performed

to reach 3 Sigma design level.

Optimal design

69


Robust Design Optimization of a rubber seal

Iterative Robust Design Optimization

• Required sigma level = 3 sigma

• 4 iterations of sequential optimization and robustness analysis

• Deterministic optimum (140 design evaluations): 14% failure

Robust optimum (540 design evaluations): 0.3% failure

• Young’s modulus is most important scattering variable

70


Robust Design Optimization of a rubber seal

Iterative RDO – Reliability proof

• 7 geometry + 2 material =9 important parameters detected

from robustness analysis

Directional Sampling on ARSM

• FORM failed

• ARSM: 116 design evaluations

• Failure probability

= 0.07%, 3.2 sigma

71


RDO on global response surface

• Approximation of model responses in

mixed optimization/stochastic space

• Simultaneous RDO is performed on

a global response surface

• Applicable to variance-, reliabilityand

Taguchi-based RDO

• Approximation quality significantly

influences RDO results

� Final robustness/reliability proof

is required

• Pure stochastic variables have small

influence compared to design variables

� Important local effects in the stochastic

space may be not represented

72


Robust Design Optimization of a rubber seal

RDO on global response surface

• Optimization variables are varied in optimization space

• Pure stochastic variables are varied +/- 4 sigma

• 200 LHS samples generated with uniform distribution

• Approximation quality between 93% and 97%

• Young’s modulus is in RDO space

minor important but in robustness

space most important

� Pure stochastic variables

are unimportant

� Poor local approximation quality

for robustness analysis

73


Robust Design Optimization of a rubber seal

RDO on global response surface

• Evolutionary algorithm (444 designs) + 50 Robustness samples for

each optimization design

• Mean values and standard deviation of contact pressures as

robustness measures

• RDO-Optimization with constraints for all contacts: 3.5 sigma

74


Robust Design Optimization of a rubber seal

RDO on global response surface – Robustness proof

Small approximation error Large approximation error

Failure probability:

• Upper left contact pressure 2.2% (2.0 sigma)

• Lower left contact pressure 1.4% (2.2 Sigma)

� Optimal design is not robust!

75


DYNARDO • © Dynardo GmbH 2012

Iterative RDO Application Connector

Goal: high safety level of connector

by courtesy of

10 contact forces have to be checked,

failure may happen if N< 1 N

The failure probability of single contact should

be lower than 10%

The failure probability of 5 contacts should be

less than 1 out 4.300.000. (6 Sigma

Design)

� Status quo: pre optimized design

using ANSYS DX and 5 optimization

parameter

Question:

how optimal and robust is the design

Solver: ANSYS Workbench

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DYNARDO • © Dynardo GmbH 2012

Step 1 - Sensitivity analysis

The Sensitivity Analysis id done in the design

space of 31 potential CAD (ProE) design

parameters

by courtesy of

Identification of n=15

most important

design parameters

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DYNARDO • © Dynardo GmbH 2012

Step 2 - Robustness analysis

The failure probability of

single contact failure

is checked with

Robustness

evaluation.

The Robustness Analysis

is done in the

Robustness space of

36 CAD tolerances

• Global variancebased

robustness

analysis using

Advanced Latin

hypercube sampling

with 90 design

evaluations

by courtesy of

Performance

critical contact

force F3o_v

With failure

probability of

89 %!

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DYNARDO • © Dynardo GmbH 2012

Step 3 - Optimization

• n=15 most important CAD design

parameters

• Objective: minimal failure distance

of every contact

by courtesy of

Step 1: ARSM

- Stagnation after 5 Iterations (126

Design evaluations), contact force

F3o_v still violating criteria

Step 2: introducing of additions constraints

Restart of Evolutionary Optimization using

best Design_ARSM, stop after 390

Design evaluations with feasible

design, but now other contact forces

become critical

Step 3: modifying the design space range

and introducing additional constraints

Restart using ARSM with best Design_EA,

stop after 172 Design evaluations

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DYNARDO • © Dynardo GmbH 2012

Step 4 Robustness Analysis • 36 scattering CAD tolerances

by courtesy of

• Global variance-based robustness

analysis using Advanced Latin

hypercube sampling with N=50 design

Failure probabilities of two forces higher

than 1%

Performance critical contact force F3o_v

with failure probability 9 %!

Contact force F2o_h with failure

probability 1 %!

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DYNARDO • © Dynardo GmbH 2012

Step 5 - Reliability analysis

Identification of n=12 most important random parameters using coefficients of

importance

Defining the limit state condition for violation more than 50% of the contact

forces are lesser than 1N

by courtesy of

Reliability analysis using ARSM with

N=137 D-optimal design of

experiment

Adaptive sampling on the MLS

surrogate model without samples

in the unsafe domain

Probability of failure is near zero,

assumption: normal distributed

random parameters

Optimized design is an Six Sigma

Design

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DYNARDO • © Dynardo GmbH 2012

Results

� Variance and probability-based robust design optimization with 31

optimization parameters and 36 scattering parameters

� Increasing the performance critical contact force F3o_v according

failure probability 89% -> 9%

� Failure probabilities of the other contact forces lesser than 1%

� System failure probability (more than 50% of the contact forces are

lesser than 1) is near zero! (Six Sigma Design)

� N=950 parallel finite element calculations

� Total calculation time 1 week

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Robustness Analysis drop test of mobile phone

A robustness evaluation is a so called global variance-based stochastic

analysis which addresses the question how much the response values

scatter under the consideration of input parameter scatter.

• 209 scattering variables (drop position, material (E,

ro, yield), geometry (thickness, radius), environment

(friction)

• 150 Latin Hypercube Samples

Statistical Post Processing include:

• The variation of the responses

• Coefficient of Determination/Importance, checking

linear and non-linear correlation

• Coefficient of Prognosis

• Statistics on Structure for critical part

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Process automation – drop test

Run the robustness

analysis in optiSLang.

209 scattering inputs

by courtesy of

Run ABAQUS which creates *.csv

files containing the results.

150 designs

Run the robusteval script

after the robustness analysis

is finished. All the designs

will be processed and *.rpt

files are created.

Post processing in

optiSLang.

- 36 responses

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DYNARDO • © Dynardo GmbH 2012

Post Processing Robustness - drop test

CoD lin

adj

CoD quad

adj

CoD lin

Adj

Spearman

• The Histogram shows a variation between 45.35

and 121.1

• Probability of violating the limit is 9.33 %

(1-0.9067=0.0933)

CoP

48 48 46 66

• Maximum Cop is 66 %, Inputs ANGLE_Y and

ANLGE_X have the most significant influence

by courtesy of

• Reference

• Maximum

85


DYNARDO • © Dynardo GmbH 2012

Statistics on Structure (SoS)

• Based on Robustness analysis results (optiSLang)

• Visualization of statistics (Maxima, Minima, Mean value, Coefficient of

variation, …) to locate „hot spots“ of variation at the FE Structure

• Benefits:

• Visualization of Min/Max and scatter range on FE Structure

• Visualization of spatial Distribution of Variation and Correlation on FE-

Structure

• Selecting and visualizing important regions and their correlations

We have to select one time

frame for every design

by courtesy of

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DYNARDO • © Dynardo GmbH 2012

Combining SoS and optiSLang

• The picture above shows the maximum of S11 (positive - tension)

• In SoS it is possible to select elements at hot spots and generate optiSLang

*.bin file (see black circles)

• Use the result_monotoring in optiSLang to identify local variation and

correlation, The CoP plots below show that ANGLE_X and ANGLE_Y have

strongest strong influence nfluence on S11 2to:Histogram for the to selected check elements

variation

Structure in

ABAQUS viewer

Element El sets – all glass element sets

by courtesy of

87


DYNARDO • © Dynardo GmbH 2012

Part 8

Costumers

88


DYNARDO • © Dynardo GmbH 2012

Our Costumers agree

89


DYNARDO • © Dynardo GmbH 2012

What‘s the Difference to Others?

Methodology

• Sensitivity analysis and optimization for large (number of variables)

non-linear problems

• COP/MOP to minimize the number of solver calls

• Optimization with robust defaults (ARSM, EA,GA,PARETO)

• Complete methodology suite to run robustness evaluation, reliability

analysis and robust design optimization

Key applications

• Optimization with large number of parameter (>10) having non

linear effects, noise, design failure

• Model update and parameter identification using sensitivity study

and optimization

• oS (+SOS) have completed the functionality for robustness

evaluation and reliability analysis and robust design optimization to

be used in production

We do not just offer a tool, we deliver a process.

We are the ones who implemented robustness evaluation at

different industries.

90


WOSD 2012 • © Dynardo GmbH 2012

optiSLang goes International

DYNARDO, CADFEM (Germany, Austria, Swiss)

SVSFEM (Czech Republic, Slovakia, Hungary)

Pera Global (China, Shanghai)

CADFEM India (India, Hyderabad)

CAE Technology Inc. (Korea, Seoul)

TaeSung S&E Inc. (Korea, Seoul)

CADFEM CIS (Russia, Moscow)

CADFEM US (USA)

Tecosim Japan (Japan, Saitama)

Introduction Weimar Optimization and Stochastic days 2012

91

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