The Development of Neural Network Based System Identification ...

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90 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION 4.3 SYSTEM IDENTIFICATION WITH NEURAL NETWORK In this section, the neural network based system identification procedures and the description of learning algorithms used for NN trainings are presented. The overall neural network modelling approach used in this work consists of several steps including the test data gathering process, neural network model structure selection, model estimation and lastly the validation process as shown in Figure 4.7. The purpose of the test data gathering process is to collect a set of data from the system behaviour over the entire operating conditions which later will be used in processes to infer a dynamic model of the system. The type of excitation signal, data collection, sampling frequency and filtering option will be discussed further in Section 4.3.1. In the model structure selection process, the users need to decide the model structure to be used before the estimating process. In this work, we use the MLP network architecture based on ARX (Autoregressive structure with extra inputs) model structure for its simplicity and stable prediction [Norgaard, 2000]. For the model structure selection process, issues of selecting the proper lag space size and the minimum number of neurons to satisfy the average generalisation error is given in Section 4.3.2. The minimisation of error criterion is done using the Levenberg-Marquardt algorithm with added regularisation term to prevent an over-fitting problem. For the final process, the model estimate is validated against one-step ahead predictions, k-step ahead predictions, correlation between prediction errors and measured outputs and reliability visualisation of the predictions. 4.3.1 Collection of Flight Test Data The flight test was conducted on the UAV helicopter platform in calm weather conditions. Different flight manoeuvres were conducted to excite the desired dynamic of interest. For example, after the helicopter reached steady and level condition, the yaw dynamics was excited using only tail collective pitch command while other input commands were used to balance the helicopter in such a way to make the vehicle oscillate roughly around the operating point of interest.
4.3 SYSTEM IDENTIFICATION WITH NEURAL NETWORK 91 • Frequency swept excitation signals • DC and offset removal • Digital filter with 10Hz cut-off frequency • Sampling frequency = 50Hz • Multilayer Perceptron Network (MLP) based on ARX model • Choose lag space using Lipschitz coefficient • Determine number of neurons which guarantee minimum FPE error (generalization ability to new data) • Minimization of the criterion was done using the Levenberg- Marquardt (LM) optimization algorithm with regularization Test Data Gathering Process NN Model Structure Selection Model Estimation Validation Process • One-step ahead prediction • k-step ahead prediction • k-fold cross validation Accept for Use? No Figure 4.7 Overview of neural network based system identification procedure. Training and validation data were collected from specifically designed frequency swept excitation signal suggested in Tischler and Remple [2006], Wang et al. [2011]. This type of signal is commonly used to collect experimental flight data in aircraft and rotorcraft system identification. The frequency swept excitation signal is not required to have constant amplitude. It is recommended that the pilot executes two good low frequency cycle inputs (20 s) and then gradually increase the swept frequency to mid and higher frequencies before ending the manoeuvre in the trim position. Starting and ending the record in aircraft trim state enables concatenating flight data collected from several test runs while at the same time ensuring rich signal content. All measurements of the helicopter’s state variables were collected using an inertial measurement unit (IMU) where the data that were recorded during the test were Euler angles: roll φ, pitch θ and yaw Ψ; angular rates in body coordinate frame: roll rate, p, pitch rate, q and yaw rate, r and body accelerations: A x , A y , A z . The control inputs measured during the experiment were the stick deflection from the pilot’s collective pitch δ col , tail pedal δ ped , longitudinal cyclic δ lon and lateral cyclic δ lat . The four servomotor
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The Development of Neural Network B
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ABSTRACT This thesis presents the d
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vii the MLP network, the prediction
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PUBLICATIONS The following is a lis
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xiv TABLE OF CONTENTS CHAPTER 4 CHA
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LIST OF FIGURES 1.1 Examples of typ
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LIST OF FIGURES xix 3.13 Overview o
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LIST OF FIGURES xxi 5.2 The predict
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LIST OF FIGURES xxiii 5.13 The pred
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LIST OF FIGURES xxv 7.1 The locatio
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LIST OF TABLES 3.1 The specificatio
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NOMENCLATURE AFCS Automatic Flight
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LIST OF TABLES xxxi NNARX QP RBF RC
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2 CHAPTER 1 INTRODUCTION Surveillan
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4 CHAPTER 1 INTRODUCTION is then de
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6 CHAPTER 1 INTRODUCTION the dynami
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8 CHAPTER 1 INTRODUCTION models [Sa
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10 CHAPTER 1 INTRODUCTION improved
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12 CHAPTER 1 INTRODUCTION Chapter 3
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Chapter 2 LITERATURE REVIEW The pur
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2.1 INTRODUCTION 17 • Inefficient
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2.1 INTRODUCTION 19 Figure 2.2 The
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2.2 HELICOPTER DYNAMICS MODELLING A
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2.3 NEURAL NETWORK BASED SYSTEM IDE
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2.4 AUTOMATIC FLIGHT CONTROL SYSTEM
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5.4 OFF-LINE BASED SYSTEM IDENTIFIC
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5.4 OFF-LINE BASED SYSTEM IDENTIFIC
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.7 MODEL PERFORMANCE COMPARISON US
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5.8 SUMMARY 151 methods such as wei
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5.8 SUMMARY 153 would enable the im
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156 CHAPTER 6 NEURAL NETWORK BASED
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Chapter 7 FLIGHT CONTROL SYSTEM DES
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7.2 FLIGHT TESTS IMPLEMENTATION 185
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7.3 EXPERIMENTAL RESULTS 187 1 0.8
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7.3 EXPERIMENTAL RESULTS 189 Longit
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7.3 EXPERIMENTAL RESULTS 191 Pitch
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7.3 EXPERIMENTAL RESULTS 193 Flight
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7.3 EXPERIMENTAL RESULTS 195 140 Ya
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7.3 EXPERIMENTAL RESULTS 197 indica
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7.3 EXPERIMENTAL RESULTS 199 20 100
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7.3 EXPERIMENTAL RESULTS 201 Yaw Ra
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7.3 EXPERIMENTAL RESULTS 203 mainta
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7.3 EXPERIMENTAL RESULTS 205 Yaw Ra
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7.4 SUMMARY 207 data measured from
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210 CHAPTER 8 CONCLUSIONS AND FUTUR
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212 CHAPTER 8 CONCLUSIONS AND FUTUR
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214 REFERENCES B. W. Bequette. Non-
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216 REFERENCES Konstantinos Dalamag
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218 REFERENCES Wayne Johnson. Helic
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220 REFERENCES B. Mettler, Mark B.
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222 REFERENCES V. R. Puttige and S.
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224 REFERENCES D.H. Shim. Hierarchi
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226 REFERENCES Nikos Vitzilaios and
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