The Development of Neural Network Based System Identification ...

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138 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION Table 5.6 The average RMSE for various noise levels applied to optimum weights of HMLP network (3 hidden neurons with 2 past outputs and 1 past input). Standard Deviation of Noise 0.01 0.1 0.3 0.5 0.7 0.9 Validation Error Statistics System Responses RMSE RMSE (%) R2 NMCIW (%) p 0.0483 11.4856 0.9867 0.1480 q 0.0120 3.7572 0.9984 0.2686 p 0.0469 11.1659 0.9873 1.6318 q 0.0125 3.9098 0.9982 2.6325 p 0.0563 13.3997 0.9819 4.7596 q 0.0576 17.9818 0.9629 8.6277 p 0.0475 11.2901 0.9871 8.3209 q 0.0478 14.9172 0.9744 14.7704 p 0.0596 14.1749 0.9797 11.2747 q 0.0674 21.0122 0.9493 18.3889 p 0.2141 50.9196 0.7379 15.1188 q 0.1942 60.5657 0.5786 23.9983 5.4 OFF-LINE BASED SYSTEM IDENTIFICATION FOR ELMAN NETWORK The system identification results for the modified Elman network are presented in this section. Similarly to the previous section, the modified Elman network architecture is used to identify the UAS helicopter attitude dynamics using off-line Levenberg- Marquardt training. Since the Elman network only uses the current measurement data to feed into the network, it is not necessary for us to predetermine the appropriate regression vector (network structure) before the NN training. Instead, the strength of self connection α in the network and the effect of hidden neuron sizes are the main factors to consider for ensuring a good generalisation performance. This could be done through the usage of k-fold cross validation technique for hidden neuron sizes selection. For selection of self connection α strength, a simple trial error approach was employed to determine the best gain for network’s memory capacity. To avoid over-fitting during training phase, the adaptability of the NN model while training is reduced with similar regularisation method as in the MLP and HMLP network. The effect of self connection α strength effect on the validation RMSE is shown in Figure 5.14. The simulations were conducted with varying strength of self connection α
5.4 OFF-LINE BASED SYSTEM IDENTIFICATION FOR ELMAN NETWORK 139 10 3 Self Connection Strengh, α 10 2 RMSE (%) 10 1 10 0 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Figure 5.14 The self connection α strength selection results using modified Elman network with reduced connection. The Elman network training are repeated 10 times and validated on a test set. The training is carried out using 6 hidden neurons. from 0 to 1 to investigate the prediction performance of basic Elman network (α = 0) and modified Elman network. Finding from the plot shows that the self connection values between 0.3 to 0.5 produced satisfactory prediction performance before RMSE values increase beyond α = 0.6. The lowest RMSE value is found at α = 0.5 with 14.24 ± 1.26% and this is used throughout the analysis. The result of neurons size selection is reproduced here for the modified Elman network using the k-fold cross validation method. The result of the hidden neurons selection for 1 past output and 1 past input (4 regressors) network structure is given in Figure 5.15. From the plot, the network structure with 1 past input and 1 past output measurement produces an acceptable RMSE percentage between hidden neuron sizes h = 4 → 10, thus it is logical to select the optimum neuron size at h = 4. Finally, we arrive at the following network specifications (Table 5.7) that adequately represent the attitude dynamics of a model scaled helicopter. Note that the total number of weights in the optimum Elman network is lesser than the optimum MLP and HMLP network. The corresponding one-step ahead prediction of the angular rate responses that are
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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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2.5 SUMMARY 53 design based on the
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56 CHAPTER 3 AERIAL PLATFORM AND CU
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Chapter 4 NEURAL NETWORK BASED SYST
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4.2 THE ARTIFICIAL NEURAL NETWORKS
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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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