The Development of Neural Network Based System Identification ...

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130 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION (a) (b) Figure 5.9 The 5 steps ahead prediction of MLP network model for (a) Pitch dynamics; and (b) Roll dynamics. The solid blue line with ‘x’ marker is the measured output while the red dashed line indicates the prediction from neural network model. and measured output data. The plots of the k-steps predictions are given in 5.9(a) and 5.9(b). The corresponding error statistics of one step and k-step ahead predictions are given in Table 5.2 for each individual prediction variable. From the error statistics, we can conclude that the discrepancy between the k-step ahead prediction (k = 5) and the measured data is insignificant. Both figures show that the trained neural network model predictions are close to the measured values and that the neural network is properly trained to mimic the rigid body dynamics of the helicopter. The MLP based NN model produced different magnitude of weight values if the NN training was conducted several times using random initial weight values at the beginning of the training. This would result in many possible sets of weights that would
5.2 OFF-LINE BASED SYSTEM IDENTIFICATION FOR MLP NETWORK 131 Table 5.2 Summaries of System Identification Error Statistics for MLP network model. Test Error Statistics System Responses RMSE RMSE (%) R 2 One-Step Ahead Prediction p 0.0351 8.4011 0.9929 q 0.0081 2.7038 0.9993 5-Step Ahead Prediction p 0.0746 17.8684 0.9681 q 0.0232 7.7531 0.9940 achieve the desired prediction response. The optimal network structure determined from k-fold cross validation method would reduce the redundant weight, and pin-point the nearly optimal number of weights in the network. However, random noise in the training process could cause the weights to fluctuate according to Samarasinghe [2007]. It is important for us to prove that the network predictions are robust against the fluctuation of weights. The network prediction performance is analysed by adding the effect of random noises with increasing magnitude to the weights obtained from the optimal network structure. Table 5.3 shows the prediction results of optimal network structure for MLP network over test data set with addition of Gaussian distributed random noise to the optimal weights. The optimal weights are corrupted by random noise with zero mean and standard deviation s of 0.01, 0.05, 0.1 and 0.2. For each noise level, 300 sets of weights around the optimum weights are generated, which results in average RMSE and R 2 in Table 5.3. The average RMSE on the test data set for various noise levels indicates that an exceptional prediction performance is achieved up until s = 0.1 random noise added to the optimal weight. Using the 300 set of weights generated, the 95% confidence intervals can be constructed for the optimal weights using the standard statistical inference method ( ¯w ± t α,n−1 σ w / √ N). Parameter ¯w is the mean of a weight, σ w is the standard deviation of that weight and N is the number of samples in the test set. The t α,n−1 is the t value from t-distribution for (1 − α) confidence level with degree of freedom of N − 1. Hence, the upper and lower limit of the network output ŷ performance can be constructed
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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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180 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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