The Development of Neural Network Based System Identification ...

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136 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION Roll Rate, p (rad/s) 1 0.5 0 −0.5 Data HMLP NNID −1 0 100 200 300 400 500 600 time (samples) 700 800 900 1000 (a) Prediction Error 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 100 200 300 400 500 600 700 800 900 1000 time (samples) (b) Figure 5.12 The prediction from the HMLP network for roll dynamics. (a) The one-step ahead prediction overlaid with the measured helicopter responses. (b) The error plot between one-step ahead prediction and the measurement data. The red dashed line indicates estimation from the HMLP neural network model while solid blue line with ‘x’ marker represents the output measurement. 1 Pitch Rate, q (rad/s) 0.5 0 −0.5 data HMLP NNID −1 0 100 200 300 400 500 600 700 800 900 1000 time (samples) (a) 0.1 Prediction Error 0.05 0 −0.05 −0.1 0 100 200 300 400 500 600 700 800 900 1000 time (samples) (b) Figure 5.13 The prediction from HMLP network for pitch dynamics. (a) The one-step ahead prediction overlaid with the measured helicopter responses. (b) The error plot between one-step ahead prediction and the measurement data. The red dashed line indicates estimation from the HMLP neural network model while solid blue line with ‘x’ marker represents the output measurement.
5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP NETWORK 137 Table 5.5 Summaries of Error Statistics of HMLP Network Model Error Statistics System Responses RMSE RMSE (%) R 2 One-Step Ahead Prediction p 0.0360 12.0944 0.9852 q 0.0082 3.6340 0.9984 5-Step Ahead Prediction p 0.1199 28.7239 0.9175 q 0.0718 23.9955 0.9424 The robustness of the HMLP network’s model structure against perturbation of weights is given in Table 5.6. Table 5.6 shows the prediction results of optimal network structure for HMLP network with addition of Gaussian distributed random noise to the optimal weights. The optimal weights is corrupted by random noise with zero mean and standard deviation s of 0.01, 0.1, 0.3, 0.5, 0.7 and 0.9. For each noise levels, 300 sets of weights around the optimum weights are generated, which results in average RMSE and R 2 values shown in Table 5.6. The average RMSE on the test data set for various noise levels indicate that an exceptional prediction performance is achieved up until random noise with standard deviation s = 0.7 added to the optimal weights. Using the 300 set of weights generated, the 95% confidence intervals can be constructed for the optimal weights using the standard statistical inference method. The average range of the upper and lower output performance (NMCIW) for each noise level case is also given in Table 5.6. As can be seen from the result, the weights set added with s = 0.9 random noise provide a wide average confidence interval (23.9983%) compared with the range of measurement between −1 rad/s to 1 rad/s. This indicates the imprecise and high level of uncertainty to produce predictions that represent the real output values.
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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 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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