The Development of Neural Network Based System Identification ...

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132 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION using the upper and lower confidence intervals (CI) limit of the optimal weights. The measure of upper U i and lower L i limit width of the network output is given by taking the average of interval range over the measurement sample [Khosravi et al., 2011]. This is also known as Normalised Mean CI width (NMCIW) and can be used to show the variation of the targets. The measure formulation is given as follows: NMCIW = 1 N ∑NR (U i − L i ) (5.1) i=1 The average range of the upper and lower output performance (NMCIW) for each noise level cases are given in Table 5.3. As can be seen from the result, the weights set added random noise with s = 0.2 provide a wide range of confidence interval (28.3546%) compared with the range of the measurement between −1 rad/s to 1 rad/s. This indicates that the prediction is imprecise and unreliable to produce predictions that represent the real target values. In this study, a 20% threshold value is used to determine whether the CI is too wide or not. Table 5.3 The average RMSE for various noise levels applied to optimum weights of MLP network (4 hidden neurons with 3 past outputs and 1 past input). Standard Deviation of Noise 0.01 0.05 0.1 0.2 Test Error Statistics System Responses RMSE RMSE (%) R2 NMCIW (%) p 0.0375 8.9256 0.9919 0.4232 q 0.0082 2.5568 0.9992 1.4598 p 0.0391 9.3019 0.9913 2.0441 q 0.0134 4.1912 0.9980 7.2532 p 0.0683 16.2613 0.9733 4.4477 q 0.0365 11.3787 0.9851 14.7242 p 0.1779 42.3673 0.8185 8.8449 q 0.0677 21.1145 0.9488 28.3546
5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP NETWORK 133 5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP NETWORK In this section, the results of the model structure and hidden neurons size selection of HMLP network are presented. The identification of UAS helicopter attitude dynamics was carried out using the off-line Levenberg-Marquardt training as in Section 4.3.4. The flight data sets was obtained by performing different flight manoeuvres to excite the dynamic of interest. Using the collected data, the suitable regression vector (network structure) and hidden neurons size were determined using the k-fold cross validation technique as previously discussed. The method for minimising the over-fitting effect in the HMLP network training is similar to regularisation method used in MLP network. The results of cross validation for HMLP network with different network structures (input nodes) are given in Figure 5.10. Six different network structures were tested and compared with each other. The plot indicates that the simple HMLP network structure with 1 past output and 1 past input (4 regressors) gives the highest percentage of RMSE, which is similar to cross validation trend in MLP, and it is not fit for predicting the non-linear dynamics of the helicopter UAS. As the number of regressors or inputs to the network increases, the RMSE value decreases and stabilises after 2 past outputs and 1 input (6 regressors) structure. Hence, the neural network model structure can be selected as a total of 6 regressors with 2 past output and 1 past input observation. This cross validation procedure was repeated for different hidden neuron sizes and an overall RMSE trend points out to the same sharp breakpoint at 2 past outputs and 1 input (6 regressors) network structure. The result of neurons size selection is reproduced here for the HMLP network using the k-fold cross validation method. The result of the hidden neurons selection for 2 past outputs and 1 past input (6 regressors) network structure is given in Figure 5.11. From the plot, the network structure with 2 past outputs and 1 past input (regression vector with dimension size of 6) yield the lowest RMSE value (9.82 %) for neurons size, h = 3. Finally, we arrive at the following network specifications (Table 5.4) that adequately represent the attitude dynamics of a model scaled helicopter. By examining the RMSE
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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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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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