The Development of Neural Network Based System Identification ...

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128 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION 10 2 Hidden Neurons Size RMSE (%) 10 1 10 0 1 2 3 4 5 6 7 8 9 10 Figure 5.6 The percentage of Root Mean Square Error (RMSE) comparison of MLP network trained with different hidden neuron sizes. The k-cross validation process was conducted for network structure with 8 regressors (n y = 3 and n u = 1). The neural network training was carried out using off-line Levenberg-Marquardt (LM) algorithm. An example of the one-step ahead prediction of the angular rate responses that are estimated from the off-line neural network system identification is shown in Figure 5.7 and Figure 5.8. The off-line LM training is carried out using the training data set from 16 s to 28 s recording, and the prediction performance is validated on roll rate and pitch rate data (test data set) from 36 s to 37 s. The network is trained using the nearly optimal structure from Table 5.1. These predicted responses from neural network identification (NNID) are overlaid with the measured helicopter responses. The results indicate that one-step ahead NNID predictions overlap the test data almost perfectly as indicated by the magnitude order of the prediction error plot. This usually happens when the sampling frequency of the data collected is high compared with the frequency of the dynamic system as suggested in Norgaard [2000]. The small prediction error from one-step ahead prediction does not necessarily indicate that the model is sufficient without further checks. The quality of the fitted model is further inspected by running k-step ahead prediction to check if there is a possibility of a significant discrepancy between prediction
5.2 OFF-LINE BASED SYSTEM IDENTIFICATION FOR MLP NETWORK 129 Figure 5.7 The prediction from MLP network model for roll dynamics. (a) The one-step ahead prediction and measurement data plot. (b) The error plot between one-step ahead prediction and the measurement data. The red dashed line indicates estimation from the neural network model while the solid blue line with ‘x’ marker represents the output measurement. Figure 5.8 The prediction from MLP network model for pitch dynamics. (a) The one-step ahead prediction and measurement data plot. (b) The error plot between one-step ahead prediction and the measurement data. The red dashed line indicates estimation from the neural network model while the solid blue line with ‘x’ marker represents the output measurement.
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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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178 CHAPTER 6 NEURAL NETWORK BASED
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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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