The Development of Neural Network Based System Identification ...

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88 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION ŷ1 yˆn Output Layer 1 Hidden Layer Bias Input 1 h x 1 1 Bias Input Context Units x k Input Layer X1 (a) Xm ŷ1 yˆn Output Layer Self Connection 1 Hidden Layer Bias Input 1 h x 1 Context Units Input Layer 1 Bias Input x k X1 Xm (b) ŷ1 yˆn Output Layer Self Connection 1 Hidden Layer Bias Input 1 h x 1 Context Units Input Layer 1 Bias Input x k X1 (c) Xm Figure 4.6 The structure and operation of Elman network. (a) The basic Elman Network (b) The modified version of Elman network with self-connections in the context units; and (c) The modified version of Elman network with reduced weight connections.
4.2 THE ARTIFICIAL NEURAL NETWORKS 89 connections from context units to hidden units. Figure 4.6(c) shows the architecture of the modified Elman network with reduced weight connections. Note that the connections from context units to hidden units are made with one to one connections instead of multiple connections from a single context unit to multiple hidden units as in Figure 4.6(b). For a single hidden layer case, the outputs formulation from hidden, context unit and output layer of a modified Elman network are given as follows: v h (t) = g h ⎛ ⎝ m∑ W 1 hj X j (t) + B1 h + j=1 ⎞ h∑ W 3 k x k (t) ⎠ for h = 1, 2, 3 · · · H (4.8) k=1 x k (t) = v h (t − 1) + αx k (t − 1) for k = 1, 2, 3 · · · H (4.9) ( H ) ∑ ŷ i (t) = g i W 2 ih v h (t) + B2 i for i = 1, 2, 3 · · · n (4.10) h=1 Similar to MLP and HMLP network architecture, variables m, n and H denote the number of inputs, outputs and hidden nodes of the Elman network respectively, B1 h and B2 i is the bias elements of input and output layer and X j (t) denotes the inputs data fed into the Elman network. The function g h and g i are the activation functions used in the hidden and output layer similar to MLP architecture. The weight connections that connects the input layer to the hidden layer is given by matrix W 1 hj . Matrix W 2 ih indicates weight matrix that connect the hidden layer to the output layer. The weight connections from context units to hidden neurons are represented by vector W 3 k . The self-connections α in the context units are set to be the same for all context units and typically selected between 0 ≤ α ≤ 1. The higher the value of α indicates that network has the higher capability to trace the gradient further into the past [Pham and Liu, 1993].
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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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5.4 OFF-LINE BASED SYSTEM IDENTIFIC
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.7 MODEL PERFORMANCE COMPARISON US
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5.8 SUMMARY 151 methods such as wei
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5.8 SUMMARY 153 would enable the im
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156 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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