The Development of Neural Network Based System Identification ...

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100 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION model estimation is a system identification technique that enables us to infer a model that adapts to time-varying dynamics based on real-time data coming from the system. In contrast to batch training methods, the recursive methods enforce update to NN parameter vector based only on a single data set at the current sample t. To achieve real-time implementation of neural network based system identification, the estimation of neural network’s parameter vector θ can be carried out using recursive algorithms as described in Billings et al. [1992], Norgaard [2000], Youmin and Li [1999], Ljung and Soderstrom [1983], Asirvadam [2008], Shamsudin and Chen [2012b]. Norgaard [2000] has suggested that the recursive identification algorithms have several advantages over the batch methods. The implementation of the method is simpler, less memory-consuming with faster convergence since the redundancy in data set is effectively utilised. Recursive algorithm can also be implemented similar to the off-line training, where the recursive training is repeated several time on the finite training set Z N collected in advance [Norgaard, 2000, Billings et al., 1991, 1992]. Figure 4.10 shows the difference between the batch algorithm, mini-batch algorithm, on-line recursive algorithm and repeated recursive algorithm. The parameter vector θ updating process usually starts with initial random weights and it is carried out forward to the next iteration as computation progresses. The implementation of batch and mini-batch algorithm is similar but differs in the number of data samples used for training. In the recursive algorithm methods, the parameter vector update is obtained in real-time as the measurement data become available from the instrumentation system. Figure 4.10(d) shows the implementation of recursive algorithm as an off-line method. The parameter vector θ is updated at each time sample t over a fixed length data sample. At the end of first iteration, the last parameter vector θ is used as the initial update to the second iteration step. This iteration process will stopped if the mean square criterion converges to pre-defined threshold as in batch training algorithm implementation.
4.3 SYSTEM IDENTIFICATION WITH NEURAL NETWORK 101 Sample No. Sample No. 0 0 Iteration No. i = 1 1 2 3 4 5 6 7 8 9 10 11 12 N f 1 i R I G f i i1 i 1 Iteration No. i = 1 1 2 3 4 5 N f 1 i R I G f i i1 i 1 i = 2 1 2 3 4 5 6 7 8 9 10 11 12 N f 1 i R I G f i i1 i 2 i = 2 1 2 3 4 5 N f 1 i R I G f i i1 i 2 i = 3 1 2 3 4 5 6 7 8 9 10 11 12 N f 1 i R I G f i i1 i i = 3 1 2 3 4 5 N f 1 i R I G f i i1 i i i i 1 2 3 4 5 6 7 8 9 10 11 12 N f 1 i R I G f i i1 i i 1 2 3 4 5 N f 1 i R I G f i i1 i (a) (b) Sample No. Recent Data In 1 2 3 N Older Data Out 0 K( t) e( ) i i 1 t K( t) e( ) i i 1 t K( t) e( ) i i 1 t K( t) e( ) i i 1 t i 1 2 (c) Sample No. 1 2 3 N Iteration No. i = 1 0 K( t) e( ) K( t) e( ) K( t) e( ) i i 1 t i i 1 t 1 2 i i 1 t Kt () e() i i 1 t i = 2 1 2 3 N K( t) e( ) K( t) e( ) K( t) e( ) i i 1 t i i 1 t i i 1 t K( t) e( ) i i 1 t 1 2 i 1 2 3 N K( t) e( ) K( t) e( ) K( t) e( ) i i 1 t i i 1 t i i 1 t K( t) e( ) i i 1 t i 1 2 (d) Figure 4.10 The different types of Neural Network model estimation methods: (a) Batch Algorithm; (b) Mini-batch Algorithm; (c) Recursive Algorithm; and (d) Repeated Recursive Algorithm
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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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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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