The Development of Neural Network Based System Identification ...

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150 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION 1.2 1.1 1 0.9 0.8 R 2 0.7 0.6 MLP (8-4-2) HMLP (6-3-2) Elman (4-4-2) 0.5 0.4 0.3 0.2 1 10 100 1000 10000 Number of data Figure 5.20 The on-line prediction performance comparison for the MLP, HMLP and modified Elman networks. All of these networks are trained by rGN method with optimum model structure identified from off-line model identification. shows that R 2 values converge to unity over certain sample range. By taking R 2 test value about 0.9, the result shows that the MLP, HMLP and modified Elman networks start to produced good prediction after 155, 92 and 68 test data respectively. All three NN network structures are able to produce good on-line prediction of helicopter attitude dynamics. Nevertheless, the HMLP and modified Elman provide slight improvements to the network’s learning rate due to their smaller network structures. 5.8 SUMMARY In this chapter, the off-line and on-line based system identification methods proposed in Chapter 4 were implemented to identify the attitude dynamics of the helicopter UAS. Three types of NN architectures were used to model the attitude dynamics of the helicopter; namely the MLP, HMLP and modified Elman networks. NN based modelling technique has a tendency to over-fit the training data since the NN model is consists of large amount of free parameters (network weights) to be determined. The over-fitting problem of NN modelling can be avoided by employing
5.8 SUMMARY 151 methods such as weight pruning or introducing regularisation term into the LM training algorithm. For system identification using the off-line LM training, results show training with regularisation term introduces a smoothing effect on the error criterion V N (θ, Z N ) in such a way that weights that have less important influence on error are forced to decay towards zero [Samarasinghe, 2007]. In this process, only the important weights that minimise the error are allowed to grow and stabilise at their optimum values. The implementation of regularisation term during NN training prevents the trained NN model from over-fitting that would occur when the NN model is presented with a new test data set. In order to get a better prediction performance from the NN model, the model structure of the NN model can be further improved through proper network structure selection. To select the NN model structure, the Lipschitz coefficient calculation and k-cross-validation test methods were proposed, and they were used to identify the optimal or near optimal model structure of the NN model without attempting the tedious trial and error approach. The validation result shows that the model structure of the MLP architecture can be identified correctly with 3 past outputs and 1 past input using the proposed methods. Further comparison with model structure selection from previous studies such as in Samal [2009] and Putro et al. [2009] show that the identified model structure using k-cross validation offers an improvement in terms of generalisation error. Similarly, the minimum number of neurons to be included in the NN model can also be selected using the proposed validation methods. The HMLP and modified Elman networks were proposed in this work to provide us with simpler representation of UAS dynamics and reduction in total number of weight connections used in the NN model. Furthermore, the reduction in the total number of weights in the network can significantly reduce the computation time needed to train the NN model. Similar methodologies to select the optimal structure in the MLP network was used to identify the network structure for both HMLP and modified Elman networks. Based on validation test results, the model structures of the HMLP and modified Elman networks are found to be much smaller than the standard MLP network. Although the total number of weights for the HMLP and modified Elman
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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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4.3 SYSTEM IDENTIFICATION WITH NEUR
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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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