The Development of Neural Network Based System Identification ...

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116 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION y t 1 y t 2 u t 1 u t 2 NN Prediction 1 y t u t ut 1 ŷ t NN Prediction t yˆ t 1 u t 1 u NN Prediction yt ˆ 1 yˆ t 1 u t 2 u t 1 yt ˆ 2 NN Prediction yt ˆ 3 Figure 4.14 [2009]. The k-step ahead predictions with three step ahead example. Adapted from Samal performance of different learning methods. The simplest method to conduct validation analysis is to use the hold-out method where the measurement data is divided into training and test sets with a user defined split ratio. Subsequently, the training set is used for model training and the test set data for error rate estimation of the trained model. However, the downside of this method is that the model evaluation can produces a high variance error. Depending on how the split ratio is defined, the prediction error evaluation may be inconsistent for different partitions of data that forms the training and test sets [Kohavi, 1995]. To overcome this problem and utilising the available overall data, the k-fold crossvalidation method was used to reduce the variance by averaging error over k data segments. In this method, the measurement data N is split into k approximately equal size data segments. Then, the training and validation are performed for k-iterations where within each iteration, a single portion of the data segment at a certain index location shown in Figure 4.15 will be used for validation after the training of the remaining k − 1 data segments are completed. For each validation, the prediction MSE is calculated for the specific segment. The MSEs from each validation segment are averaged and combined together at the end of the iteration process using percentage root mean square error (% RMSE) given by: % RMSE = [ N kM ∑ k i=1 ∑ M t=1 (ŷ i(t) − y i (t)) 2 ∑ N t=1 (y(t) − ȳ(t))2 ] 1/2 × 100 (4.62)
4.4 SUMMARY 117 Segment 1 Segment 2 Segment 3 Segment 4 Segment 5 k = 1 V T T T T k = 2 T V T T T k = 3 T T V T T k = 4 T T T V T k = 5 T T T T V T Training V Validation Figure 4.15 The procedure of k-fold cross-validation for k = 5. where ŷ i (t) denotes the predicted NN model output from a specific k-validation data segment, y i (t) indicates the k-validation data segment, M is the data size in each of the segment and ȳ(t) is the mean value of the measurement data. 4.4 SUMMARY This chapter outlines the basic ANN concepts and proposed various network architectures for the use in NN based system identification. The general guidelines for NN based system identification for modelling the dynamics of the helicopter UAS are presented. The flight data preparations for the off-line system identification are also discussed, followed by detailed explanation of implementation of off-line NN training using LM algorithm. In order to avoid over-fitting problem during training phase, regularisation method with weight decay is introduced to limit the flexibility of the network without relying on early stopping criterion. To overcome the disadvantages of off-line (batch LM) methods, the recursive Gauss-Newton algorithm is used to track the time varying dynamics of the helicopter UAS. The recursive model estimation is a system identification
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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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166 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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