The Development of Neural Network Based System Identification ...

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34 CHAPTER 2 LITERATURE REVIEW Neural Network Model Target Output Training Data Prediction Compare Error Signal NN Weights Modification Learning/Training Algorithm Figure 2.6 The representation of neural network training process. The choice of training algorithm is an important factor to consider before the NN model is trained for prediction tasks. Empirical findings indicated that NN models trained with the back-propagation or steepest descent (SD) method were unable to generalise well with new observations and even failed to match the prediction quality of the first principle model. It is well known that steepest descent algorithm has several disadvantages compared with second order algorithms such as slow convergence rate; and the minimisation search can easily be trapped in local minima [Billings et al., 1991, Mashor, 2003, Wilamowski, 2011a]. Among all mentioned training methods, the LM optimisation algorithm is the most widely used training method for off-line NN training. The algorithm is capable of providing fast solution convergence, robust and simple to implement. The convergence of the LM algorithm is shown to be faster than other training methods [Samarasinghe, 2007, Garratt and Anavatti, 2012, Demuth and Beale, 2000]. However, the computation time of the LM algorithm increases as the size of the network grows. As the network becomes larger, the Jacobian and Hessian matrices that need to be calculated and stored in memory increase. Subsequently, this leads to increased computational time of the LM algorithm due to memory limitation [Wilamowski and Hao, 2010]. This prevents the LM algorithm from being implemented for large networks or modelling problems that involve an enormous size of training data.
2.3 NEURAL NETWORK BASED SYSTEM IDENTIFICATION 35 Well known global optimisers such as the differential evolution (DE) algorithm can also be used to train the NN model [Ilonen et al., 2003]. The DE approach has the main advantage over the gradient based method such that the convergence to a global minimum is expected. Ilonen et al. [2003] comprehensively studied the effectiveness of the DE algorithm to find the global optimum in the context of the NN training. In this study, the DE algorithm was analysed as a candidate global optimisation method for the feed-forward MLP networks. However, the authors suggested that the DE algorithm did not provide any distinct advantages over the gradient based method in terms of learning rate or solution quality. This conclusion was also supported in the work of Subudhi and Jena [2011, 2008]. Results obtained envisage that the proposed NN training using the DE alone does not provide improved prediction capability and convergence speed of the training compared with the standard LM training. However, the authors suggested that a combination of DE and LM training algorithms provides better prediction accuracy which can be seen in the example cases provided. It is noticed from the result that the convergence time for the proposed training method (DE+LM+NN) is still slower than the NN model trained with the standard LM algorithm. Subsequently, the conclusion can be drawn that the DE training is unattractive for the real-time system identification framework. Most NN based modelling techniques attempt to model the time varying dynamics of a UAS helicopter system using off-line modelling approach. The model which is generated and trained once from previously collected data is not able to represent the entire operating points of the flight envelope very well [Samal, 2009, Ljung and Soderstrom, 1983]. Several attempts such as Samal [2009], Samal et al. [2008, 2009] were made to update the NN prediction model during flight using mini-batch LM training (LM training with small number of data samples). However due to a limited amount of processing power available in the real-time processor, such methods can only be employed to relatively small networks and they are limited to model uncoupled helicopter dynamics. In order to accommodate the time-varying properties of helicopter dynamics which change frequently during flight, a recursive based learning algorithm is required to
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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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4.2 THE ARTIFICIAL NEURAL NETWORKS
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4.3 SYSTEM IDENTIFICATION WITH NEUR
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4.4 SUMMARY 117 Segment 1 Segment 2
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Chapter 5 NN BASED SYSTEM IDENTIFIC
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5.2 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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