The Development of Neural Network Based System Identification ...

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148 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION essential since the control decisions need to be updated at the specific timing requirement (22 ms). There are two types of recursive algorithm methods that exist to approximate the non-linear dynamics in real-time; a) mini-batch methods [Samal, 2009, Puttige, 2009], and b) recursive prediction method as presented in previous Section 4.3.5. For mini-batch wise methods, off-line training such as LM algorithm was used to train the NN in real-time by choosing smaller data length to achieve faster convergence time. Typically, a fixed amount of input-output data is collected and stored in a queue. Table 5.11 shows the average training time for mini-batch LM and rGN training algorithms for attitude dynamics identification using the optimal MLP model structure (n y = 3, n u = 1 with 4 hidden neurons). The minimum criterion error (MSE) was selected at 0.001, 0.01 and 0.05 as stopping criteria for mini-batch LM training. The training time comparison test was conducted using a 400 MHz National Instrument’s real-time embedded controller. Result from the comparison test shows that mini-batch LM training produces faster training convergence with smaller batch sizes. However, mini-batch LM method requires high computation resources and would not finish within the targeted control sampling period (22 ms). Attempts to reduce the training time of the NN training through manipulation of target MSE values could improve the algorithm training performance, but at the expense of poor training error. A recursive training algorithm such as rGN usually demonstrates faster prediction updates and offers rapid computation of weight adaptation with average training time of 3.88 ms. The average training time for rGN algorithm is well below the control loop sampling period (22 ms) and this indicates that such recursive training algorithms are well suited for real-time applications.
5.7 MODEL PERFORMANCE COMPARISON USING RECURSIVE TRAINING 149 Table 5.11 Training time comparison between mini-batch LM method and rGN method. The values in bracket indicate the total training error (% RMSE). Target MSE mini batch LM 1 0.001 mini batch LM 2 0.01 mini batch LM 3 0.05 rGN Average Training Time (ms) Data Sample N=5 N=10 N=15 N=20 N=25 38.29 44.98 46.373 50.84 54.78 [5.02%] [6.61%] [7.13%] [7.53%] [7.89%] 24.48 25.11 24.89 26.38 27.53 [13.19] [15.72%] [16.87%] [18.00%] [18.47] 23.22 23.13 26.38 27.37 28.86 [22.07%] [24.16%] [26.83%] [28.16] [28.48] Data Sample N=1 3.88 [5.50%] 5.7 MODEL PERFORMANCE COMPARISON USING RECURSIVE TRAINING Prediction performance analysis of the MLP, HMLP and Modified Elman networks are repeated in this section using the recursive training algorithm (rGN) to identify whether the proposed network architectures (HMLP and modified Elman network) improve the prediction performance over the standard MLP network. The NN models are trained to predict the future response of helicopter attitude dynamics with 2 output variables. Since the network architectures of the MLP, HMLP and modified Elman networks are different from each other, the network models should be compared at their best model structure. The model specifications of MLP, HMLP and modified Elman network in Table 5.1, 5.4 and 5.7 are used to carry out the prediction performance comparison analysis in this section. The structure for the MLP network for this analysis is 8 input nodes, 4 hidden neurons (8-4-2) and for the HMLP network, 6 input nodes and 3 hidden neurons are used for prediction (6-3-2). The optimal model structure for the modified Elman network is set with 4 input nodes and 4 hidden neurons (4-4-2). The rGN design parameters are initialised as Q(0) = 25I, λ 0 = 0.99 and λ(0) = 0.997. Figure 5.20 shows the plot of R 2 values calculated for the MLP, HMLP and modified Elman networks using an independent data set (data length = 10000 samples). The results from the plot
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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 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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