The Development of Neural Network Based System Identification ...

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142 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION 1 Pitch Rate, q (rad/s) 0.5 0 −0.5 data Elman NNID −1 0 100 200 300 400 500 600 700 800 900 1000 time (samples) (a) 0.05 Prediction Error 0 −0.05 0 100 200 300 400 500 600 700 800 900 1000 time (samples) (b) Figure 5.17 The prediction from the modified Elman network for pitch dynamics. (a) The one-step ahead prediction overlaid with the measured helicopter responses. (b) The error plot between one-step ahead prediction and the measurement data. The red dashed line indicates estimation from the modified Elman network while solid blue line with ‘x’ marker represents the output measurement. various noise levels indicate that an exceptional prediction performance is achieved up until random noise with s = 0.5 added to the optimal weights. Using the 300 set of weights generated, the 95% confidence intervals can be constructed for the optimal weights using the standard statistical inference method. The average range of the upper and lower output performance (NMCIW) for each noise level case is given in Table 5.9. As can be seen from the result, the weights set added with s = 0.7 random noise provides a wide average confidence interval (22.4513%) compare Table 5.8 The Summaries of Error Statistics for Modified Elman Network. Error Statistics System Responses RMSE RMSE (%) R 2 One-Step Ahead Prediction p 0.0604 14.3606 0.9792 q 0.0184 5.7498 0.9962 5-Step Ahead Prediction p 0.0967 23.0956 0.9467 q 0.0468 15.6510 0.9755
5.4 OFF-LINE BASED SYSTEM IDENTIFICATION FOR ELMAN NETWORK 143 to the range of measurement between −1 rad/s to 1 rad/s. This indicates the imprecise and high level of uncertainty to produce prediction that represent the real output values. Table 5.9 The average RMSE for various noise levels applied to optimum weights of the modified Elman network (4 hidden neurons). Standard Deviation of Noise 0.01 0.05 0.1 0.3 0.5 0.7 Test Error Statistics System Responses RMSE RMSE (%) R2 NMCIW (%) p 0.0658 15.6337 0.9753 0.0876 q 0.0174 5.4138 0.9966 0.2425 p 0.0666 15.8336 0.9747 0.5408 q 0.0163 5.0892 0.9970 1.1632 p 0.0661 15.7048 0.9751 0.8776 q 0.0188 5.8519 0.9961 2.5763 p 0.0703 16.7037 0.9718 2.7539 q 0.0699 21.8101 0.9453 6.8574 p 0.0713 16.9354 0.9710 5.9380 q 0.0745 23.2384 0.9379 13.1676 p 0.0985 23.4007 0.9447 12.6861 q 0.0459 14.3050 0.9765 22.4513
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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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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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