Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach

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Springer Science & Business Media, Nov 18, 2004 - Technology & Engineering - 199 pages

This monograph systematically presents the existing identification methods of nonlinear systems using the block-oriented approach It surveys various known approaches to the identification of Wiener and Hammerstein systems which are applicable to both neural network and polynomial models. The book gives a comparative study of their gradient approximation accuracy, computational complexity, and convergence rates and furthermore presents some new and original methods concerning the model parameter adjusting with gradient-based techniques. "Identification of Nonlinear Systems Using Neural Networks and Polynomal Models" is useful for researchers, engineers and graduate students in nonlinear systems and neural network theory.

 

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Contents

Introduction
1
11 Models of dynamic systems
5
112 Nonlinear models
8
113 Seriesparallel and parallel models
10
115 Nonlinear models composed of submodels
11
116 Statespace Wiener models
15
12 Multilayer perceptron
16
122 Learning algorithms
17
3411 Computational complexity
97
36 Combined steepest descent and least squares learning algorithms
104
37 Summary
106
38 Appendix 31 Gradient derivation of truncated BPTT SISO Hammerstein models
108
39 Appendix 32 Gradient derivation of truncated BPTT MIMO Hammerstein models
109
310 Appendix 33 Proof of Theorem 31
111
311 Appendix 34 Proof of Theorem 32
113
312 Appendix 35 Proof of Theorem 33
114

123 Optimizing the model architecture
18
13 Identification of Wiener systems
19
14 Identification of Hammerstein systems
25
15 Summary
30
Neural network Wiener models
31
22 Problem formulation
32
23 Seriesparallel and parallel neural network Wiener models
34
232 MIMO Wiener models
37
24 Gradient calculation
40
242 Parallel SISO model Backpropagation method
42
244 Parallel SISO model Backpropagation through time method
43
245 Seriesparallel MIMO model Backpropagation method
46
246 Parallel MIMO model Backpropagation method
48
248 Parallel MIMO model Backpropagation through time method
49
2410 Gradient calculation in the sequential mode
51
2411 Computational complexity
52
25 Simulation example
53
26 Twotank system example
61
27 Prediction error method
65
272 Pneumatic valve simulation example
66
28 Summary
69
29 Appendix 21 Gradient derivation of truncated BPTT SISO Wiener models
71
210 Appendix 22 Gradient derivation of truncated BPTT MIMO Wiener models
72
211 Appendix 23 Proof of Theorem 21
73
212 Appendix 24 Proof of Theorem 22
74
Neural network Hammerstein models
77
32 Problem formulation
78
33 Seriesparallel and parallel neural network Hammerstein models
79
332 MIMO Hammerstein models
82
34 Gradient calculation
84
342 Parallel SISO model Backpropagation method
85
344 Parallel SISO model Backpropagation through time method
87
346 Parallel MIMO model Backpropagation method
90
348 Parallel MIMO model Backpropagation through time method
91
349 Accuracy of gradient calculation with truncated BPTT
92
3410 Gradient calculation in the sequential mode
96
313 Appendix 36 Proof of Theorem 34
115
Polynomial Wiener models
117
41 Least squares approach to the identification of Wiener systems
118
411 Identification error
119
412 Nonlinear characteristic with the linear term
121
413 Nonlinear characteristic without the linear term
122
414 Asymptotic bias error of the LS estimator
123
415 Instrumental variables method
125
416 Simulation example Nonlinear characteristic with the linear term
126
417 Simulation example Nonlinear characteristic without the linear term
128
42 Identification of Wiener systems with the prediction error method
130
422 Recursive prediction error method
132
424 Pneumatic valve simulation example
133
43 Pseudolinear regression method
137
432 Pseudolinear regression identification method
138
44 Summary
141
Polynomial Hammerstein models
143
52 Iterative least squares identification of Hammerstein systems
145
53 Identification of Hammerstein systems in the presence of correlated noise
147
54 Identification of Hammerstein systems with the Laguerre function expansion
149
55 Prediction error method
151
56 Identification of MISO systems with the pseudolinear regression method
153
57 Identification of systems with twosegment nonlinearities
155
58 Summary
157
Applications
159
62 Fault detection and isolation with Wiener and Hammerstein models
166
621 Definitions of residuals
167
622 Hammerstein system Parameter estimation of the residual equation
171
623 Wiener system Parameter estimation of the residual equation
175
63 Sugar evaporator Identification of the nominal model of steam pressure dynamics
180
632 Experimental models of steam pressure dynamics
181
633 Estimation results
182
64 Summary
185
References
187
Index
195
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Page 187 - Identification of a Class of Non-linear Systems Using Correlation Analysis,
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