## Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented ApproachThis 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 |

187 | |

195 | |

### Other editions - View all

Identification of Nonlinear Systems Using Neural Networks and Polynomial ... Andrzej Janczak No preview available - 2009 |

Identification of Nonlinear Systems Using Neural Networks and Polynomial ... Andrzej Janczak No preview available - 2004 |