Identification of Nonlinear Systems Using Neural Networks and Polynomial Models

Transcription

1 A.Janczak Identification of Nonlinear Systems Using Neural Networks and Polynomial Models A Block-Oriented Approach With 79 Figures and 22 Tables Springer

2 Contents Symbols and notation XI 1 Introduction Models of dynamic Systems Linear modeis Nonlinear modeis Series-parallel and parallel modeis State space modeis Nonlinear modeis composed of sub-modeis State-space Wiener modeis State-space Hammerstein modeis Multilayer perceptron MLP architecture Learning algorithms Optimizing the model architecture Identification of Wiener Systems Identification of Hammerstein Systems Summary 30 2 Neural network Wiener modeis Introduction Problem formulation Series-parallel and parallel neural network Wiener modeis SISO Wiener modeis MIMO Wiener modeis Gradient calculation Series-parallel SISO model. Backpropagation method Parallel SISO model. Backpropagation method Parallel SISO model. Sensitivity method Parallel SISO model. Backpropagation through time method 43

3 VIII Contents Series-parallel MIMO model. Backpropagation method Parallel MIMO model. Backpropagation method Parallel MIMO model. Sensitivity method Parallel MIMO model. Backpropagation through time method Accuracy of gradient calculation with truncated BPTT Gradient calculation in the sequential mode Computational complexity Simulation example Two-tank System example Prediction error method Recursive prediction error learning algorithm Pneumatic valve Simulation example Summary Appendix 2.1. Gradient derivation of the truncated BPTT. SISO Wiener modeis Appendix 2.2. Gradient derivation of truncated BPTT. MIMO Wiener modeis Appendix 2.3. Proof of Theorem Appendix 2.4. Proof of Theorem Neural network Hammerstein modeis Introduction Problem formulation Series-parallel and parallel neural network Hammerstein modeis SISO Hammerstein modeis MIMO Hammerstein modeis Gradient calculation Series-parallel SISO model. Backpropagation method Parallel SISO model. Backpropagation method Parallel SISO model. Sensitivity method Parallel SISO model. Backpropagation through time method Series-parallel MIMO model. Backpropagation method Parallel MIMO model. Backpropagation method Parallel MIMO model. Sensitivity method Parallel MIMO model. Backpropagation through time method Accuracy of gradient calculation with truncated BPTT Gradient calculation in the sequential mode Computational complexity Simulation example Combined steepest descent and least Squares learning algorithms Summary 106

4 Contents IX 3.8 Appendix 3.1. Gradient derivation of truncated BPTT. SISO Hammerstein modeis Appendix 3.2. Gradient derivation of truncated BPTT. MIMO Hammerstein modeis Appendix 3.3. Proof of Theorem Appendix 3.4. Proof of Theorem Appendix 3.5. Proof of Theorem Appendix 3.6. Proof of Theorem Polynomial Wiener modeis Least Squares approach to the identification of Wiener Systems Identification error Nonlinear characteristic with the linear term Nonlinear characteristic without the linear term Asymptotic bias error of the LS estimator Instrumental variables method Simulation example. Nonlinear characteristic with the linear term Simulation example. Nonlinear characteristic without the linear term Identification of Wiener Systems with the prediction error method Polynomial Wiener model Recursive prediction error method Gradient calculation Pneumatic valve Simulation example Pseudolinear regression method Pseudolinear-in-parameters polynomial Wiener model Pseudolinear regression identification method Simulation example Summary Polynomial Hammerstein modeis Noniterative least Squares identification of Hammerstein Systems Iterative least Squares identification of Hammerstein Systems Identification of Hammerstein Systems in the presence of correlated noise Identification of Hammerstein Systems with the Laguerre function expansion Prediction error method Identification of MISO Systems with the pseudolinear regression method Identification of Systems with two-segment nonlinearities Summary 157

5 X Contents 6 Applications General review of applications Fault detection and isolation with Wiener and Hammerstein modeis Defmitions of residuals Hammerstein System. Parameter estimation of the residual equation Wiener System. Parameter estimation of the residual equation Sugar evaporator. Identification of the nominal model of steam pressure dynamics Theoretical model Experimental modeis of steam pressure dynamics Estimation results Summary 185 References 187 Index 195