本书主要研究了一类非线性系统的时域辨识、频域辨识、总体最小二乘辨识及应用、非线性系统建模、非线性系统故障诊断应用等内容。本书内容大体上可分为三部分，第一部分研究了一类非线性系统--Volterra级数模型基本理论，介绍了其时域分析和频域分析方法；第二部分研究了Volterra级数模型的辨识与建模方法，介绍了Volterra级数模型的时域辨识和频域辨识等多种迭代方法；第三部分研究了Volterra级数时域、频域方法及混沌方法等在电路等复杂系统参数估计、故障诊断中的应用。本书的很大一部分内容十分新颖，反映了国内外非线性系统建模与辨识领域方向上研究和应用的最新进展。

Chapter 1 Introduction
1.1 Feature Extraction
1.1.1 PCA and Subspace Tracking
1.1.2 PCA Neural Networks
1.1.3 Extension or Generalization of PCA
1.2 Basis for Subspace Tracking
1.2.1 Concept of Subspace
1.2.2 Subspace Tracking Method
1.3 Main Features of This Book
1.4 Organization of This Book
References
Chapter 2 Matrix Analysis Basics
2.1 Introduction
2.2 Singular Value Decomposition
2.2.1 Theorem and Uniqueness of SVD
2.2.2 Properties of SVD
2.3 Eigenvalue Decomposition
2.3.1 Eigenvalue Problem and Eigen Equation
2.3.2 Eigenvalue and Eigenvector
2.3.3 Eigenvalue Decomposition of Hermitian Matrix
2.3.4 Generalized Eigenvalue Decomposition
2.4 Rayleigh Quotient and Its Characteristics
2.4.1 Rayleigh Quotient
2.4.2 Gradient and Conjugate Gradient Algorithm for RQ
2.4.3 Generalized Rayleigh Quotient
2.5 Matrix Analysis
2.5.1 Differential and Integral of Matrix with Respect to Scalar
2.5.2 Gradient of Real Function with Respect to Real Vector
2.5.3 Gradient Matrix of Real Function
2.5.4 Gradient Matrix of Trace Function
2.5.5 Gradient Matrix of Determinant
2.5.6 Hessian Matrix
2.6 Summary
References
Chapter 3 Neural Networks for Principal Component Analysis
3.1 Introduction
3.2 Review of Neural Based PCA algorithms
3.3 Neural based PCA Algorithms Foundation
3.3.1 Hebbian Learning Rule
3.3.2 Oja's Learning Rule
3.4 Hebbian/Anti-Hebbian Rule based Principal Component Analysis
3.4.1 Subspace Learning Algorithms
3.4.2 Generalized Hebbian Algorithm
3.4.3 Learning Machine for Adaptive Feature Extraction via PCA
3.4.4 The Dot-Product-Decorrelation Algorithm
3.4.5 Anti-Hebbian Rule based Principal Component Analysis
3.5 Least Mean Squared Error based Principal Component Analysis
3.5.1 Least Mean Square Error Reconstruction Algorithm
3.5.2 Projection Approximation Subspace Tracking Algorithm
3.5.3 Robust RLS Algorithm
3.6 Optimization based Principal Component Analysis
3.6.1 Novel Information Criterion Algorithm
3.6.2 Coupled Principal Component Analysis
3.7 Nonlinear Principal Component Analysis
3.7.1 Kernel Principal Component Analysis
3.7.2 Robust/Nonlinear Principal Component Analysis
3.7.3 Autoassociative Network based Nonlinear PCA
3.8 Other PCA or Extensions of PCA
3.9 Summary
References
Chapter 4 Neural Networks for Minor Component Analysis
4.1 Introduction
4.2 Review of Neural Network Based MCA Algorithms
4.2.1 Extracting the First Minor Component
4.2.2 Oja's Minor Subspace Analysis
4.2.3 Self-stabilizing MCA
4.2.4 Orthogonal Oja Algorithm
4.2.5 Other MCA Algorithm
4.3 MCA EXIN Linear Neuron
4.3.1 The Sudden Divergence
4.3.2 The Instability Divergence
4.3.3 The Numerical Divergence
4.4 A Novel Self-stabilizing MCA Linear Neurons
4.4.1 A Self-stabilizing Algorithm for Tracking one MC
4.4.2 MS Tracking Algorithm
4.4.3 Computer Simulations
4.5 Total Least Squares Problem Application
4.5.1 A Novel Neural Algorithm for Total Least Squares Filtering
4.5.2 Computer Simulations
4.6 Summary
References
Chapter 5 Dual Purpose for Principal and Minor Component Analysis
5.1 Introduction
5.2 Review of Neural Network Based Dual Purpose Methods
5.2.1 Chen's Unified Stabilization Approach
5.2.2 Hasan's Self-normalizing Dual Systems
5.2.3 Peng's Unified Learning Algorithm to Extract Principal and Minor Components
5.2.4 Manton's Dual Purpose Principal and Minor Component Flow
5.3 A Novel Dual Purpose Method for Principal and Minor Subspace Tracking
5.3.1 Preliminaries
5.3.2 A Novel Information Criterion and Its Landscape
5.3.3 Dual Purpose Subspace Gradient Flow
5.3.4 Global Convergence