Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains

Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains /

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Bibliographic Details
Main Author: Billings, S. A. (Author)
Corporate Author: Ebooks Corporation
Format: Electronic eBook
Language:English
Published: Chichester, West Sussex : Wiley, 2013.
Subjects:
Nonlinear systems.
Nonlinear theories > Mathematical models.
Systems engineering.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)
Table of Contents:
  • Machine generated contents note: 1.1. Introduction to System Identification
  • 1.1.1. System Models and Simulation
  • 1.1.2. Systems and Signals
  • 1.1.3. System Identification
  • 1.2. Linear System Identification
  • 1.3. Nonlinear System Identification
  • 1.4. NARMAX Methods
  • 1.5. NARMAX Philosophy
  • 1.6. What is System Identification For?
  • 1.7. Frequency Response of Nonlinear Systems
  • 1.8. Continuous-Time, Severely Nonlinear, and Time-Varying Models and Systems
  • 1.9. Spatio-temporal Systems
  • 1.10. Using Nonlinear System Identification in Practice and Case Study Examples
  • References
  • 2.1. Introduction
  • 2.2. Linear Models
  • 2.2.1. Autoregressive Moving Average with Exogenous Input Model
  • 2.2.2. Parameter Estimation for Linear Models
  • 2.3. Piecewise Linear Models
  • 2.3.1. Spatial Piecewise Linear Models
  • 2.3.2. Models with Signal-Dependent Parameters
  • 2.3.3. Remarks on Piecewise Linear Models
  • 2.4. Volterra Series Models
  • 2.5. Block-Structured Models
  • 2.5.1. Parallel Cascade Models
  • 2.5.2. Feedback Block-Structured Models
  • 2.6. NARMAX Models
  • 2.6.1. Polynomial NARMAX Model
  • 2.6.2. Rational NARMAX Model
  • 2.6.3. Extended Model Set Representation
  • 2.7. Generalised Additive Models
  • 2.8. Neural Networks
  • 2.8.1. Multi-layer Networks
  • 2.8.2. Single-Layer Networks
  • 2.9. Wavelet Models
  • 2.9.1. Dynamic Wavelet Models
  • 2.10. State-Space Models
  • 2.11. Extensions to the MIMO Case
  • 2.12. Noise Modelling
  • 2.12.1. Noise-Free
  • 2.12.2. Additive Random Noise
  • 2.12.3. Additive Coloured Noise
  • 2.12.4. General Noise
  • 2.13. Spatio-temporal Models
  • References
  • 3.1. Introduction
  • 3.2. Orthogonal Least Squares Estimator and the Error Reduction Ratio
  • 3.2.1. Linear-in-the-Parameters Representation
  • 3.2.2. Matrix Form of the Linear-in-the-Parameters Representation
  • 3.2.3. Basic OLS Estimator
  • 3.2.4. Matrix Formulation of the OLS Estimator
  • 3.2.5. Error Reduction Ratio
  • 3.2.6. Illustrative Example of the Basic OLS Estimator
  • 3.3. Forward Regression OLS Algorithm
  • 3.3.1. Forward Regression with OLS
  • 3.3.2. Illustrative Example of Forward Regression with OLS
  • 3.3.3. OLS Estimation Engine and Identification Procedure
  • 3.4. Term and Variable Selection
  • 3.5. OLS and Sum of Error Reduction Ratios
  • 3.5.1. Sum of Error Reduction Ratios
  • 3.5.2. Variance of the s-Step-Ahead Prediction Error
  • 3.5.3. Final Prediction Error
  • 3.5.4. Variable Selection Algorithm
  • 3.6. Noise Model Identification
  • 3.6.1. Noise Model
  • 3.6.2. Simulation Example with Noise Modelling
  • 3.7. Example of Variable and Term Selection for a Real Data Set
  • 3.8. ERR is Not Affected by Noise
  • 3.9. Common Structured Models to Accommodate Different Parameters
  • 3.10. Model Parameters as a Function of Another Variable
  • 3.10.1. System Internal and External Parameters
  • 3.10.2. Parameter-Dependent Model Structure
  • 3.10.3. Modelling Auxetic Foams - An Example of External Parameter-Dependent Model Identification
  • 3.11. OLS and Model Reduction
  • 3.12. Recursive Versions of OLS
  • References
  • 4.1. Introduction
  • 4.2. Feature Selection and Feature Extraction
  • 4.3. Principal Components Analysis
  • 4.4. Forward Orthogonal Search Algorithm
  • 4.4.1. Basic Idea of the FOS-MOD Algorithm
  • 4.4.2. Feature Detection and Ranking
  • 4.4.3. Monitoring the Search Procedure
  • 4.4.4. Illustrative Examples
  • 4.5. Basis Ranking Algorithm Based on PCA
  • 4.5.1. Principal Component-Derived Multiple Regression
  • 4.5.2. PCA-Based MFROLS Algorithms
  • 4.5.3. Illustrative Example
  • References
  • 5.1. Introduction
  • 5.2. Detection of Nonlinearity
  • 5.3. Estimation and Test Data Sets
  • 5.4. Model Predictions
  • 5.4.1. One-Step-Ahead Prediction
  • 5.4.2. Model Predicted Output
  • 5.5. Statistical Validation
  • 5.5.1. Correlation Tests for Input-Output Models
  • 5.5.2. Correlation Tests for Time Series Models
  • 5.5.3. Correlation Tests for MIMO Models
  • 5.5.4. Output-Based Tests
  • 5.6. Term Clustering
  • 5.7. Qualitative Validation of Nonlinear Dynamic Models
  • 5.7.1. Poincare Sections
  • 5.7.2. Bifurcation Diagrams
  • 5.7.3. Cell Maps
  • 5.7.4. Qualitative Validation in Nonlinear System Identification
  • References
  • 6.1. Introduction
  • 6.2. Generalised Frequency Response Functions
  • 6.2.1. Volterra Series Representation of Nonlinear Systems
  • 6.2.2. Generalised Frequency Response Functions
  • 6.2.3. Relationship Between GFRFs and Output Response of Nonlinear Systems
  • 6.2.4. Interpretation of the Composition of the Output Frequency Response of Nonlinear Systems
  • 6.2.5. Estimation and Computation of GFRFs
  • 6.2.6. Analysis of Nonlinear Systems Using GFRFs
  • 6.3. Output Frequencies of Nonlinear Systems
  • 6.3.1. Output Frequencies of Nonlinear Systems under Multi-tone Inputs
  • 6.3.2. Output Frequencies of Nonlinear Systems for General Inputs
  • 6.4. Nonlinear Output Frequency Response Functions
  • 6.4.1. Definition and Properties of NOFRFs
  • 6.4.2. Evaluation of NOFRFs
  • 6.4.3. Damage Detection Using NARMAX Modelling and NOFRF-Based Analysis
  • 6.5. Output Frequency Response Function of Nonlinear Systems
  • 6.5.1. Definition of the OFRF
  • 6.5.2. Determination of the OFRF
  • 6.5.3. Application of the OFRF to Analysis of Nonlinear Damping for Vibration Control
  • References
  • 7.1. Introduction
  • 7.2. Energy Transfer Filters
  • 7.2.1. Time and Frequency Domain Representation of the NARX Model with Input Nonlinearity
  • 7.2.2. Energy Transfer Filter Designs
  • 7.3. Energy Focus Filters
  • 7.3.1. Output Frequencies of Nonlinear Systems with Input Signal Energy Located in Two Separate Frequency Intervals
  • 7.3.2. Energy Focus Filter Design Procedure and an Example
  • 7.4. OFRF-Based Approach for the Design of Nonlinear Systems in the Frequency Domain
  • 7.4.1. OFRF-Based Design of Nonlinear Systems in the Frequency Domain
  • 7.4.2. Design of Nonlinear Damping in the Frequency Domain for Vibration Isolation: An Experimental Study
  • References
  • 8.1. Introduction
  • 8.2. Multi-layered Perceptron
  • 8.3. Radial Basis Function Networks
  • 8.3.1. Training Schemes for RBF Networks
  • 8.3.2. Fixed Kernel Centres with a Single Width
  • 8.3.3. Limitation of RBF Networks with a Single Kernel Width
  • 8.3.4. Fixed Kernel Centres and Multiple Kernel Widths
  • 8.4. Wavelet Networks
  • 8.4.1. Wavelet Decompositions
  • 8.4.2. Wavelet Networks
  • 8.4.3. Limitations of Fixed Grid Wavelet Networks
  • 8.4.4. New Class of Wavelet Networks
  • 8.5. Multi-resolution Wavelet Models and Networks
  • 8.5.1. Multi-resolution Wavelet Decompositions
  • 8.5.2. Multi-resolution Wavelet Models and Networks
  • 8.5.3. Illustrative Example
  • References
  • 9.1. Introduction
  • 9.2. Wavelet NARMAX Models
  • 9.2.1. Nonlinear System Identification Using Wavelet Multi-resolution NARMAX Models
  • 9.2.2. Strategy for Identifying Nonlinear Systems
  • 9.3. Systems that Exhibit Sub-harmonics and Chaos
  • 9.3.1. Limitations of the Volterra Series Representation
  • 9.3.2. Time Domain Analysis
  • 9.4. Response Spectrum Map
  • 9.4.1. Introduction
  • 9.4.2. Examples of the Response Spectrum Map
  • 9.5. Modelling Framework for Sub-harmonic and Severely Nonlinear Systems
  • 9.5.1. Input Signal Decomposition
  • 9.5.2. MISO NARX Modelling in the Time Domain
  • 9.6. Frequency Response Functions for Sub-harmonic Systems
  • 9.6.1. MISO Frequency Domain Volterra Representation
  • 9.6.2. Generating the GFRFs from the MISO Model
  • 9.7. Analysis of Sub-harmonic Systems and the Cascade to Chaos
  • 9.7.1. Frequency Domain Response Synthesis
  • 9.7.2. Example of Frequency Domain Analysis for Sub-harmonic Systems
  • References
  • 10.1. Introduction
  • 10.2. Kernel Invariance Method
  • 10.2.1. Definitions
  • 10.2.2. Reconstructing the Linear Model Terms
  • 10.2.3. Reconstructing the Quadratic Model Terms
  • 10.2.4. Model Structure Determination
  • 10.3. Using the GFRFs to Reconstruct Nonlinear Integro-differential Equation Models Without Differentiation
  • 10.3.1. Introduction
  • 10.3.2. Reconstructing the Linear Model Terms
  • 10.3.3. Reconstructing the Quadratic Model Terms
  • 10.3.4. Reconstructing the Higher-Order Model Terms
  • 10.3.5. Real Application
  • References
  • 11.1. Introduction
  • 11.2. Adaptive Parameter Estimation Algorithms
  • 11.2.1. Kalman Filter Algorithm
  • 11.2.2. RLS and LMS Algorithms
  • 11.2.3. Some Practical Considerations for the KF, RLS, and LMS Algorithms
  • 11.3. Tracking Rapid Parameter Variations Using Wavelets
  • 11.3.1. General Form of TV-ARX Models Using Wavelets
  • 11.3.2. Multi-wavelet Approach for Time-Varying Parameter Estimation
  • 11.4. Time-Dependent Spectral Characterisation
  • 11.4.1. Definition of a Time-Dependent Spectral Function
  • 11.5. Nonlinear Time-Varying Model Estimation
  • 11.6. Mapping and Tracking in the Frequency Domain
  • 11.6.1. Time-Varying Frequency Response Functions
  • 11.6.2. First and Second-Order TV-GFRFs
  • 11.7. Sliding Window Approach
  • References
  • 12.1. Introduction
  • 12.2. Cellular Automata
  • 12.2.1. History of Cellular Automata
  • 12.2.2. Discrete Lattice
  • 12.2.3. Neighbourhood
  • 12.2.4. Transition Rules
  • 12.2.5. Simulation Examples of Cellular Automata
  • 12.3. Identification of Cellular Automata
  • 12.3.1. Introduction and Review
  • 12.3.2. Polynomial Representation
  • Contents note continued: 12.3.3. Neighbourhood Detection and Rule Identification
  • 12.4. N-State Systems
  • 12.4.1. Introduction to Excitable Media Systems
  • 12.4.2. Simulation of Excitable Media
  • 12.4.3. Identification of Excitable Media Using a CA Model
  • 12.4.4. General N-State Systems
  • References
  • 13.1. Introduction
  • 13.2. Spatio-temporal Patterns and Continuous-State Models
  • 13.2.1. Stem Cell Colonies
  • 13.2.2. Belousov-Zhabotinsky Reaction
  • 13.2.3. Oxygenation in Brain
  • 13.2.4. Growth Patterns
  • 13.2.5. Simulated Example Showing Spatio-temporal Chaos from CML Models
  • 13.3. Identification of Coupled Map Lattice Models
  • 13.3.1. Deterministic CML Models
  • 13.3.2. Identification of Stochastic CML Models
  • 13.4. Identification of Partial Differential Equation Models
  • 13.4.1. Model Structure
  • 13.4.2. Time Discretisation
  • 13.4.3. Nonlinear Function Approximation
  • 13.5. Nonlinear Frequency Response Functions for Spatio-temporal Systems
  • 13.5.1. One-Dimensional Example
  • 13.5.2. Higher-Order Frequency Response Functions
  • References
  • 14.1. Introduction
  • 14.2. Practical System Identification
  • 14.3. Characterisation of Robot Behaviour
  • 14.3.1. Door Traversal
  • 14.3.2. Route Learning
  • 14.4. System Identification for Space Weather and the Magnetosphere
  • 14.5. Detecting and Tracking Iceberg Calving in Greenland
  • 14.5.1. Causality Detection
  • 14.5.2. Results
  • 14.6. Detecting and Tracking Time-Varying Causality for EEG Data
  • 14.6.1. Data Acquisition
  • 14.6.2. Causality Detection
  • 14.6.3. Detecting Linearity and Nonlinearity
  • 14.7. Identification and Analysis of Fly Photoreceptors
  • 14.7.1. Identification of the Fly Photoreceptor
  • 14.7.2. Model-Based System Analysis in the Time and Frequency Domain
  • 14.8. Real-Time Diffuse Optical Tomography Using RBF Reduced-Order Models of the Propagation of Light for Monitoring Brain Haemodynamics
  • 14.8.1. Diffuse Optical Imaging
  • 14.8.2. In-vivo Real-Time 3-D Brain Imaging Using Reduced-Order Forward Models
  • 14.9. Identification of Hysteresis Effects in Metal Rubber Damping Devices
  • 14.9.1. Dynamic Modelling of Metal Rubber Damping Devices
  • 14.9.2. Model Identification of a Metal Rubber Specimen
  • 14.10. Identification of the Belousov-Zhabotinsky Reaction
  • 14.10.1. Data Acquisition
  • 14.10.2. Model Identification
  • 14.11. Dynamic Modelling of Synthetic Bioparts
  • 14.11.1. Biopart and the Experiments
  • 14.11.2. NARMAX Model of the Synthetic Biopart
  • 14.12. Forecasting High Tides in the Venice Lagoon
  • 14.12.1. Time Series Forecasting Problem
  • 14.12.2. Water-Level Modelling and High-Tide Forecasting
  • References.

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