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Model identification and data analysis /
This book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control. Written for graduate students, this textbook of...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, NJ :
John Wiley & Sons, Inc.,
2019.
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Contents; Introduction; Acknowledgments; Chapter 1 Stationary Processes and Time Series; 1.1 Introduction; 1.2 The Prediction Problem; 1.3 Random Variable; 1.4 Random Vector; 1.4.1 Covariance Coefficient; 1.5 Stationary Process; 1.6 White Process; 1.7 MA Process; 1.8 AR Process; 1.8.1 Study of the AR(1) Process; 1.9 Yule-Walker Equations; 1.9.1 Yule-Walker Equations for the AR(1) Process; 1.9.2 Yule-Walker Equations for the AR(2) and AR(n) Process; 1.10 ARMA Process; 1.11 Spectrum of a Stationary Process; 1.11.1 Spectrum Properties
- 1.11.1.0 Proof of the Spectrum Properties1.11.2 Spectral Diagram; 1.11.3 Maximum Frequency in Discrete Time; 1.11.4 White Noise Spectrum; 1.11.5 Complex Spectrum; 1.12 ARMA Model: Stability Test and Variance Computation; 1.12.1 Ruzicka Stability Criterion; 1.12.2 Variance of an ARMA Process; 1.13 Fundamental Theorem of Spectral Analysis; 1.14 Spectrum Drawing; 1.15 Proof of the Fundamental Theorem of Spectral Analysis; 1.16 Representations of a Stationary Process; Chapter 2 Estimation of Process Characteristics; 2.1 Introduction; 2.2 General Properties of the Covariance Function
- 2.3 Covariance Function of ARMA Processes2.4 Estimation of the Mean; 2.5 Estimation of the Covariance Function; 2.6 Estimation of the Spectrum; 2.7 Whiteness Test; Chapter 3 Prediction; 3.1 Introduction; 3.2 Fake Predictor; 3.2.1 Practical Determination of the Fake Predictor; 3.3 Spectral Factorization; 3.4 Whitening Filter; 3.5 Optimal Predictor from Data; 3.6 Prediction of an ARMA Process; 3.7 ARMAX Process; 3.8 Prediction of an ARMAX Process; Chapter 4 Model Identification; 4.1 Introduction; 4.2 Setting the Identification Problem; 4.2.1 Learning from Maxwell
- 4.2.2 A General Identification Problem4.3 Static Modeling; 4.3.1 Learning from Gauss; 4.3.2 Least Squares Made Simple; 4.3.2.1 Trend Search; 4.3.2.2 Seasonality Search; 4.3.2.3 Linear Regression; 4.3.3 Estimating the Expansion of the Universe; 4.4 Dynamic Modeling; 4.5 External Representation Models; 4.5.1 Box and Jenkins Model; 4.5.2 ARX and AR Models; 4.5.3 ARMAX and ARMA Models; 4.5.4 Multivariable Models; 4.6 Internal Representation Models; 4.7 The Model Identification Process; 4.8 The Predictive Approach; 4.9 Models in Predictive Form; 4.9.1 Box and Jenkins Model; 4.9.2 ARX and AR Models
- 4.9.3 ARMAX and ARMA ModelsChapter 5 Identification of Input-Output Models; 5.1 Introduction; 5.2 Estimating AR and ARX Models: The Least Squares Method; 5.3 Identifiability; 5.3.1 The R Matrix for the ARX(1, 1) Model; 5.3.2 The R Matrix for a General ARX Model; 5.4 Estimating ARMA and ARMAX Models; 5.4.1 Computing the Gradient and the Hessian from Data; 5.5 Asymptotic Analysis; 5.5.1 Data Generation System Within the Class of Models; 5.5.2 Data Generation System Outside the Class of Models; 5.5.2.1 Simulation Trial; 5.5.3 General Considerations on the Asymptotics of Predictive Identification