Model identification and data analysis

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...

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Detalles Bibliográficos
Otros Autores: Bittanti, Sergio, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, New Jersey : Wiley [2019]
Edición:1st edition
Colección:THEi Wiley ebooks.
Materias:
System identification > Mathematical models.
Quantitative research.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630610506719
Tabla de Contenidos:
  • Intro
  • Introduction
  • Acknowledgments
  • 1 Stationary Processes and Time Series
  • 1.1 Introduction
  • 1.2 The Prediction Problem
  • 1.3 Random Variable
  • 1.4 Random Vector
  • 1.5 Stationary Process
  • 1.6 White Process
  • 1.7 MA Process
  • 1.8 AR Process
  • 1.9 Yule-Walker Equations
  • 1.10 ARMA Process
  • 1.11 Spectrum of a Stationary Process
  • 1.12 ARMA Model: Stability Test and Variance Computation
  • 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
  • 2 Estimation of Process Characteristics
  • 2.1 Introduction
  • 2.2 General Properties of the Covariance Function
  • 2.3 Covariance Function of ARMA Processes
  • 2.4 Estimation of the Mean
  • 2.5 Estimation of the Covariance Function
  • 2.6 Estimation of the Spectrum
  • 2.7 Whiteness Test
  • 3 Prediction
  • 3.1 Introduction
  • 3.2 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
  • 4 Model Identification
  • 4.1 Introduction
  • 4.2 Setting the Identification Problem
  • 4.3 Static Modeling
  • 4.4 Dynamic Modeling
  • 4.5 External Representation Models
  • 4.6 Internal Representation Models
  • 4.7 The Model Identification Process
  • 4.8 The Predictive Approach
  • 4.9 Models in Predictive Form
  • 5 Identification of Input-Output Models
  • 5.1 Introduction
  • 5.2 Estimating AR and ARX Models: The Least Squares Method
  • 5.3 Identifiability
  • 5.4 Estimating ARMA and ARMAX Models
  • 5.5 Asymptotic Analysis
  • 5.6 Recursive Identification
  • 5.7 Robustness of Identification Methods
  • 5.8 Parameter Tracking
  • 6 Model Complexity Selection
  • 6.1 Introduction
  • 6.2 Cross‐validation
  • 6.3 FPE Criterion.
  • 6.4 AIC Criterion
  • 6.5 MDL Criterion
  • 6.6 Durbin-Levinson Algorithm
  • 7 Identification of State Space Models
  • 7.1 Introduction
  • 7.2 Hankel Matrix
  • 7.3 Order Determination
  • 7.4 Determination of Matrices and
  • 7.5 Determination of Matrix
  • 7.6 Mid Summary: An Ideal Procedure
  • 7.7 Order Determination with SVD
  • 7.8 Reliable Identification of a State Space Model
  • 8 Predictive Control
  • 8.1 Introduction
  • 8.2 Minimum Variance Control
  • 8.3 Generalized Minimum Variance Control
  • 8.4 Model‐Based Predictive Control
  • 8.5 Data‐Driven Control Synthesis
  • 9 Kalman Filtering and Prediction
  • 9.1 Introduction
  • 9.2 Kalman Approach to Prediction and Filtering Problems
  • 9.3 The Bayes Estimation Problem
  • 9.4 One‐step‐ahead Kalman Predictor
  • 9.5 Multistep Optimal Predictor
  • 9.6 Optimal Filter
  • 9.7 Steady‐State Predictor
  • 9.8 Innovation Representation
  • 9.9 Innovation Representation Versus Canonical Representation
  • 9.10 K‐Theory Versus K-W Theory
  • 9.11 Extended Kalman Filter - EKF
  • 9.12 The Robust Approach to Filtering
  • 10 Parameter Identification in a Given Model
  • 10.1 Introduction
  • 10.2 Kalman Filter‐Based Approaches
  • 10.3 Two‐Stage Method
  • 11 Case Studies
  • 11.1 Introduction
  • 11.2 Kobe Earthquake Data Analysis
  • 11.3 Estimation of a Sinusoid in Noise
  • Appendix A: Linear Dynamical Systems
  • A.1 State Space and Input-Output Models
  • A.2 Lagrange Formula
  • A.3 Stability
  • A.4 Impulse Response
  • A.5 Frequency Response
  • A.6 Multiplicity of State Space Models
  • A.7 Reachability and Observability
  • A.8 System Decomposition
  • A.9 Stabilizability and Detectability
  • Appendix B: Matrices
  • B.1 Basics
  • B.2 Eigenvalues
  • B.3 Determinant and Inverse
  • B.4 Rank
  • B.5 Annihilating Polynomial
  • B.6 Algebraic and Geometric Multiplicity
  • B.7 Range and Null Space
  • B.8 Quadratic Forms.
  • B.9 Derivative of a Scalar Function with Respect to a Vector
  • B.10 Matrix Diagonalization via Similarity
  • B.11 Matrix Diagonalization via Singular Value Decomposition
  • B.12 Matrix Norm and Condition Number
  • Appendix C: Problems and Solutions
  • Bibliography
  • Further reading
  • Index
  • End User License Agreement.

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