Model identification and data analysis / Sergio Bittanti.

Format:

Book

Author/Creator:

Bittanti, Sergio, author.

Series:

THEi Wiley ebooks.

Language:

English

Subjects (All):

System identification--Mathematical models.

System identification.

Quantitative research.

Physical Description:

1 online resource (419 pages)

Edition:

1st edition

Place of Publication:

Hoboken, New Jersey : Wiley, [2019]

System Details:

Access using campus network via VPN at home (THEi Users Only).

text file

Summary:

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 offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University. The book: Contains accessible methods explained step-by-step in simple terms Offers an essential tool useful in a variety of fields, especially engineering, statistics, and mathematics Includes an overview on random variables and stationary processes, as well as an introduction to discrete time models and matrix analysis Incorporates historical commentaries to put into perspective the developments that have brought the discipline to its current state Provides many examples and solved problems to complement the presentation and facilitate comprehension of the techniques presented

Contents:

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.

Notes:

Description based on print version record.

ISBN:

1-119-54631-1

1-119-54640-0

1-119-54641-9

OCLC:

1057242269