Walter Identifiability of Parametric Models

1. Auflage 2014
ISBN: 978-1-4831-5595-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 132 Seiten, Web PDF

Identifiability of Parametric Models provides a comprehensive presentation of identifiability. This book is divided into 11 chapters. Chapter 1 reviews the basic methods for structural identifiability testing. The methods that deal with large-scale models and propose conjectures on global identifiability are considered in Chapter 2, while the problems of initial model selection and generating the set of models that have the exact same input-output behavior are evaluated in Chapter 3. Chapters 4 and 5 cover nonlinear models. The relations between identifiability and the well-posedness of the estimation problem are analyzed in Chapter 6, followed by a description of the algebraic manipulations required for testing a model for structural controllability, observability, identifiability, or distinguishability in chapter 7. The rest of the chapters are devoted to the relations between identifiability and parameter uncertainty. This publication is beneficial to students and researchers aiming to acquire knowledge of the identifiability of parametric models.

Autoren/Hrsg.

Walter, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Identifiability of Parametric Models;4
3;Copyright Page;5
4;Table of Contents;8
5;FOREWORD;6
6;Part 1: Tutorial;14
6.1;CHAPTER 1. IDENTlFlABlLlTY OF MODEL PARAMETERS;14
6.1.1;1. Introduction;14
6.1.2;2 Basic concepts and identifiability analysis for noise-free linear time-invariant models;15
6.1.3;3 Complete models, general definitions and nonlinear systems;23
6.1.4;4 Parameter bounds for unidentifiable linear models;28
6.1.5;5 Numerical identifiability: is this really a new problem?;32
6.1.6;6 Concluding remarks;32
6.1.7;References;32
7;Part 2: Linear Models;34
7.1;CHAPTER 2: RESULTS AND CONJECTURESON THE IDENTlFlABlLlTY OF LINEAR SYSTEMS;34
7.1.1;1 Introduction;34
7.1.2;2 Equations derived from experimental data;34
7.1.3;3 Results on local identifiability;36
7.1.4;4 A particular result on global identifiability;39
7.1.5;5 Examples of the application of Conjecture 1;42
7.1.6;6 Examples of the application of Conjecture 2;43
7.1.7;7 Conclusion;43
7.1.8;References;44
7.2;CHAPTER 3: ON STRUCTURAL EQUIVALENCEAND IDENTIFIABILITY CONSTRAINT ORDERING;45
7.2.1;1 Introduction;45
7.2.2;2 Mathematical background;45
7.2.3;3 Structural equivalence;46
7.2.4;4 Exhaustive modelling;48
7.2.5;References;51
7.2.6;Appendix;52
8;Part 3: Nonlinear and Time-Varying Models;55
8.1;CHAPTER 4: IDENTIFIABILITY OF POLYNOMIAL SYSTEMS:STRUCTURAL AND NUMERICAL ASPECTS;55
8.1.1;1 Introduction;55
8.1.2;2 Deterministic identifiability: problem statement;55
8.1.3;3 Algebraic invariants for homogeneous polynomial models;56
8.1.4;4 Analysis of deterministic identifiability;57
8.1.5;5 Practical identifiability: problem statement;58
8.1.6;6 Principal component analysis of practical identifiability;59
8.1.7;7 A case study on methane pyrolysis;60
8.1.8;8 Conclusions;61
8.1.9;References;61
8.2;CHAPTER 5: VOLTERRA AND GENERATING POWER SERIES APPROACHESTO IDENTIFIABILITY TESTING;63
8.2.1;1 Introduction;63
8.2.2;2 Problem statement;63
8.2.3;3 Generating series approach;64
8.2.4;4 Volterra series approach;72
8.2.5;5 Conclusions;78
8.2.6;References;78
9;Part 5: Infinite-Dimensional Models;80
9.1;CHAPTER 6: IDENTIFIABILITY OF PARAMETERSIN THE OUTPUT LEAST SQUARE FORMULATION;80
9.1.1;1 Introduction;80
9.1.2;2 A sufficient condition for OLSI;84
9.1.3;3 Finite dimensional parameters;85
9.1.4;4 A weaker condition on the derivative;85
9.1.5;5 OLS-identifiability by regularization;87
9.1.6;References;87
10;Part 6: Computer Algebra;88
10.1;CHAPTER 7: THE TESTING OF STRUCTURAL PROPERTIESTHROUGH SYMBOLIC COMPUTATION;88
10.1.1;1 Introduction;88
10.1.2;2 Definitions and problem statement;88
10.1.3;3 Jacobian matrix and global injectivity;90
10.1.4;4 Methods for testing structural controllability and structural observability;90
10.1.5;5 Methods for testing structural identifiability;91
10.1.6;6 Methods for testing structural distinguishability;92
10.1.7;7 Solution of a set of polynomial equations;93
10.1.8;Conclusion;95
10.1.9;Appendix 1: Proof of reducing to zero;95
10.1.10;Appendix 2: Using REDUCE;96
10.1.11;References;97
11;Part 7: Identifiability and Parameter Uncertainty;98
11.1;CHAPTER 8: THEORETICAL ASPECTS AND PRACTICAL STRATEGIESFOR THE IDENTIFICATION OF UNIDENTIFIABLE COMPARTMENTAL SYSTEMS;98
11.1.1;1 Introduction;98
11.1.2;2 An unidentifiable model of glucose kinetics;98
11.1.3;3 Identifiability from parameter bounds;99
11.1.4;4 Identifiability using additional a priori knowledge;103
11.1.5;5 Conclusions;103
11.1.6;References;103
11.2;CHAPTER 9: IDENTIFIABILITY OF SYSTEMS WITH MODELING ERRORA NEW FORMULATION;105
11.2.1;1 Introduction;105
11.2.2;2 Statement of the problem;105
11.2.3;3 Bounds on the solution error;106
11.2.4;4 Identifiability of nearly-equivalent models;107
11.2.5;5 Conclusion;109
11.2.6;References;109
11.3;CHAPTER 10: APPLICATION TO HETEROGENEOUS CATALYSIS;110
11.3.1;1 Introduction;110
11.3.2;2 Listing of possible mechanisms;111
11.3.3;3 Compartmental models;111
11.3.4;4 Identifiability;112
11.3.5;5 Distinguishability;113
11.3.6;6 Membership set estimation;113
11.3.7;7 Discussion;115
11.3.8;8 Conclusions;115
11.3.9;References;115
11.4;CHAPTER 11 : ROBUST EXPERIMENT DESIGN:BETWEEN QUALITATIVE AND QUANTITATIVE IDENTIFIABILITIES;117
11.4.1;1 Introduction;117
11.4.2;2 Classical non-robust design;118
11.4.3;3 Classical robust approaches;118
11.4.4;4 Robust optimal design in the average sense;119
11.4.5;5 Robust optimal design in the min-max sense;124
11.4.6;6 Conclusions;125
11.4.7;References;125
12;Author Index;128
13;Subject Index;130