Identifiability of Parametric Models - 1st Edition - ISBN: 9780080349299, 9781483155951

Identifiability of Parametric Models

1st Edition

Editors: E. Walter
eBook ISBN: 9781483155951
Imprint: Pergamon
Published Date: 1st January 1987
Page Count: 132
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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.

Table of Contents


Chapter 1: Identifiability of Model Parameters

1 Introduction

2 Basic concepts and Identifiability Analysis for Noise-Free Linear Time-Invariant Models

2.1 Basic Concepts and Linear Models

2.2 The Laplace Transform or Transfer Function Approach

2.3 Taylor Series Expansion of the Observations

2.4 Markov Parameter Matrix Approach

2.5 Modal Matrix Approach

2.6 Exhaustive Modeling Approach

2.7 Discussion and Other Problems

3 Complete Models, General Definitions and Nonlinear Systems

3.1 Complete Models and General Definitions

3.3 Identifiability Analysis of Nonlinear Models: The Taylor Series Approach

3.4 Discussion

4 Parameter Bounds for Unidentifiable Linear Models

4.1 Interval Analysis: An Alternative to Multiinput-Multioutput Experiments

4.2 Compartmental Models

4.3 Two-Compartment System

4.4 Three-Compartment Mammillary System

4.5 Discussion

5 Numerical Identifiability: Is this Really a New Problem?

6 Concluding Remarks


Linear Models

Chapter 2: Results and Conjectures on the Identifiability of Linear Systems

1 Introduction

2 Equations Derived from Experimental Data

2.1 Equations for the Evolution of Linear Models

2.2 Equations for the Identifiability Problem

3 Results on Local Identifiability

3.1 Introduction

3.2 Construction of Matrix K

3.3 Principle of the Method

3.4 Main Results

4 A Particular Result on Global Identifiability

4.1 Introduction

4.2 A Simple Example

4.3 Use of the Norm-Coerciveness Theorem

4.4 Conjectures on Global Identifiability

5 Examples of the Application of Conjecture 1

6 Examples of the Application of Conjecture 2

7 Conclusion


Chapter 3: On Structural Equivalence and Identifiability Constraint Ordering

1 Introduction

2 Mathematical Background

3 Structural Equivalence

4 Exhaustive Modeling



Nonlinear and Time-Varying Models

Chapter 4: Identifiability of Polynomial Systems: Structural and Numerical Aspects

1 Introduction

2 Deterministic Identifiability: Problem Statement

3 Algebraic Invariants for Homogeneous Polynomial Models

4 Analysis of Deterministic Identifiability

5 Practical Identifiability: Problem Statement

6 Principal Component Analysis of Practical Identifiability

7 A Case Study on Methane Pyrolysis

8 Conclusions


Chapter 5: Volterra and Generating Power Series Approaches to Identifiability Testing

1 Introduction

2 Problem Statement

3 Generating Series Approach

3.1 Iterated Integrals

3.2 Analytic Causal Functionals and Generating Power Series

3.3 A First Method for Computing Terms of a gps

3.4 Identifiability Testing with gps

3.5 A Second Method for Computing a gps

4 Volterra Series Approach

4.1 Volterra Series and Differential Operators

4.2 A Third Method for Computing Terms of a gps

4.3 Identifiability Testing

5 Conclusions


Infinite-Dimensional Models

Chapter 6: Identifiability of Parameters in the Output Least Square Formulation

1 Introduction

2 A Sufficient Condition for OLSI

3 Finite Dimensional Parameters

4 A Weaker Condition on the Derivative

5 OLS-Identifiability by Regularization


Computer Algebra

Chapter 7: The Testing of Structural Properties Through Symbolic Computation

1 Introduction

2 Definitions and Problem Statement

3 Jacobian Matrix and Global Injectivity

4 Methods for Testing Structural Controllability and Structural Observability

5 Methods for Testing Structural Identifiability

6 Methods for Testing Structural Distinguishability

7 Solution of a Set of Polynomial Equations

7.1 Triangulation by Euclidian Division (ES1)

7.2 Reduction/Construction Algorithm (ES2)


Appendix 1: Proof of Reducing to Zero

Appendix 2: Using Reduce


Identifiability and Parameter Uncertainty

Chapter 8: Theoretical Aspects and Practical Strategies for the Identification of Unidentifiable Compartmental Systems

1 Introduction

2 An Unidentifiable Model of Glucose Kinetics

2.1 Model of Data

2.2 Model of System

3 Identifiability from Parameter Bounds

3.1 Rationale and Bounds of Glucose Model Parameters

3.2 Bound Computation from Exponentials

3.3 Bound Computation from Submodels

3.4 Physiological Information from Parameter Bounds

3.5 On the Formalization of the Parameter Bound Strategy

4 Identifiability Using Additional a Priori Knowledge

5 Conclusions


Chapter 9: Identifiability of Systems with Modeling Error a New Formulation

1 Introduction

2 Statement of the Problem

2.1 Theoretical Identification

2.2 Practical Identification

3 Bounds on the Solution Error

4 Identifiability of Nearly-Equivalent Models

5 Conclusion


Chapter 10: Application to Heterogeneous Catalysis

1 Introduction

2 Listing of Possible Mechanisms

3 Compartmental Models

4 Identifiability

5 Distinguishability

6 Membership Set Estimation

7 Discussion

8 Conclusions


Chapter 11: Robust Experiment Design: Between Qualitative and Quantitative Identifiabilities

1 Introduction

2 Classical Non-Robust Design

2.1 Fisher Information Matrix

2.2 D-Optimal Design

3 Classical Robust Approaches

4 Robust Optimal Design in the Average Sense

4.1 Criteria

4.2 ED Versus EID Optimality

4.3 Algorithms

4.4 Examples

5 Robust Optimal Design in the Min-Max Sense

6 Conclusions


Author Index

Subject Index


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© Pergamon 1987
eBook ISBN:

About the Editor

E. Walter

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