Identifiability of Parametric Models
- 1st Edition - September 12, 2014
- Latest edition
- Editor: E. Walter
- Language: English
Identifiability of Parametric Models provides a comprehensive presentation of identifiability. This book is divided into 11 chapters. Chapter 1 reviews the basic methods for… Read more
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.
Tutorial
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
References
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
References
Chapter 3: On Structural Equivalence and Identifiability Constraint Ordering
1 Introduction
2 Mathematical Background
3 Structural Equivalence
4 Exhaustive Modeling
References
Appendix
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
References
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
References
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
References
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)
Conclusion
Appendix 1: Proof of Reducing to Zero
Appendix 2: Using Reduce
References
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
References
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
References
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
References
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
References
Author Index
Subject Index
- Edition: 1
- Latest edition
- Published: September 12, 2014
- Language: English
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