| 1. |
- Gerdin, Markus, et al.
(författare)
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Global Identifiability of Complex Models, Constructed from Simple Submodels
- 2007
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Ingår i: Modeling, Estimation and Control. - Linköping : Linköping University Electronic Press. - 9783540735694 ; , s. 123-133
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- It is a typical situation in modern modeling that a total model is built up from simpler submodels, or modules, for example residing in a model library. The total model could be quite complex, while the modules are well understood and analysed. A procedure to decide global parameter identifiability for such a collection of model equations of differential-algebraic nature is suggested. It is shown how to make use of the natural modularization of the model structure. Basically, global identifiability is obtained if and only if each module is identifiable, and the connecting signals can be retrieved from the external signals, without knowledge of the values of the parameters.
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| 2. |
- Gerdin, Markus, 1977-
(författare)
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Identification and Estimation for Models Described by Differential-Algebraic Equations
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Differential-algebraic equations (DAEs) form the natural way in which models of physical systems are delivered from an object-oriented modeling tool like Modelica. Differential-algebraic equations are also known as descriptor systems, singular systems, and implicit systems. If some constant parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. It may also be of interest to estimate the value of time-varying variables in the model. This is often referred to as state estimation. The objective of this work is to examine how gray box identification and estimation of time-varying variables can be performed for models described by differential-algebraic equations.If a model has external stimuli that are not measured or uncertain measurements, it is often appropriate to model this as stochastic processes. This is called noise modeling. Noise modeling is an important part of system identification and state estimation, so we examine how well-posedness of noise models for differential-algebraic equations can be characterized. For well-posed models, we then discuss how particle filters can be implemented for estimation of time-varying variables. We also discuss how constant parameters can be estimated.When estimating time-varying variables, it is of interest to examine if the problem is observable, that is, if it has a unique solution. The corresponding property when estimating constant parameters is identifiability. In this thesis, we discuss how observability and identifiability can be determined for DAEs. We propose three approaches, where one can be seen as an extension of standard methods for state-space systems based on rank tests.For linear DAEs, a more detailed analysis is performed. We use some well-known canonical forms to examine well-posedness of noise models and to implement estimation of time-varying variables and constant parameters. This includes formulation of Kalman filters for linear DAE models. To be able to implement the suggested methods, we show how the canonical forms can be computed using numerical software from the linear algebra package LAPACK.
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| 3. |
- Gerdin, Markus, et al.
(författare)
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Identification of a Nonlinear Cell Cycle System with Linear Models
- 2005
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Ingår i: Proceedings of the Conference on Modeling and Simulation in Biology, Medicine and Biomedical EngineeringMay 26-27, 2005, Linköping, Sweden. - Linköping : Linköping University Electronic Press. ; , s. 129-138
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A mathematical model by Chen et al. representing the cell cycle of the budding yeast cell (Saccharomyces cerevisiae) is used to simulate levels of 13 different cell biological variables. By using a linear systems approach on the generated data the goal is to identify the original equations of the mathematical model. Since this model is described by a nonlinear system the linear systems approach only gives correct estimations of the linear parts of the system, with one exception. A main issue thus becomes to identify which data that belongs to the linear equations and which does not. This problem is solved using two local linear models on different time intervals. Parameter estimations of coefficients from linear and time invariant equations should be the same over all time intervals.
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| 4. |
- Gerdin, Markus, 1977-
(författare)
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Local Identifiability and Observability of Nonlinear Differential-Algebraic Equations
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 802-807
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Konferensbidrag (refereegranskat)abstract
- Identifiability is important to guarantee convergence in system identification applications, and observability is important in applications such as control and diagnosis. In this paper, recent results on analysis of nonlinear differential-algebraic equations are used to derive criteria for local identifiability and local weak observability for such models. The criteria are based on rank tests. Examples show the relationship between the new criteria and standard methods for state-space systems.
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| 5. |
- Gerdin, Markus
(författare)
-
Local Identifiability and Observability of Nonlinear Differential-Algebraic Equations
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Identifiability is important to guarantee convergence in system identification applications, and observability is important in applications such as control and diagnosis. In this paper, recent results on analysis of nonlinear differential-algebraic equations are used to derive criteria for local identifiability and local weak observability for such models. The criteria are based on rank tests. Examples show the relationship between the new criteria and standard methods for state-space systems.
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| 6. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering
- 2006
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Ingår i: Proceedings of the 45th IEEE Conference on Decision and Control. - 1424401712 ; , s. 6630-6635
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Konferensbidrag (refereegranskat)abstract
- Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.
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| 7. |
- Gerdin, Markus, et al.
(författare)
-
Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.
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| 8. |
- Gerdin, Markus, 1977-, et al.
(författare)
-
On Identifiability of Object-Oriented Models
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 820-825
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Konferensbidrag (refereegranskat)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 9. |
- Gerdin, Markus, et al.
(författare)
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On Identifiability of Object-Oriented Models
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 10. |
- Gerdin, Markus, 1977-, et al.
(författare)
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On Parameter and State Estimation for Linear Differential-Algebraic Equations
- 2007
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Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 43:3, s. 416-425
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Tidskriftsartikel (refereegranskat)abstract
- The current demand for more complex models has initiated a shift away from state-space models towards models described by differential-algebraic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic differential-algebraic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of efficient numerical methods.
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| 11. |
- Gerdin, Markus, 1977-
(författare)
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Using DAE Solvers to Examine Local Identifiability for Linear and Nonlinear Systems
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 808-813
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Konferensbidrag (refereegranskat)abstract
- If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also possible to examine which functions of the parameters that are locally identifiable.
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| 12. |
- Gerdin, Markus
(författare)
-
Using DAE Solvers to Examine Local Identifiability for Linear and Nonlinear Systems
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also possible to examine which functions of the parameters that are locally identifiable.
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| 13. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Well-Posedness of Filtering Problems for Stochastic Linear DAE Models
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 350-355
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Konferensbidrag (refereegranskat)abstract
- Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white noise. The result might be that certain physical variables get infinite variance or contain formal differentiations of white noise. The paper gives conditions for well-posedness in terms of certain subspaces defined by the system matrices.
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