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- Anguelova, Milena, 1978, et al.
(författare)
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An Efficient Method for Structural Identiability Analysis of Large Dynamic Systems
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - 1474-6670. - 9783902823069 ; 16:1, s. 941-946
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Konferensbidrag (refereegranskat)abstract
- Ordinary differential equation models often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not structurally identifiable with the given set of outputs selected as measurements. We describe the implementation of a recent probabilistic semi-numerical method for testing local structural identifiability based on computing the rank of a numerically instantiated Jacobian matrix (observability/identifiability matrix). To obtain this, matrix parameters and initial conditions are specialized to random integer numbers, inputs are specialized to truncated random integer coefficient power series, and the corresponding output of the state space system is computed in terms of a truncated power series, which then is utilized to calculate the elements of a Jacobian matrix. To reduce the memory requirements and increase the speed of the computations all operations are done modulo a large prime number. The method has been extended to handle parametrized initial conditions and is demonstrated to be capable of handling systems in the order of a hundred state variables and equally many parameters on a standard desktop computer.
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- Anguelova, Milena, 1978, et al.
(författare)
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Input-Output Representation and Identifiability of Delay Parameters for Nonlinear Systems with Multiple Time-Delays
- 2009
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Ingår i: Lecture Notes in Control and Information Sciences: TOPICS IN TIME DELAY SYSTEMS: ANALYSIS, ALGORITHMS AND CONTROL; 7th IFAC Workshop on Time Delay Systems. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0170-8643. - 9783642028960 ; 388, s. 243-253
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We have analyzed the identifiability of time-lag parameters in nonlinear delay systems using an algebraic framework. The identifiability is determined by the form of the system's input-output representation. The values of the time lags can be found directly from the input-output equations, if these can be obtained explicitly. Linear-algebraic criteria are formulated to decide the identifiability of the delay parameters when explicit computation of the input-output relations is not possible.
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- Anguelova, Milena, 1978, et al.
(författare)
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Minimal output sets for identifiability
- 2012
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564.
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Tidskriftsartikel (refereegranskat)abstract
- Ordinary differential equation models in biology often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not uniquely structurally identifiable with the given set of outputs selected as measurements. In designing an experiment for the purpose of parameter estimation, given a set of feasible but resource-consuming measurements, it is useful to know which ones must be included in order to obtain an identifiable system, or whether the system is unidentifiable from the feasible measurement set. We have developed an algorithm that, from a user-provided set of variables and parameters or functions of them assumed to be measurable or known, determines all subsets that when used as outputs give a locally structurally identifiable system and are such that any output set for which the system is structurally identifiable must contain at least one of the calculated subsets. The algorithm has been implemented in Mathematica and shown to be feasible and efficient. We have successfully applied it in the analysis of large signalling pathway models from the literat
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- Anguelova, Milena, 1978
(författare)
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Observability and identifiability of nonlinear systems with applications in biology
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns the properties of observability and identifiability of nonlinear systems. It consists of two parts, the first dealing with systems of ordinary differential equations and the second with delay-differential equations with discrete time delays. The first part presents a review of two different approaches to study the observability of nonlinear ODE-systems found in literature. The differential-geometric and algebraic approaches both lead to the so-called rank test where the observability of a control system is determined by calculating the dimension of the space spanned by gradients of the time-derivatives of its output functions. We show that for analytic systems affine in the input variables, the number of time-derivatives of the output that have to be considered in the rank test is limited by the number of state variables. Parameter identifiability is a special case of the observability problem. A case study is presented in which the parameter identifiability of a previously published kinetic model for the metabolism of S. cerevisiae (baker's yeast) has been analysed. The results show that some of the model parameters cannot be identified from any set of experimental data. The general features of kinetic models of metabolism are examined and shown to allow a simplified identifiability analysis, where all sources of structural unidentifiability are to be found in single reaction rate expressions. We show how the assumption of an algebraic relation between concentrations in metabolic models can cause parameters to be unidentifiable. The second part concerning delay systems begins by an introduction to the algebraic framework of modules over noncommutative rings. We then present both previously published and new results on the problem of observability. New results are shown on the problems of state elimination and characterisation of the identifiability of time-lag parameters. Their identifiability is determined by the form of the system's input-output representation. Linear-algebraic criteria are formulated to decide the identifiability of the delay parameters which eliminate the need for explicit computation of the input-output equations. The criteria are applied in the analysis of biological models from the literature.
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- Anguelova, Milena, 1978, et al.
(författare)
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On analytic and algebraic observability of nonlinear delay systems
- 2010
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098. ; 46:4, s. 682-686
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Tidskriftsartikel (refereegranskat)abstract
- The observability of nonlinear delay systems has previously been defined in an algebraic setting by a rank condition on modules over noncommutative rings. We introduce an analytic definition of observability to ensure the local uniqueness of state and initial conditions that correspond to a given input-output behaviour. It is shown that an algebraically observable delay system can be reformulated as a system of ordinary differential equations. Analytic observability is then decided by the local uniqueness of solutions to a boundary value problem for this ODE system. (C) 2010 Elsevier Ltd. All rights reserved.
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| 10. |
- Anguelova, Milena, 1978, et al.
(författare)
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State elimination and identifiability of the delay parameter for nonlinear time-delay systems
- 2008
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098. ; 44:5, s. 1373-1378
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Tidskriftsartikel (refereegranskat)abstract
- The identifiability of the delay parameter for nonlinear systems with a single constant time delay is analyzed. We show the existence of input–output equations and relate the identifiability of the delay parameter to their form. Explicit criteria based on rank calculations are formulated. The identifiability of the delay parameter is shown not to be directly related to the well-characterized identifiability/observability of the other system parameters/states.
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