Nonlinear Systems Fault Diagnosis with Differential Elimination

Zhang, Jia Fan

doi:10.1109/cinc.2009.38

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…For example, computing these input-output relations explicitly is a key step in a so-called differential algebra approach to assessing structural identifiability of a dynamical model [4,39,42,44]. Other application include linearization [24], model selection [27], parameter estimation [19,61], fault diagnosis [35,57], and control [36].…”

Section: Overviewmentioning

confidence: 99%

Differential elimination for dynamical models via projections with applications to structural identifiability

Dong,

Goodbrake,

Harrington

et al. 2021

Preprint

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Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination.We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature.We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before.Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl.

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Section: Overviewmentioning

confidence: 99%

Differential elimination for dynamical models via projections with applications to structural identifiability

Dong,

Goodbrake,

Harrington

et al. 2021

Preprint

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“…Elimination of unknowns for systems of equations of different types, starting from Gaussian elimination for linear systems, is a classical problem. In this paper, we study elimination of unknowns in systems of differential-algebraic equations (DAEs), existing applications of which include combinatorics [1], mathematical analysis of dynamic models [3,9,22,27], and control theory [11,12]. The first theoretical method for elimination of unknowns in systems of DAEs was developed in [36, §67] by Ritt, the founder of differential algebra.…”

Section: Introductionmentioning

confidence: 99%

Bounds for elimination of unknowns in systems of differential-algebraic equations

Ovchinnikov¹,

Pogudin²,

Vo³

2016

Preprint

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Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a problem of general interest. The problem of finding an a priori upper bound for the number of differentiations in elimination of unknowns in a system of differential-algebraic equations (DAEs) is an important challenge, going back to Ritt (1932). The first characterization of this via an asymptotic analysis is due to Grigoriev's result (1989) on quantifier elimination in differential fields, but the challenge still remained.In this paper, we present a new bound, which is a major improvement over the previously known results. We also present a new lower bound, which shows asymptotic tightness of our upper bound in low dimensions, which are frequently occurring in applications. Finally, we discuss applications of our results to designing new algorithms for elimination of unknowns in systems of DAEs.

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Bounds for Elimination of Unknowns in Systems of Differential-Algebraic Equations

Ovchinnikov

Pogudin

2021

International Mathematics Research Notices

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Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a problem of general interest. The problem of finding an a priori upper bound for the number of differentiations in elimination of unknowns in a system of differential-algebraic equations (DAEs) is an important challenge, going back to Ritt (1932). The first characterization of this via an asymptotic analysis is due to Grigoriev’s result (1989) on quantifier elimination in differential fields, but the challenge still remained. In this paper, we present a new bound, which is a major improvement over the previously known results. We also present a new lower bound, which shows asymptotic tightness of our upper bound in low dimensions, which are frequently occurring in applications. Finally, we discuss applications of our results to designing new algorithms for elimination of unknowns in systems of DAEs.

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Nonlinear Systems Fault Diagnosis with Differential Elimination

Cited by 3 publications

References 10 publications

Differential elimination for dynamical models via projections with applications to structural identifiability

Differential elimination for dynamical models via projections with applications to structural identifiability

Bounds for elimination of unknowns in systems of differential-algebraic equations

Bounds for Elimination of Unknowns in Systems of Differential-Algebraic Equations

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