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Parameter identification using moment of velocity.

ABSTRACT: Many physical systems can be adequately modelled using a second-order approximation. Thus, the problem of system identification often reduces to the problem of estimating the position of a single pair of complex-conjugate poles. This paper presents a convenient but approximate technique for the estimation of the position of a single pair of complex-conjugate poles, using the moment of velocity (MoV). The MoV is a Hilbert transform based signal processing tool that addresses the shortcomings of instantaneous frequency. We demonstrate that the MoV can be employed for parameter identification of a dynamical system. We estimate the damping coefficient and oscillation frequency via MoV of the impulse response.

SUBMITTER: Dorraki M

PROVIDER: S-EPMC6894592 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature

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Parameter identification using moment of velocity.

Dorraki M M Islam M S MS Allison A A Abbott D D

Royal Society open science 20191113 11

Many physical systems can be adequately modelled using a second-order approximation. Thus, the problem of system identification often reduces to the problem of estimating the position of a single pair of complex-conjugate poles. This paper presents a convenient but approximate technique for the estimation of the position of a single pair of complex-conjugate poles, using the moment of velocity (MoV). The MoV is a Hilbert transform based signal processing tool that addresses the shortcomings of i ...[more]

PMID: 31827825

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Project description:The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. Based on the chemical master equation we furthermore derive closed systems of parameter dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. We demonstrate the potential of moment fitting for parameter inference by means of illustrative stochastic biological models from the literature and address topics for future research.

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Parameter identification using moment of velocity.

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Parameter identification using moment of velocity.

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