Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations

Murphy, Katherine A.

doi:10.1137/0150060

Cited by 18 publications

(7 citation statements)

References 16 publications

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“…Time-delay systems are increasingly used in numerous application areas that include physiological kinetics [27], population dynamics [28], infectious diseases [29] and so on. The problem of identifying unknown parameters and time delays in time-delay systems has been extensively studied [20,30,31].…”

Section: Introductionmentioning

confidence: 99%

Experimental design suboptimization for the enzyme-catalytic nonlinear time-delay system in microbial batch culture

Shao

Zhang

Feng

et al. 2014

Journal of Process Control

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Section: Introductionmentioning

confidence: 99%

Experimental design suboptimization for the enzyme-catalytic nonlinear time-delay system in microbial batch culture

Shao

Zhang

Feng

et al. 2014

Journal of Process Control

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“…Works on identification of time-delay systems have shown the complexity of the question [3]. As a result, the problem of identifying delays and parameters in time-delay systems has been extensively studied, see, for example, [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Liu

2014

Applied Mathematical Modelling

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a b s t r a c tDeveloping suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a global optimization method is developed to seek the optimal key parameters. Numerical results show that the nonlinear time-delay system can describe the fed-batch fermentation process reasonably.

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“…There have been some investigations (see [16], [19]) which address this difficulty by introducing splines to define the initial values and delay parameters. By carefully matching the nodes of the splines to the locations of the discontinuities, they are able to improve the effectiveness of this approach.…”

Section: ∂S(θ) ∂θmentioning

confidence: 99%

Parameter Estimation for ODEs Using a Cross-Entropy Approach

Wang¹,

Enright²

2013

SIAM J. Sci. Comput.

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Parameter Estimation for ODEs using a Cross-Entropy Approach Bo Wang Master of Science Graduate Department of Computer Science University of Toronto 2012Parameter Estimation for ODEs and DDEs is an important topic in numerical analysis.In this paper, we present a novel approach to address this inverse problem. Cross-entropy algorithms are general algorithm which can be applied to solve global optimization problems. The main steps of cross-entropy methods are first to generate a set of trial samples from a certain distribution, then to update the distribution based on these generated sample trials. To overcome the prohibitive computation of standard cross-entropy algorithms, we develop a modification combining local search techniques. The modified cross-entropy algorithm can speed the convergence rate and improve the accuracy simultaneously. Two different coding schemes (continuous coding and discrete coding) are also introduced. Continuous coding uses a truncated multivariate Gaussian to generate trial samples, while discrete coding reduces the search space to a finite (but dense) subset of the feasible parameter values and uses a Bernoulli distribution to generate the trial samples (which are fixed point approximation of the actual parameters) . Extensive numerical and real experiments are conducted to illustrate the power and advantages of the proposed methods. Compared to other existing state-of-the-art approaches on some benchmark problems for parameter estimation, our methods have three main advantages: 1) They are robust to noise in the data to be fitted; 2) They are not sensitive to the number of observation points (in contrast to most existing approaches) ; 3) The modified versions exhibit faster convergence than the original versions, thus they are more efficient, without sacrificing accuracy.iii

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Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations

Cited by 18 publications

References 16 publications

Experimental design suboptimization for the enzyme-catalytic nonlinear time-delay system in microbial batch culture

Experimental design suboptimization for the enzyme-catalytic nonlinear time-delay system in microbial batch culture

Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Parameter Estimation for ODEs Using a Cross-Entropy Approach

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