Parameter estimation in nonlinear chemical and biological processes with unmeasured variables from small data sets

Jang, Seung-Hee; Gopaluni, R. Bhushan

doi:10.1016/j.ces.2011.03.029

Cited by 20 publications

(25 citation statements)

References 44 publications

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“…[52] To address this problem, Varziri et al [25] extended their AMLE methodology, based on a technique developed by Heald and Stark [26] for estimating parameters in timeseries models with unknown noise variance. Varziri et al [25] proposed a two-step optimisation algorithm where u and B are determined in an inner loop, using the objective function in Equation (11) and an assumed value of Q. In the second step (outer loop) Q is updated using the following objective function assuming that u and B are known [25] :…”

Section: Amle Algorithmmentioning

confidence: 99%

“…[11,35] When computing Rðz; z k Þ in Equation (15), it is possible to use v ¼ 1 (i.e. a single term rather than a summation), if X q ðlÞ is replaced by the mode of pðX q ; Y m jzÞ [35] :…”

Section: Em Algorithmmentioning

confidence: 99%

“…[10] In the presence of unmeasured states and missing observations, it is difficult to find a closed form for the likelihood function. [11] Several techniques have been proposed for approximating the likelihood function. Some of these techniques are: simulated maximum likelihood methods [such as Markov Chain Monte Carlo (MCMC) techniques], [11][12][13][14][15][16] expansion of the likelihood function using Hermite polynomial basis functions, [17,18] solving the FokkerPlanck equation numerically [19][20][21] and recursive maximum likelihood parameter estimation using polynomial chaos theory.…”

mentioning

confidence: 99%

“…[12,28,29,[37][38][39][40] In the MCMC methods, a probability density function is numerically approximated by drawing samples from a target density function. [11,18] MCMC methods are effective parameter estimation tools that do not require assumptions about the form of the density functions. These methods asymptotically approximate the EM algorithm with zero error.…”

mentioning

confidence: 99%

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An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

Karimi

McAuley

2013

Can J Chem Eng

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Stochastic terms are included in fundamental dynamic models of chemical processes to account for disturbances, input uncertainties and model mismatch. The resulting equations are called stochastic differential equations (SDEs). An approximate expectation maximisation (AEM) algorithm using B-splines is developed for estimating parameters in SDE models when the magnitude of the disturbances and model mismatch is unknown. The AEM method is evaluated using a two-state nonlinear continuous stirred tank reactor (CSTR) model. [Varziri et al., Can. J. Chem. Eng. 2008; 86: 828]). For the CSTR examples studied, the AEM algorithm provides more accurate estimates of model parameters, unknown initial conditions and disturbance intensities. SDE models and associated parameter estimates obtained using AEM will be helpful to engineers who subsequently implement on-line state estimation and process monitoring schemes because the two types of uncertainties that are considered (i.e. measurement noise and stochastic process disturbances) are consistent with the error structure used in extended Kalman filters.

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Section: Amle Algorithmmentioning

confidence: 99%

Section: Em Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

Karimi

McAuley

2013

Can J Chem Eng

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“…Although no formal definition of the practical identifiability is accepted, a common definition is that the coefficient is practically identifiable if the estimate is considered sufficiently accurate, e.g. if the confidence interval of the estimate is a subset of a predetermined uncertainty region B in the coefficient space [4,5]:…”

Section: Introductionmentioning

confidence: 99%

Effect of the water content measurements on the estimation and identifiability of water diffusion and convection mass transfer coefficients

Mercier

Marcos

Moresoli

et al. 2015

International Journal of Heat and Mass Transfer

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Noise aware parameter estimation in bioprocesses: Using neural network surrogate models with nonuniform data sampling

Weir,

Mathias,

Corbett

et al. 2024

AIChE Journal

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This article demonstrates a parameter estimation technique for bioprocesses that utilizes measurement noise in experimental data to determine credible intervals on parameter estimates, with this information of potential use in prediction, robust control, and optimization. To determine these estimates, the work implements Bayesian inference using nested sampling, presenting an approach to develop neural network‐ (NN) based surrogate models. To address challenges associated with nonuniform sampling of experimental measurements, an NN structure is proposed. The resultant surrogate model is utilized within a Nested Sampling Algorithm that samples possible parameter values from the parameter space and uses the NN to calculate model output for use in the likelihood function based on the joint probability distribution of the noise of output variables. This method is illustrated against simulated data, then with experimental data from a Sartorius fed‐batch bioprocess. Results demonstrate the feasibility of the proposed technique to enable rapid parameter estimation for bioprocesses.

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Parameter estimation in nonlinear chemical and biological processes with unmeasured variables from small data sets

Cited by 20 publications

References 44 publications

An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

Effect of the water content measurements on the estimation and identifiability of water diffusion and convection mass transfer coefficients

Noise aware parameter estimation in bioprocesses: Using neural network surrogate models with nonuniform data sampling

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