Journal ArticleDOI
Selection of optimal parameter set using estimability analysis and MSE-based model-selection criterion
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In this article, a mean squared error (MSE)-based model selection criterion is used to determine the optimal number of parameters to estimate from the ranked parameter list, so that the most reliable model predictions can be obtained.Abstract:
Parameter estimation in complex mathematical models is difficult, especially when there are too many unknown parameters to estimate, and the available data for parameter estimation are limited. Estimability analysis ranks parameters from most estimable to least estimable based on the model structure, uncertainties in initial parameter guesses, measurement uncertainties, and experimental settings. Difficulties associated with poor numerical conditioning are avoided by only estimating those parameters that are most estimable. The remaining parameters are left at their initial values or can be removed from the model via simplification. In this paper, a mean squared error (MSE)-based model-selection criterion is used to determine the optimal number of parameters to estimate from the ranked parameter list, so that the most reliable model predictions can be obtained. This methodology is illustrated using a dynamic chemical reactor model.read more
Citations
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Nonlinear modeling, estimation and predictive control in APMonitor
TL;DR: This paper describes nonlinear methods in model building, dynamic data reconciliation, and dynamic optimization that are inspired by researchers and motivated by industrial applications and a new formulation of the l1-norm objective with a dead-band for estimation and control.
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Mathematical modelling of chemical processes—obtaining the best model predictions and parameter estimates using identifiability and estimability procedures
TL;DR: In this article, the authors reviewed techniques for assessing identifiability and estimability, as well as techniques for estimating a reduced number of parameters can lead to better model predictions with lower mean squared error (MSE).
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Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design
TL;DR: This contribution provides a tutorial review on methods for identifiability analysis, regularization techniques and optimal experimental design, and a guideline for the analysis and classification of nonlinear ill-posed problems to detect practical identifiable problems.
Journal ArticleDOI
Mean-Squared-Error Methods for Selecting Optimal Parameter Subsets for Estimation
TL;DR: In this paper, an orthogonalization algorithm combined with a mean squared error (MSE) based selection criterion has been used to rank parameters from most to least estimable and to determine the parameter subset that should be estimated to obtain the best predictions.
Journal ArticleDOI
Model-based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio-ethanol production.
TL;DR: The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space, and it is shown by a cross‐validation that using the identified parameters, the model is still able to predict the experimental data properly.
References
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Cross-Validatory Choice and Assessment of Statistical Predictions
TL;DR: In this article, a generalized form of the cross-validation criterion is applied to the choice and assessment of prediction using the data-analytic concept of a prescription, and examples used to illustrate the application are drawn from the problem areas of univariate estimation, linear regression and analysis of variance.
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Nonlinear Regression Analysis and Its Applications
Douglas M. Bates,Donald G. Watts +1 more
TL;DR: This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares.
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A Biometrics Invited Paper. The Analysis and Selection of Variables in Linear Regression
Journal ArticleDOI
Practical identifiability of ASM2d parameters—systematic selection and tuning of parameter subsets
TL;DR: A more systematic approach based on parameter identifiability analysis of parameter subsets is applied and it is demonstrated as to how these measures can be used to identify the most important model parameters and to analyze their interdependencies.