Optimal constraint-based regularization for parameter estimation problems

Nakama, Caroline S.M.; Roux, G.; Zavala, Ví­ctor M.

doi:10.1016/j.compchemeng.2020.106873

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…Note that the sample size of the neighborhood is selected to be twice the dimensionality of the design space since an ideal neighborhood is supposed to resemble the cross-polytope in the corresponding design space. The rule Equation (19) holds on a precondition n u > 1 without loss of generality.…”

Section: Local Nonlinearitymentioning

confidence: 99%

“…In practice, a variety of parameter regularization techniques are commonly employed to tackle the ill-conditioned estimation problem [18]. For linear cases, regularization using ridge regression, principle component regression or the elastic net approach can effectively stabilize the parameters [19]. These techniques reduce the feasible parameter subspace by adding objective penalization terms or enforcing extra constraints on parameters.…”

Section: Introductionmentioning

confidence: 99%

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Global Model Calibration of High-Temperature Gas-Cooled Reactor Pebble-Bed Module Using an Adaptive Experimental Design

et al. 2023

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The world’s first high-temperature gas-cooled reactor pebble-bed module (HTR-PM) nuclear power plant adopts an innovative reactor type and a modular structure design. Parameter estimation and model calibration are of great significance prior to the implementation of model-based control and optimization. This paper focuses on identifying the thermal hydraulic parameters of HTR-PM over the global operating domain. The process technology and model mechanism of HTR-PM are reviewed. A parameter submodel named global parameter mapping is presented to quantify the relationship between an unknown model parameter and different operating conditions in a data-driven manner. The ideal construction of such a mapping requires reliable estimates, a well-poised sample set and an appropriate global surrogate. An adaptive model calibration scheme is designed to tackle these three issues correspondingly. First, a systematic parameter estimation approach is developed to ensure reliable estimates via heuristic subset selection consisting of estimability analysis and reliability evaluation. To capture the parameter behavior among the multiple experimental conditions and meanwhile reduce the operating cost, an adaptive experimental design is employed to guide condition testing. Experimental conditions are sequentially determined by comprehensively considering the criteria of sampling density, local nonlinearity and parameter uncertainty. Support vector regression is introduced as the global surrogate due to its capability of small-sample learning. Finally, the effectiveness of the model calibration scheme and its application performance in HTR-PM are validated by the simulation results.

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Section: Local Nonlinearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Model Calibration of High-Temperature Gas-Cooled Reactor Pebble-Bed Module Using an Adaptive Experimental Design

et al. 2023

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“…The application of this regularization for linear models is demonstrated in a case study estimating kinetic parameters of enzymatic reactions in steady state. This study, presented in Chapter 9, has been published in the journal Computers & Chemical Engineering (NAKAMA et al, 2020). This regularization approach is also implemented for nonlinear parameter estimation.…”

Section: Regularization Of Parameter Estimation Problems 7 Introductionmentioning

confidence: 99%

Desenvolvimentos de ferramentas matemáticas para modelagem de sistemas biológicos baseados em fluxos metabólicos e estimação de parâmetros de problemas mal condicionados.

Nakama¹

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Mathematical modeling is one of the basis of metabolic engineering, guiding genetic modifications through the study of metabolic fluxes. Stoichiometric models are an important tool to analyze metabolic networks, especially for non-model organisms or during initial analysis, since they linear models and essentially require the stoichiometry matrix and information on reversibility of the reactions as input. They can be used to explore different assumptions and scenarios, and elucidate some properties of the metabolism. Therefore some stoichiometric modeling techniques were implemented in a single stand-alone software and used to study the core metabolism of the bacteria Burkholderia sacchari for polyhydroxyalkanoate production, showing that they are a valuable tool for exploring how metabolisms work and guiding future experiment design. However, cellular metabolism is actually subjected to nonlinear dynamics and, therefore, nonlinear models are better suited to represent more diverse physiological states, which can result in better predictions. Mechanistic models are a class of such models; however, in the metabolic engineering context, all frameworks that have been proposed to estimate the kinetic parameters involved are prone to identifiability issues. Based on this obstacle, an investigation on regularization methods for ill-conditioned parameter estimation problems was conducted. Regularization methods based on the eigenvalue decomposition of the (reduced) Hessian matrix were shown to be optimal for linear parameter estimation, in the sense of reducing parameter variance, and helpful in dealing with nonlinear problems with nearly flat neighborhood around the solution. Moreover, the eigenvector-based regularization in both cases was able to recognize groups of correlated parameters, which allows for better understanding the underlying identifiability issues.

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