Uncertainty quantification for chromatography model parameters by Bayesian inference using sequential Monte Carlo method

Yamamoto, Yota; Yajima, Tomoyuki; Kawajiri, Yoshiaki

doi:10.1016/j.cherd.2021.09.003

Cited by 18 publications

(10 citation statements)

References 39 publications

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“…Yamamoto; Yajima; Kawajiri (2021) proposed a low computational effort Monte Carlo-based algorithm for parameter uncertainty estimation for chromatographic processes, such as SMB, taking glucose and fructose resolution as a case study. 30 Grosfils (2009) and Grosfils et al (2007Grosfils et al ( , 2010, in turn, developed pioneer works of uncertainty analysis for batch experiments in the adsorption field. 3,22,31 The work proposed herein deepens the subject by adding data reconciliation to SMB parameter estimation, model topology evaluation, optimization of the number of experiments, and estimability analysis without a need for available system knowledge such as suitable AIE, minimum number of experiments, and best operating conditions.…”

Section: Introductionmentioning

confidence: 99%

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Santos,

Rebello,

Prudente

et al. 2023

Ind. Eng. Chem. Res.

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The simulated moving bed (SMB) is a widely recognized technique for the resolution of several high-value-added compounds, and its mathematical modeling plays a crucial role in predicting its behavior. However, modeling can be challenging as it needs parameter estimation and topology definition, especially for such complex systems. SMB modeling might incorporate different adsorption isotherm equations (AIEs), which might better represent the behavior of a certain mixture to be separated. This work proposes two methodologies for SMB modeling and AIE selection relying on minimal system knowledge that can provide a representative model by a global parameter estimation instead of the traditional "Step by Step" approach. The first methodology proposes an architecture for global parameter estimation that encompasses the screening of the most suitable AIE in the lower level and the definition of the minimum number of experiments necessary for model identification in the upper level. In the second methodology, an extended generic isotherm, a combination of AIE, is formulated; and an estimability analysis is carried out to determine the estimable parameters. Both methodologies apply Latin Hypercube Sampling (LHS) for the design of experiments and emulation of a real unit by incorporating noise in the experimental data under a Gaussian error distribution. Moreover, uncertainty evaluation and data reconciliation are performed to enhance the robustness, reliability, and precision of the proposed approaches. The methodologies are validated by considering experimental data from the literature, apart from the LHS-generated samples, and are subject to cross-validations. Finally, the two methodologies are compared, with the first methodology demonstrating a superior performance for the case study. This work contributes to the advancement of SMB modeling, providing valuable tools for parameter estimation and AIE selection.

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Section: Introductionmentioning

confidence: 99%

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Santos,

Rebello,

Prudente

et al. 2023

Ind. Eng. Chem. Res.

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“…In recent years, UQ based on Bayesian statistics has been used in various areas of chemical engineering. [21,22] In particular, Kalyanaraman et al [22] quantified the uncertainty of the model parameters for the gas adsorption process using hollow fiber membrane adsorbent. To date, however, there has not been a study on modeling the gas adsorption process of flexible MOFs quantifying the uncertainty of the model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…[23,24] Bayesian approaches have been reported in many fields [23] including medicine and biology, as well as chemical engineering. [25][26][27] Recently, applications to a CO 2 adsorption process [22] and a liquid chromatographic process [21] have been reported.…”

Section: Introductionmentioning

confidence: 99%

Modeling, parameter estimation, and uncertainty quantification for CO₂ adsorption process using flexible metal–organic frameworks by Bayesian Monte Carlo methods

Sugimoto

Takakura

Fujiki

et al. 2023

J Adv Manuf & Process

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Flexible metal–organic frameworks (flexible MOFs) are considered promising adsorbents for CO2 capture, some of which have sigmoidal isotherm shapes that allow adsorption and desorption operations within a narrow partial pressure range. Nevertheless, modeling of adsorption processes employing flexible MOFs remains a challenge due to the unique isotherm shapes and kinetics. In this work, a Bayesian estimation framework is applied sequentially to handle two experimental data sets: isotherm and breakthrough measurements. The computational challenge for estimating the isotherm and kinetic parameters from the isotherm measurements and breakthrough experiments is resolved by Markov chain and sequential Monte Carlo methods. The uncertainties of the model parameters are obtained as probability distributions.

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“…Some of the popularly used acquisition functions are expected improvement (EI), maximum probability improvement (MPI), lower confidence bound (LCB), etc. Bayesian optimization is becoming popular in process optimization as well, for instance, multiobjective optimization based on the optimal design of the reactor using CFD data, , optimization-based design and optimization of toluene di-isocyanate (TDI) reactors, robust optimization with uncertainty quantification, development of data-driven decision-making systems for chemical synthesis, , optimization of process parameters for the conversion of a mixture of waste terpenes to p -cymene, process design, and an optimized process model built by implying aspen plus . The multiobjective optimization for maximizing methanol production and reducing carbon emission uses the genetic algorithm .…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Bayesian Optimization Framework for the Synthesis of Methanol from Syngas Using Interpretable Gaussian Process Models

et al. 2022

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Methanol production has gained considerable interest on the laboratory and industrial scale as it is a renewable fuel and an excellent hydrogen energy storehouse. The formation of synthesis gas (CO/H 2 ) and the conversion of synthesis gas to methanol are the two basic catalytic processes used in methanol production. Machine learning (ML) approaches have recently emerged as powerful tools in reaction informatics. Inspired by these, we employ Gaussian process regression (GPR) to the model conversion of carbon monoxide (CO) and selectivity of the methanol product using data sets obtained from experimental investigations to capture uncertainty in prediction values. The results indicate that the proposed GPR model can accurately predict CO conversion and methanol selectivity as compared to other ML models. Further, the factors that influence the predictions are identified from the best GPR model employing "Shapley Additive exPlanations" (SHAP). After interpretation, the essential input features are found to be the inlet mole fraction of CO (Y(CO, in)) and the net inlet flow rate (Fin(nL/min)) for our best prediction GPR models, irrespective of our data sets. These interpretable models are employed for Bayesian optimization in a weighted multiobjective framework to obtain the optimal operating points, namely, maximization of both selectivity and conversion.

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Uncertainty quantification for chromatography model parameters by Bayesian inference using sequential Monte Carlo method

Cited by 18 publications

References 39 publications

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Modeling, parameter estimation, and uncertainty quantification for CO₂ adsorption process using flexible metal–organic frameworks by Bayesian Monte Carlo methods

Multiobjective Bayesian Optimization Framework for the Synthesis of Methanol from Syngas Using Interpretable Gaussian Process Models

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Uncertainty quantification for chromatography model parameters by Bayesian inference using sequential Monte Carlo method

Cited by 18 publications

References 39 publications

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

Modeling, parameter estimation, and uncertainty quantification for CO2 adsorption process using flexible metal–organic frameworks by Bayesian Monte Carlo methods

Multiobjective Bayesian Optimization Framework for the Synthesis of Methanol from Syngas Using Interpretable Gaussian Process Models

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Modeling, parameter estimation, and uncertainty quantification for CO₂ adsorption process using flexible metal–organic frameworks by Bayesian Monte Carlo methods