Real-time adaptive input design for the determination of competitive adsorption isotherms in liquid chromatography

Barz, Tilman; López, C C Diana; Bournazou, Mariano Nicolás Cruz; Körkel, Stefan; Walter, Sebastian F.

doi:10.1016/j.compchemeng.2016.07.009

Cited by 18 publications

(16 citation statements)

References 45 publications

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“…Equations (14) and (16) are exact for monomials of up to degrees five and three [33]. Thus, in what follows, we use the terms PEM5 and PEM3 to distinguish between the two PEM approximation schemes.…”

Section: Point Estimate Methodsmentioning

confidence: 99%

“…Moreover, robustification against model parameter uncertainties further complicates the problem, as statistical quantities must be considered when solving the underlying optimization problem. In addition to the actual MBDoE optimization framework and data acquisition, recent studies have shown that a well-posed parameter identification and model selection problem is equally important [12][13][14]. In this context, the consideration of input residuals in parameter estimation beyond the classical approach of output residuals has drawn attention in the literature [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…An essential problem with all mathematical models and model-based design concepts, including MBDoE, is the uncertainty in model parameters. To ensure reliable inferences, parametric uncertainty should be taken into account in the MBDoE approach [6,14,25,26]. In general, probability-based concepts have attracted considerable attention in robust optimization.…”

Section: Introductionmentioning

confidence: 99%

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Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Schulze

Schenkendorf

2020

Processes

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Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

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Section: Point Estimate Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Schulze

Schenkendorf

2020

Processes

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“…A number of regularization techniques were proposed to solve ill‐conditioned parameter estimation and experimental design problems . Regularization involves the introduction of a bias in the parameter estimates with the aim of reducing their variance and, concomitantly, reducing the condition number of the problem .…”

Section: Introductionmentioning

confidence: 99%

“…A number of regularization techniques were proposed to solve ill-conditioned parameter estimation and experimental design problems [9 -13]. Regularization involves the introduction of a bias in the parameter estimates with the aim of reducing their variance and, concomitantly, reducing the condition number of the problem [10]. Popular regularization techniques are i) the Tikhonov regularization [12,13], ii) the truncated singular value decomposition [9,12], and iii) the parameter subset selection [9,11,12].…”

Section: Introductionmentioning

confidence: 99%

On the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification

Quaglio

Waldron

Pankajakshan

et al. 2019

Chemie Ingenieur Technik

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Parameter estimation algorithms integrated in automated platforms for kinetic model identification are required to solve two optimization problems: i) a parameter estimation problem given the available samples; ii) a model‐based design of experiments problem to select the conditions for collecting future samples. These problems may be ill‐posed, leading to numerical failures when optimization routines are applied. In this work, an approach of online reparametrization is introduced to enhance the robustness of model identification algorithms towards ill‐posed parameter estimation problems.

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Pyomo.DOE: An open‐source package for model‐based design of experiments in Python

Wang

Dowling

2022

AIChE Journal

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Predictive mathematical models are a cornerstone of science and engineering. Yet selecting, calibrating, and validating said science‐based models often remains an art in practice. Model‐based design of experiments (MBDoE) provides a systematic framework to maximize information gain from experiments while minimizing time and resource costs. But MBDoE remains limited to niche application areas, in part because practitioners must integrate expertise in statistics, computational optimization, and modeling. To help reduce this barrier, we introduce Pyomo.DOE, an open‐source package for MBDoE. Pyomo.DOE uses a nonlinear sensitivity analysis code k_aug to quickly approximate the Fisher information matrix and leverages a new stochastic programming abstraction. We demonstrate Pyomo.DOE with the first application of MBDoE to fixed‐bed breakthrough experiments, which highlights the power of Pyomo.DOE to quantify the value of experimental modifications a priori for large‐scale partial differential‐algebraic equation (PDAE) models. We also provide a mathematical primer on MBDoE targeted at general chemical engineers.

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Real-time adaptive input design for the determination of competitive adsorption isotherms in liquid chromatography

Cited by 18 publications

References 45 publications

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

On the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification

Pyomo.DOE: An open‐source package for model‐based design of experiments in Python

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