Robust optimization of chemical processes using Bayesian description of parametric uncertainty

• Robust optimization problem is solved using Bayesian uncertainty in the parameters.
• An adaptive approach based on multi-resolution is proposed to approximate the model.
• PC expansions are used to propagate parametric uncertainty into objective function.
• Fed-batch example is used to illustrate the computational efficiency of the approach.

This paper presents a computationally efficient algorithm for solving a robust optimization problem when the description of parametric uncertainty is obtained using the Bayes’ Theorem. In the Bayesian framework, the calculation of the probability distribution requires a large number of model runs. To this end, an approach based on multi-resolution analysis (MRA) is proposed to approximate the model with higher accuracy in the regions of parameter space where the probability is relatively higher. The approach is iterative where at each resolution level, the Kullback–Leibler divergence is used to select the parameter regions where the change in probability distribution is larger than a specified threshold. Then, at the next resolution level, basis functions are added only in these regions, resulting in an adaptive refinement. Once the uncertainty description in the parameters is obtained, an approach based on Polynomial Chaos (PC) expansions is used to propagate the estimated parametric uncertainty into the objective function at each functional evaluation. Since the PC expansion allows computing mean and variances analytically, significant reduction in the computational time, when compared to Monte Carlo sampling, is obtained. A fed-batch process for penicillin production is used as a case study to illustrate the strength of the algorithm both in terms of computational efficiency as well as in terms of accuracy when compared to results obtained with more simplistic (e.g. normal) representations of parametric uncertainty.