Jasdeep Singh Mandur, Department of Chemical Engineering, University of Waterloo
Robust Optimization of Chemical Processes Based on Bayesian Uncertainty
In this talk, a computationally efficient algorithm for solving a robust optimization problem when the description of parametric uncertainty is obtained using the Bayes’ Theorem will be discussed. In the Bayesian framework, the major computational time in the calculation of posterior distribution is spent in the calculation of the likelihood function, which can be improved significantly y using an approximation of model. To this end, an adaptive approach based on multi-resolution analysis (MRA) is proposed that progressively refines the approximation of the model in high probability regions of the parameter space. At each resolution level, the Kullback-Leibler divergence is used to select the parameter regions where the change in posterior 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 on 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.