Robust Optimization of Dynamical Systems with Correlated Random Variables using the Point Estimate Method ⁎ ⁎Financial support of Promotionsprogramm “μ-Props” by MWK Niedersachsen is gratefully acknowledged.

Abstract

Robust optimization of dynamical systems requires the proper uncertainty quantification. Monte Carlo simulations and polynomial chaos expansion are frequently used methods for uncertainty quantification and have been applied to a number of problems in process design and optimization. Both methods, however, are either computationally prohibitive for robust optimization or inappropriate for correlated random variables. The aim of this study is to introduce the point estimate method for optimization of dynamical systems with correlated random variables. The point estimate method requires only a few deterministic evaluations of the analyzed process model and estimates the statistical moments for robust optimization. The derived sample points can be adapted to random variables of arbitrary distributions and correlations. The contribution of this paper consists of presenting the point estimate method for correlated random variables in the field of model-based robust process design. The performance of the method is demonstrated with a case study of a continuous tubular reactor.

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