Article2016

Polynomial chaos‐based robust design of systems with probabilistic uncertainties

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Probabilistic and Robust Engineering Design Process Optimization and Integration Advanced Multi-Objective Optimization Algorithms

Abstract

A new algorithm is proposed for the design of nonlinear dynamical systems with probabilistic uncertainties. The dependence of the design objective and constraints on uncertainties is quantified by the polynomial chaos expansions (PCEs), while the relationships between the design parameters and the design objective/constraints are parameterized by Legendre polynomials. In two case studies, the polynomial chaos‐based algorithm reduces the number of system evaluations required by optimization by an order of magnitude. Quantifying the dependence on uncertain parameters via the PCEs and including the quantification in design optimization simultaneously improved the distribution of the performance index and the probability of constraint fulfillment. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3310–3318, 2016

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References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2003Optimization under uncertainty: state-of-the-art and opportunities 1980Small sample sensitivity analysis techniques for computer models.with an application to risk assessment 2008Polynomial chaos expansion for sensitivity analysis 2010A robust optimization approach to closed-loop supply chain network design under uncertainty 2009Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design 2004A review of robust optimal design and its application in dynamics 1997Efficient sampling technique for optimization under uncertainty

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