Stochastic engineering simulations using sparse grid collocation method and Kriging based approaches

Abstract

The estimation of probabilistic moments is central to robust design process. Typically one would like to estimate the mean and variance of some performance critical metric such as stress, life, etc., of a component in any engineering system, aiming a robustly optimized design that is less sensitive to the input variations/uncertainties. For complex aerospace engineering systems such as aero-engine, a single numerical simulation of any component can often take a substantial amount of time and few samples can be afforded at which the deterministic simulations can be carried out. Considering the variations in the parameters and performing a large number of simulations on such problems is unrealistic and necessitate the improvement of existing UQ approaches.

In this study, we present the significance of probabilistic moment estimation approaches for uncertainty quantification and its importance in robust design optimization studies. The background for few popular approaches is provided, where emphasis is put on sparse grid collocation method, adaptive sparse grid collocation approach and Kriging based Bayesian approaches.

A non-intrusive multi-point adaptive strategy using sparse grid based collocation design and Kriging based approaches is proposed to reduce the problems arising in high dimensional probabilistic moment estimation studies. The comparison of multi-point adaptive approach with other existing approaches for probabilistic moment estimation in terms of efficiency and accuracy is provided. Further on, the effectiveness of the proposed approach is demonstrated for few mathematical test functions and stochastic structural problems with varying dimensionality and strong interaction among the random variables.

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