Global sensitivity analysis for medium-dimensional structural engineering problems using stochastic collocation

Abstract

For many engineering problems, it is important to know which random input variables have significant influence on relevant outputs, since, for example, these inputs are of special interest in optimisation tasks or their uncertainty can significantly influence the structural reliability. For the identification of influential inputs, sensitivity analyses can be used. Sobol’ indices are an accurate sensitivity measure for non-linear problems. However, for most structural engineering problems with high computing times per model evaluation, standard calculation procedures of Sobol’ indices using random sampling (e.g. Monte Carlo) are conditionally suitable. That is why stochastic expansion methods for the computation of Sobol’ indices have been developed recently. Especially for low-dimensional problems, these methods have the ability to significantly reduce the number of function evaluations compared to standard sampling approaches. In this work, a two-step approach consisting of a meta-model-based dimensional reduction and a subsequent calculation of Sobol’ indices using stochastic collocation is proposed to extend this ability to medium-dimensional engineering problems with arbitrary input distributions. The efficiency of the proposed approach is verified using several analytical examples. More complex applications from the field of wind energy engineering are used to demonstrate the practical relevance and the benefits in, for example, structural reliability engineering.