A Computational Method for Sensitivity Analysis under Uncertainty

Sensitivity analysis (SA) is an important part in engineering design under the uncertainty to provide valuable information about the probabilistic characteristics of a response. In this paper, the variance-based methods and the cumulative distribution function (CDF)-based sensitivity coefficients were used in sensitivity analysis. The combination of sparse grid stochastic collocation (SC) and the generalized polynomial chaos (gPC) are proposed as a method to perform the sensitivity analysis. The computational method employs the gPC as a high-order representation for random quantities, a stochastic collocation (SC) approach to deal with complex/implicit response functions, and sparse grid to use a reduced set of samples. It can reduce the computational cost associated with uncertainty assessment without much sacrifice on the optimum solution. The effectiveness is demonstrated in two numerical examples. KeywordsGeneralized Polynomial Chaos; Sensitivity Analysis; Stochastic Collocation; Sensitivity Coefficient; Uncertainty