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.