Response CDF sensitivity and its solution based on sparse grid integration

The sensitivity of the cumulative distribution function (CDF) of the response with respect to the input parameters is studied in this work, to quantify how the model output is affected by input uncertainty. To solve the response CDF sensitivity more efficiently, a novel method based on the sparse grid integration (SGI) is proposed. The response CDF sensitivity is transformed into expressions involving probability moments, which can be efficiently estimated by the SGI technique. Once the response CDF sensitivity at one percentile level of the response is obtained, the sensitivity values at any other percentile level can be immediately obtained with no further call to the performance function. The proposed method finds a good balance between the computational burden and accuracy, and is applicable for engineering problems involving implicit performance functions. The characteristics and effectiveness of the proposed method are demonstrated by several engineering examples. Discussions on these examples have also validated the significance of the response CDF sensitivity for the purpose of variable screening and ranking.