Sparse grid integration based solutions for moment-independent importance measures

• Discussions on two moment-independent importance measures.
• Review on the sparse grid integration (SGI) technique.
• Propose a new method based on SGI to solve the two importance measures.
• Efficiency and accuracy of the proposed method have been proved.

Different importance measures exist in the literature, aiming to quantify the contributions of model inputs to the output uncertainty. Among them, the moment-independent importance measures consider the entire model output without dependence on any of its particular moments (e.g., variance), and have attracted growing attention among both academics and practitioners. However, until now robust and efficient computational methods for moment-independent importance measures are unavailable in the literature. To properly address this issue, a new computational method based on sparse grid integration (SGI) is proposed to perform moment-independent importance analysis in an efficient framework. In the proposed method, SGI is combined with the moment method to obtain the conditional and unconditional distributions of the model output, which are further used to estimate the moment-independent importance measures. The proposed method makes full use of the advantages of the SGI technique, and is easy to implement. Numerical and engineering examples are studied in this work and the results have demonstrated that the proposed method is feasible and applicable for practical use.