Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

Abstract

This paper introduces innovative sensitivity indices based on Cliff's Delta for global sensitivity analysis of structural reliability. These indices build on Sobol's method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff's Delta, originally for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff's Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff's Delta​, exhibit properties analogous to those in Sobol's sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a comprehensive framework for evaluating the contributions of input variables and their interactions on structural reliability. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff's Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff's Delta is a disadvantage. Future research should optimize computational demands, especially for small Pf​, where the inner loop may often be unnecessary.