Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

The failure probability-based global sensitivity is proposed to evaluate the influence of input variables on the failure probability. But for the problem that the distribution parameters of variables are uncertain due to the lack of data or acknowledgement, if the original failure probability-based global sensitivity is employed to evaluate the influences of different uncertainty sources directly, the computational cost will be prohibitive. To address this issue, this work proposes the novel predictive failure probability (PFP) based on global sensitivity. By separating the overall uncertainty of variables into inherent uncertainty and distribution parameter uncertainty, the PFP can be evaluated by a single loop with equivalent transformation. Then, the PFP based global sensitivities with respect to (w.r.t) the overall uncertainty, inherent uncertainty and distribution parameter uncertainty are proposed, respectively, and their relationships are discussed, which can be used to measure the influences of different uncertainty sources. To compute those global sensitivities efficiently, the Monte Carlo method and Kriging-based method are employed for comparison. Several examples including two numerical examples and three engineering practices are investigated to validate the reasonability and efficiency of the proposed method.