A derivative based sensitivity measure of failure probability in the presence of epistemic and aleatory uncertainties

In order to analyze the effect of the epistemic uncertainty of random variables' distribution parameters on the safety of the structure system, a novel sensitivity measure of the failure probability is constructed by integrating the derivative of failure probability in the parameter space. Compared with the variance based sensitivity index, the new derivative based sensitivity measure can be evaluated with less computational cost. It is noticed that the ranking of the new derivative based sensitivity measure is the same as that of the variance based one. For the problem of the variance based sensitivity index with large computational cost, the standard Sobol's method is employed, and the quasi-Monte Carlo method and double-loop point estimate method are then utilized to compute the derivative based sensitivity measure for comparison. Four examples are employed to demonstrate the reasonability of the proposed sensitivity measure and the efficiency of the proposed method.