A novel estimation method for failure-probability-based-sensitivity by conditional probability theorem

By the average absolute difference between the unconditional failure probability and the conditional one on fixing an input at its realization, the failure-probability-based-sensitivity (FP-S) is defined to quantify the effect of the fixed input on the failure probability, which provides important information for reliability-based design optimization of the structure. Among the estimation methods for FP-S, the Bayes theorem-based methods are competitive, but the conditional probability density function (PDF) should be estimated in this type method. To alleviate the computational complexity of estimating conditional PDF, a novel FP-S estimation method is proposed by use of the conditional probability theorem. In the proposed method, the conditional failure probability on fixing the input at its realization is approximated by the conditional failure probability on fixing the input in a small interval, in which the conditional probability theorem of the random event can be used to transform FP-S as estimations of a series of probabilities, and they can be simultaneously completed by a numerical simulation for estimating the unconditional failure probability. For ensuring the precision of the approximation introduced by replacing the realization with the small interval, a selection strategy for the small interval is proposed. Comparing with the competitive Bayes theorem-based estimation for FP-S, the proposed method replaces the conditional PDF estimation with the conditional probability estimation, which greatly reduces the computational complexity and improves the accuracy of the FP-S estimation. By combining with the adaptive kriging surrogate model, the efficiency of the proposed method can be drastically improved, and the presented examples demonstrate the efficiency and accuracy of the proposed method.