Importance measure analysis with epistemic uncertainty and its moving least squares solution

For the structural systems with both epistemic and aleatory uncertainties, in order to analyze the effect of the epistemic uncertainty on the safety of the systems, a variance based importance measure of failure probability is constructed. Due to the large computational cost of the proposed measure, a novel moving least squares (MLS) based method is employed. By fitting the relationship of parameters and failure probability with moving least squares strategy, the conditional failure probability can be obtained conveniently, then the corresponding importance measure can be calculated. Compared with Sobol's method for the variance based importance measure, the proposed method is more efficient with sufficient accuracy. The Ishigami function is used to test the efficiency of the proposed method. Then the proposed importance measure is used in two engineering applications, including a roof truss and a riveting process.