An efficient approximate optimization algorithm and its application to non-probabilistic reliability importance measures

There are inevitably a large number of uncertainties in the actual engineering structures. How to measure the degree of influence of the uncertainty of input variables on structural response is an important issue in structural design. Global sensitivity analysis is an effective means of addressing this problem, in which, the non-probabilistic reliability sensitivity analysis method has received more attention because it is not restricted by the distribution type of random variables. However, the non-probabilistic importance analysis method requires optimization analysis to obtain the extreme values of the performance function, resulting in its application in practical engineering problems being somewhat limited. To address this problem, this paper firstly proposed an efficient optimization method based on the high-dimensional model decomposition and Taylor expansion series combined with the quadratic function; Secondly, the non-probabilistic reliability importance analysis method is improved based on the proposed optimization method; Finally, two numerical cases are utilized to illustrate the accuracy and efficiency of the proposed method, and an engineering example is used to illustrate the engineering practicality of the proposed method. It was found that regardless of the value of the safety threshold, it affects only the non-probability reliability indicators and has little effect on the magnitude of the non-probability reliability importance indicators and the order of importance of the parameters.