Backward Recursive Method for Structural Reliability Calculation Based on the Universal Generating Function

For structural performance functions with characteristics of multivariable, non-normality, small failure probability and nonlinearity, it is usually difficult to pursue satisfactory accuracy by means of traditional probabilistic methods such as first-order reliability method and second-order reliability method. According to the idea of adaptive subdivision, a backward recursive method based on the universal generating function is suggested for structural reliability calculation. In the sensitive region, the variable space is subdivided partially, the discrete interval length is reduced, and the random variables are discretized nonuniformly and adaptively by the backward recursion operation. Compared with the current method of forward recursion operator and the corresponding similar items merging operation, the backward recursion operator can not only avoid low accuracy owing to subdividing the state combinations in the sensitive region, but avert the high cost of calculation owing to merging state combinations in the nonsensitive region of the variable space as well. Three examples are presented to demonstrate the rationality of the backward recursive algorithm. The results indicate that the accuracy of the proposed method is significantly higher than that of traditional methods, and the computational efficiency of the proposed method meets the engineering requirement. The research work provides a new path for reliability calculation with consideration of complex performance functions.