Reliability computation via a transformed mixed-degree cubature rule and maximum entropy

Based on the maximum entropy method with fractional exponential moments, a new method is proposed for deriving the probability density function of the limit state function for reliability calculation. Since numerical evaluation of fractional exponential moments is of critical significance, a novel transformed mixed-degree cubature rule is developed. First, the integral related to fractional exponential moment evaluation is transformed over the standard normal space, where the cubature rule can be employed for the numerical evaluation. Then, the spherical and radial rules with different degrees are combined to formulate a novel mixed-degree cubature rule, where the sample size only increases linearly with the dimension. To further enhance and improve the precision, a rotational transformation is performed over the samples produced by the mixed-degree cubature rule to obtain a transformed cubature rule, in which a proper angle needs to be specified. A two-step strategy is then put forward to specify the appropriate angle in the transformed mixeddegree cubature rule, where the standard deviations of input variables and Kullback-Leibler divergence are used to formulate the objective functions. The proposed approach is verified via a set of numerical examples involving different types of problems. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

A new method based on the maximum entropy method is proposed for deriving the probability density function of the limit state function in reliability calculation. The method utilizes a transformed mixed-degree cubature rule to enhance numerical evaluation. The approach is verified through numerical examples, demonstrating its effectiveness.