Dimensional reduction technique-based maximum entropy principle method for safety degree analysis under twofold random uncertainty

A modified failure chance measure (FCM) was proposed to assess the safety degree of structures under the influence of twofold random uncertainty. This uncertainty arises from random inputs with random distribution parameters. The aim of this paper is to effectively evaluate the safety degree of structures in such conditions. This paper introduces a method named dimensional reduction technique-based maximum entropy principle to address the issue at hand. The proposed method utilizes maximum entropy principle method to efficiently approach optimal probability density characteristics while adhering to the constraints imposed by fractional moments. Additionally, the dimensional reduction strategy is employed to estimate fractional moments, resulting in a linear increase in computational cost with respect to the dimensionality. The primary contribution of this work involves the detailed decoupling of the double-uncertainty analysis used to estimate FCM into a single-uncertainty analysis. This approach allows for the innovative re-use of the same group integral grid points to estimate different fractional moments required for solving FCM. The results of applying the proposed method to solve FCM under acceptable accuracy demonstrate that the number of evaluations required for the performance function can be reduced to less than 100 when the uncertainty dimensionality is limited to 20. This finding confirms the high efficiency of the proposed method for solving FCM.