An enhanced unified uncertainty analysis approach based on first order reliability method with single‐level optimization

In engineering, there exist both aleatory uncertainties due to the inherent variation of the physical system and its operational environment, and epistemic uncertainties due to lack of knowledge and which can be reduced with the collection of more data. To analyze the uncertain distribution of the system performance under both aleatory and epistemic uncertainties, combined probability and evidence theory can be employed to quantify the compound effects of the mixed uncertainties. The existing First Order Reliability Method (FORM) based Unified Uncertainty Analysis (UUA) approach nests the optimization based interval analysis in the improved Hasofer–Lind–Rackwitz–Fiessler (iHLRF) algorithm based Most Probable Point (MPP) searching procedure, which is computationally inhibitive for complex systems and may encounter convergence problem as well. Therefore, in this paper it is proposed to use general optimization solvers to search MPP in the outer loop and then reformulate the double-loop optimization problem into an equivalent single-level optimization (SLO) problem, so as to simplify the uncertainty analysis process, improve the robustness of the algorithm, and alleviate the computational complexity. The effectiveness and efficiency of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.