A novel weight index-based uniform partition technique of multi-dimensional probability space for structural uncertainty quantification

Abstract

Accurately and efficiently achieving the uncertainty quantification of engineering structures is a challenging issue. The direct probability integral method (DPIM) provides an effective pathway to address this issue. However, the key partition technique via Voronoi cell of DPIM requires a prohibitive computational burden for multi-dimensional probability space. Moreover, due to the distributed nonuniformity of representative points, the accuracy of DPIM with the partition technique via Voronoi cell (DPIM-Voronoi) for obtaining the response probability density function (PDF) of structures with multi-dimensional probability space still needs to be improved. To this end, a novel weight index-based uniform partition technique is proposed in this study. This technique can generate uniformly distributed representative points and calculate their assigned probabilities using the weight indexes of representative regions. This feature ensures that the representative points can fill the probability space in a highly uniform manner, and avoid the resource-consuming calculation process of assigned probability by Monte Carlo simulation in the original partition technique via Voronoi cell. Based on the proposed technique, DPIM with a Weight index-based Uniform partition technique (DPIM-WU) is developed. Compared to DPIM-Voronoi, the advantages of DPIM-WU include: (1) improving the computational accuracy of response PDF for structures with multi-dimensional probability space, especially in the tail region, leading to improved accuracy of the dynamic reliability; (2) remarkably reducing the computational cost, with minimal computer memory required for the partition process of multi-dimensional probability space; (3) enhancing the robustness to the number of representative points. These advantages are verified through the stochastic response and dynamic reliability analyses of four typical examples, including the 5-story buildings, dry friction system, cylinder structure, and adjacent buildings with pounding motion. Notably, in the stochastic pounding response analysis of adjacent buildings, a stochastic P-bifurcation occurs as the coefficient of variation of the structural parameters decreases.