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.

中文翻译：

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一种基于权重指数的结构不确定性量化多维概率空间均匀划分技术


准确有效地实现工程结构的不确定性量化是一个具有挑战性的问题。直接概率积分法（DPIM）为解决这一问题提供了有效途径。然而，通过 DPIM 的 Voronoi 单元的关键分区技术需要多维概率空间的计算负担。此外，由于代表点分布的不均匀性，采用Voronoi单元划分技术（DPIM-Voronoi）获得多维概率空间结构的响应概率密度函数（PDF）的DPIM精度仍有待提高。为此，本研究提出了一种基于权重指数的均匀划分技术。该技术可以生成均匀分布的代表点，并使用代表区域的权重指数计算它们的分配概率。这一特性保证了代表点能够以高度均匀的方式填充概率空间，避免了原始Voronoi单元划分技术中蒙特卡罗模拟分配概率的耗时计算过程。基于所提出的技术，开发了具有基于权重索引的均匀分区技术的DPIM（DPIM-WU）。与DPIM-Voronoi相比，DPIM-WU的优点包括：（1）提高了多维概率空间结构的响应PDF的计算精度，特别是在尾部区域，从而提高了动力可靠度的精度； (2)显着降低计算成本，多维概率空间的划分过程所需的计算机内存最少； (3)增强对代表点数量的鲁棒性。 通过对五层建筑、干摩擦系统、圆柱体结构以及邻近冲击运动建筑等四个典型算例的随机响应和动态可靠性分析，验证了这些优点。值得注意的是，在相邻建筑物的随机冲击响应分析中，随着结构参数变异系数的减小，会出现随机 P 分岔。