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Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique

机译：基于多项式混沌，Voronoi单元和降维技术的结构可靠性分析

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摘要

Polynomial chaos expansions (PCEs) has been widely used to construct meta-models for structural reliability analysis. The computational effort of classical PCEs is unaffordable as the required number of deterministic model analyses grows exponentially with the dimension. Alternatively, the sparse PCEs are always built to alleviate this problem. This paper proposes an efficient method, which combines the sparse PCE with a novel unequal-weighted sampling strategy, i.e. Voronoi cells and the dimension reduction technique for structural reliability analysis. The unequal-weighted sampling strategy could converge fast to the ultimate goal of sequentially building a sparse PCE. Besides, when the dimension is high, the sliced inverse regression technique is employed to convert the original high-dimensional problem to a low-dimensional one. Then, a stepwise weighted regression method is involved to automatically determine the significant terms of the PCE and discard the insignificant ones for the reduced model. In this regard, the sparsity of the basis, the dimension reduction technique and the fast convergence of unequal-weighted sampling strategy lead to a considerably reduced computational cost. Four numerical examples with a large number of random variables are presented to validate the proposed method. The computational results show that the proposed method can establish fairly accurate meta-models for structural reliability assessment with low computational effort.
机译：多项式混沌扩展（PCE）已被广泛用于构造用于结构可靠性分析的元模型。由于所需的确定性模型分析数量随维数呈指数增长，因此经典PCE的计算工作量负担不起。或者，总是构建稀疏的PCE来缓解此问题。本文提出了一种有效的方法，该方法将稀疏PCE与新颖的不等权抽样策略（即Voronoi单元）和降维技术相结合来进行结构可靠性分析。不等权抽样策略可以快速收敛到依次构建稀疏PCE的最终目标。此外，当维数较高时，采用切片逆回归技术将原始的高维问题转换为低维问题。然后，采用逐步加权回归方法来自动确定PCE的有效项，并为简化模型丢弃无关紧要的项。在这方面，基础的稀疏性，降维技术和不等权抽样策略的快速收敛导致计算成本大大降低。给出了带有大量随机变量的四个数值示例，以验证所提出的方法。计算结果表明，所提出的方法能够以较低的计算量建立较为准确的结构可靠性评估元模型。

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