分析概率输入和模糊状态条件下的广义失效概率函数对于掌握分布参数在其设计域内变化时影响结构可靠性水平的规律至关重要，现有的单层重要抽样算法虽然可以避免直接双层蒙特卡洛要求的重复分析以及高可靠时要求的大容量样本池而带来的高耗时问题，但这类方法仍没有解决高维高可靠场景下构造单层重要抽样密度耗时且抽样效率低的问题。为此，本文构造了一种显式且易于抽样的统一重要抽样密度，并提出了渐进分层聚类的策略，使得所构造的统一重要抽样密度的样本能够覆盖对广义失效概率函数估计贡献大的区域，从而通过降低广义失效概率函数估计的方差来提高计算效率。相对于已有的单层重要抽样法，本文方法的主要创新表现在构造统一重要抽样密度时采用了渐进分层聚类的策略，避免了对附加计算量高的优化算法的依赖，显著地提升了高维高可靠性时探索目标模糊失效域来构造统一重要抽样密度及估计广义失效概率函数的效率，该优越性得到了文中算例的充分验证。
Analyzing generalized failure probability function considering probabilistic inputs and fuzzy state is crucial for capturing how variations in distribution parameters within their design regions affect structural safety levels. The existing single loop importance sampling method can avoid the highly time-consuming problem resulting from redundant reliability analysis and the large sample pool in high reliability requirements for direct double-loop Monte Carlo method. However, this method still cannot handle the time-consuming issues of constructing unified importance sampling density and low sampling efficiency. To address this, this paper constructs an explicit and easy to sample expression of the unified importance sampling density and proposes its progressive stratification strategy, which render the importance samples of constructing unified importance sampling density cover the regions with higher contribution to generalized failure probability, and enhance the computational efficiency by reducing the estimate variance. Compared to the existing single loop importance sampling density method, the main innovation of the proposed method is the progressive stratification strategy of constructing unified importance sampling density, which alleviates the optimization requirement with high additional computational cost, thus enhancing the efficiency of exploring target fuzzy failure domain to construct unified importance sampling density and estimate the generalized failure probability function in high-dimensional and high-reliability scenarios. This superiority is fully validated by the examples presented in this paper.
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