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基于反应时程分解的子集模拟法是计算受随机激励作用的结构小失效概率的高效算法,该法将失效域划分为子集序列,通过分解反应时程来生成子集计算所需的样本。条件反应法计算动力可靠度时,通过线性反应来估计非线性反应,或通过单自由度结构的反应来估计多自由度结构的反应。该文将基于反应时程分解的子集模拟法用于条件反应法中,提出修正的条件反应法。该法利用全概率公式得出失效概率的表达式,将条件反应法中互不相交的子集序列与基于反应时程分解的子集模拟法中的子集序列建立关系,利用基于反应时程分解的子集模拟法求解失效概率,大大减少了非线性反应分析的次数或多自由度结构反应的求解次数。应用该文所提方法对受随机激励作用的三自由度线性结构和单自由度非线性结构进行计算,结果表明修正的条件反应法是计算动力可靠度的有效算法,对小失效概率的计算效率较高。
The subset simulation method based on reaction time-history decomposition is an efficient algorithm for calculating the small failure probability of structures under random excitation. This method divides the failure fields into subsets and decomposes the reaction time series to generate the samples needed for subset calculation . When the kinetic reliability is calculated by conditional reaction method, the nonlinear reaction is estimated by the linear reaction or the reaction of the multi-degree-of-freedom structure is estimated by the reaction of the one-degree-freedom structure. In this paper, the sub-set simulation method based on reaction time-history decomposition is used in the condition-reaction method, and a modified conditional reaction method is proposed. The method uses the total probability formula to derive the expression of the failure probability. The disjoint subsets of the conditional reaction method are related to the subsets of subsets simulation based on the reaction time-history decomposition. Based on the reaction time-history Decomposition subset simulation method to solve the failure probability, greatly reducing the number of nonlinear response analysis or multi-degree of freedom structural response to the number of times. The results show that the modified conditional reaction method is an effective algorithm to calculate the dynamic reliability, and the calculation efficiency of the small failure probability Higher.