结构动力可靠度计算的修正条件反应法

MODIFIED RESPONSE CONDITIONING METHOD FOR STRUCTURAL DYNAMIC RELIABILITY ESTIMATIONS

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。

Subset simulation with splitting is an efficient method for small failure probability estimations ofstructures subjected to random excitation. A nested sequence of failure regions is assumed and offspring trajectories are derived through splitting. For a response conditioning method, a linear response can be used to estimate a nonlinear response, or the response of a single degree-of-freedom structure can be used to estimate the response of a multi-degree-of-freedom structure. A modified response conditioning method is proposed by combining subset simulation with splitting and a response conditioning method. The failure probability formula is developed using the theorem of total probability for the modified method. The non-overlapping bins of a response conditioning method are related to the sets of subset simulation with splitting. Then the failure probability can be expressed through subset simulation with splitting. The computational times of nonlinear structure responses or multi-degree-of-freedom structure responses are decreased obviously. A three DOF linear structure and a single DOF nonlinear structure subjected to random excitations are calculated using the modified response conditioning method. The computational results show that the proposed method is an effective way for dynamic reliability estimations, and is efficient for small failure probabilitv calculations.