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中文摘要：
结构失效概率为设计参数的函数的求解是可靠性优化中的关键问题。提出一种失效概率函数的高效求解方法及一种新的可靠性度量指标,它为失效概率函数在分布参数空间上的统计特征值。所提方法的主要思路是采用条件概率模拟及三阶最大熵法来求解失效概率函数。条件概率模拟法是引入中间失效域,将所求失效概率转化成条件概率比值与中间失效域的概率的乘积形式,并通过两次马尔科夫链模拟分别对失效域及中间失效域的模拟来得到条件概率的比值。中间失效域为线性形式,其失效概率可容易求得。此外还采用三阶最大熵法来得到失效域样本的条件密度分布,最终得到所求的失效概率函数。结合算例探讨所提方法的精度、效率和适用性,结果表明所提的求解方法在确保精度的情况下具有较高的效率,在工程上是可行的。
英文摘要：
The solution of the failure probability as a function of the distribution parameters is the key problem in reliability-based optimization.A novel method is proposed to obtain the failure probability function and a new reliability measure,which is the statistics characteristic value of the failure probability function.The key idea of the proposed method is using the conditional probability Markov chain simulation and the third order maximum entropy method to obtain the failure probability function.The conditional probability Markov chain simulation firstly transforms the failure probability into the product of a feature ratio factor and the probability of an introduced linear failure region,and then Markov chain algorithm is adopted to calculate the ratio factor by directly simulating the samples of the failure regions,the probability of the introduced linear failure region can be calculated easily.The third order maximum entropy method is implemented to estimate the conditional density function based on failure samples and obtain the failure probability function finally.The accuracy,efficiency and applicability of the proposed method are demonstrated by several examples.The results show that the proposed method can efficiently estimate the failure probability with high accuracy.The proposed method should be valuable for reliability-based optimization and reliability sensitivity analysis.
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