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基于对失效域样本的高效马尔可夫链模拟方法和鞍点估计法,提出了一种可快速分析高维小失效概率情况下含非正态变量的非线性极限状态函数的可靠性方法.所提方法在非正态空间中,将所求失效概率转化为线性极限状态函数的失效概率与一个特征比例因子的乘积.线性极限状态函数是通过马尔可夫链模拟非线性极限状态函数失效域中的样本而获得的,它与非线性极限状态函数具有近似相同的设计点.而概率论中的乘法定理是获取特征比例因子的理论依据,它反映了非线性极限状态函数失效概率与线性极限状态函数失效概率的关系.线性极限状态函数的失效概率可以由鞍点估计法求得,而特征比例因子可以由马尔可夫链快速模拟线性与非线性失效域中的样本而近似算得.定性分析和定量的算例对比分析表明,所提算法具有较广的适用范围,并且它的实现过程较为简单,计算精度和效率均较高.
Based on the efficient Markov chain simulation method and the saddle point estimation method of the failure domain samples, a method of reliability analysis of non-linear limit state function with non-normal variables can be quickly analyzed in the case of high-dimensional and small failure probability In the non-normal space, the probability of failure is converted into the product of the failure probability of a linear limit state function and a characteristic scaling factor.The linear limit state function is obtained by simulating the failure domain of the nonlinear limit state function Sample and it has approximately the same design point as the nonlinear limit state function.The multiplicative theorem in probability theory is the theoretical basis for obtaining the feature scale factor and it reflects the failure probability of the nonlinear limit state function and the linear limit state function The failure probability of the linear limit state function can be obtained by the saddle point estimation method, and the characteristic scaling factor can be approximated by the Markov chain quickly simulating the samples in the linear and non-linear failure domains.Qualitative analysis and quantitative The comparative analysis of examples shows that the proposed algorithm has a wide scope of application, and its implementation process is relatively Mono-, accuracy and efficiency are high.