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基于自适应重要抽样(AIS,Adaptive Importance Sampling)的可靠性分析方法,能够克服基于蒙特卡洛方法分析小概率事件时存在的效率低、精度差问题.为解决显性失效方程不存在时寻找失效点困难问题,首先利用条件递归寻找失效点,并使之尽可能在失效面附近;以该失效点为采样中心,抽取失效样本,并不断调整采样中心,使失效样本不断靠近设计点;然后利用这组失效样本估计重要抽样函数的参数,再执行自适应迭代过程,直至失效概率的误差缩小到允许误差限内.最后通过两个典型案例对方法进行应用验证,仿真结果表明在没有失效方程的情况下,能够通过仿真方法很快找到失效点,表明对于不存在显性失效方程的系统,该方法同样适用.与蒙特卡洛方法的对比结果表明该方法在仿真效率上具有较大优越性,且失效概率越小,这种优越性越明显.
Based on the reliability analysis method of Adaptive Importance Sampling (AIS), this method can overcome the low efficiency and poor accuracy problem of Monte Carlo method based on Monte Carlo method in analyzing small probability events.In order to solve the problem of explicit failure equation Point difficult problem, the first use of conditional recursion to find the failure point, and make it as near as possible in the failure surface; the failure point as the sampling center, the failure of the sample drawn, and continue to adjust the sampling center, so that the failure of samples close to the design point; and then use This set of invalid samples estimates the parameters of the important sampling function and then executes the adaptive iterative process until the error of the failure probability is reduced to within the allowable error limit.Finally, two typical cases are used to verify the method. The simulation results show that in the absence of failure equations , The failure point can be quickly found through the simulation method, which shows that this method is also applicable to the system without explicit failure equation.Comparison with the Monte Carlo method shows that this method has greater superiority in simulation efficiency, And the smaller the probability of failure, the more obvious the superiority.