基于MCMC的模糊自适应重要抽样法

针对传统的基于马尔可夫链蒙特卡罗 (Markov chain Monte Carlo，MCMC)的自适应重要抽样法只适用于失效边界确定的系统，而不适用于失效域模糊的渐变结构系统问题，提出基于MCMC的模糊自适应重要抽样法。首先从模糊失效域内的某个初始点出发，根据Metropolis准则构造马尔可夫模拟样本点；然后利用自适应核密度估计构建核抽样概率密度函数并进行重要抽样；最后离散化模糊失效域以计算系统的模糊失效概率。该方法合理地解决了以往渐变结构系统性能可靠性难以仿真分析及仿真效率低的难题，具有较高的仿真效率和精度。应用舵机案例对方法的适用性及高效性进行了验证。

Fuzzy adaptive importance sampling method based on MCMC

The traditional adaptive importance sampling method based on Markov chain Monte Carlo (MCMC) can only be applied to the system of determined failure domain but not to the gradual structure system of fuzzy failure domain. A new fuzzy adaptive importance sampling method based on MCMC is proposed. Firstly, the Markov chain samples are constructed according to Metropolis algorithm from the initial sample in the failure domain. Then a kernel sampling probability density function is obtained by adaptive kernel density estimation and the importance sampling is carried out. Finally, the fuzzy failure domain is discretized to compute the fuzzy failure probability. This approach solves the problems that the performance reliability of gradual structure systems is hard to be analyzed through simulation, and the efficiency of simulation is very low. The feasibility and effectiveness of this method are demonstrated by the case of the actuator system.