基于模拟退火的并联系统失效概率的计算方法

ESTIMATION OF FAILURE PROBABILITY FOR PARALLEL SYSTEM BASED ON SIMULATED ANNEALING METHOD

针对并联系统失效概率计算问题,定义多模式并联系统的最可能失效点,并采用模拟退火优化算法寻找此点。在逐步寻找此最可能失效点的过程中,建立自适应的重要抽样法来求解并联系统的失效概率,推导该方法失效概率估计值、方差和变异系数的计算公式。文中所提方法与计算并联系统失效概率的Monte Carlo法相比,具有更快的收敛速度,尤其是针对失效概率较小的问题,与连续顺序近似方法相比,具有更高的计算精度和更广的适应范围。算例结果显示所提方法的优越性。

For the failure probability of parallel system with multiple failure modes, the most probable failure point in the failure domain is defined, and the simulated annealing optimization method is employed to search for this point. The adaptive importance sampling method based on the most probable failure point is presented to estimate the failure probability of the parallel system. The formulae of the failure probability, the variance and the coefficient of variation are derived for the presented adaptive importance sampling method. The presented method is more efficient than Monte Carlo method especially for the small failure probability. And comparing with the successive sequential approximation, the presented method has higher precision and wider applicability. The examples illustrate the feasibility and advantage of the presented mothod.