动态系统元器件失效率的矩独立重要性测度分析

针对不确定性元器件失效率对动态系统失效概率影响程度的度量问题,研究了动态系统元器件失效率的重要性分析方法。分析了不确定性情况下动态系统失效概率的特点;依据Borgonovo的矩独立灵敏度分析思想,提出了两种新的矩独立不确定性重要性测度,给出了基于蒙特卡罗数值仿真的一般求解方法,分别用来分析系统工作时间给定和在区间变化两种情况下元器件失效率不确定对系统失效概率分布函数的贡献程度;建立了重要性测度的高效算法,通过稀疏网格积分技术将多元函数的积分问题转化成一元函数积分的张量积组合,通过Edgeworth级数方法将响应量分布函数的求解问题转化为基于其前四阶矩的失效概率估计,从而有效降低了功能函数的调用次数,提高了重要性测度的求解效率。最后,通过两个算例验证了所提方法的合理性和算法的高效性。

Moment-Independent Importance Measure Analysis on Failure Rates for Dynamic Systematic Components

In order to study the influence of component failure rates on failure probability in dynamic systems, a new importance measure technique for component failure rates is presented in this paper. Characteristics of systematic dynamic failure probability in the presence of uncertainty are analyzed. Based on the Borgonovo moment-independent importance measure analysis method and Monte Carlo simulation, two new moment-independent uncertainty importance measures are proposed to estimate the contribution of component failure rates to system failure probabilities in two situations:A fixed and an interval variant working time. Moreover, an efficient algorithm of importance measure is developed to decrease the runs of performance function by combining the sparse grid integration (SGI) with the Edgeworth series. The SGI technique successfully transfers the multivariate functional integral to the tensor product of one-variable integrals, and the ES method transfers the cumulative distribution function of system response to a failure probability estimation of the response first four moments. Rationality and efficiency of the proposed method are finally illustrated by two examples.