动态系统失效的不确定性分析及其高效算法
Uncertainty analysis of failure of dynamic system and its efficient algorithm

摘要 为了分析在不确定性元器件失效率影响条件下动态系统的失效问题，提出了满足工作时间要求的系统失效概率和满足失效概率限制的系统正常工作时间的分析方法。同时，为了研究元器件失效率对动态系统失效的影响程度，提出了元器件失效率对系统失效概率以及系统正常工作时间不确定性影响的重要性分析方法，建立了元器件失效率对系统失效概率和系统正常工作时间方差贡献的重要性测度指标。首先给出了指标求解的直接蒙特卡罗方法，然后采用基于分数矩的极大熵方法来高效估计系统失效的概率密度函数，采用乘法降维积分建立了2种重要性测度指标的高效解法。阀门控制系统和民用飞机电液舵机系统的算例结果表明所提方法的合理性和算法的高效性。
Abstract：In order to study the failure of dynamic system when the failure rates of components are uncertain, a new method is proposed to analyze the system failure probability when function time is given and function time when the threshold of failure probability is shown in system. Meanwhile, a new importance measure technique is developed to estimate the impact of components' failure rates on system failure probability and function time in dynamic system. In this paper, the Monte Carlo procedure is given to solve the proposed indices. The fractional moments-based maximum entropy method is used to obtain failure probability density function in system efficiently. An efficient technique with multiplication dimensionality reduction is developed to estimate two importance measure indices. Valve control system and civil aircraft electro-hydraulic actuator system are presented to illustrate the rationality and efficiency of the proposed method.