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根据可靠性灵敏度分析的需求和特点,选择似然比方法作为基础的导数/梯度估计方法.立足经典可靠性系统和基于元件的蒙特卡罗方法,推导了原始蒙特卡罗仿真环境下的似然比导数估计方法.为加速仿真,进一步提出了一种偏倚技巧,该技巧在系统结构函数的基础上定义一个应用重要抽样的无偏估计量,并通过最小化该估计量的方差来获得最优偏倚参数值.该估计量拥有的一个重要优势是其方差优化任务可以分解到单个元件的层次上进行,从而避免了高维优化的难题.通过一个可解析求解的简单实例验证了似然比导数估计方法应用于可靠性灵敏度分析的有效性,以及所提出的偏倚技巧对于降低导数估计方差的有效性.对于所考虑的实例系统,提出的偏倚蒙特卡罗方法对各个感兴趣的量都给出了很好的估计,与原始蒙特卡罗方法相比,各个估计量的方差均降低了至少6个数量级.
According to the requirements and characteristics of reliability sensitivity analysis, the method of likelihood ratio is chosen as the basic derivative / gradient estimation method.Based on the classical reliability system and element-based Monte Carlo method, the likelihood of the original Monte Carlo simulation environment Proportional Derivatives Estimation Method To speed up the simulation, a biased technique is further proposed. This technique defines an unbiased estimator that uses an important sample based on the system structural function and obtains the optimum by minimizing the variance of the estimator Bias parameter value.An important advantage of this estimator is that its variance optimization task can be decomposed into a single component level to avoid the problem of high-dimensional optimization.Through a simple example that can be solved analytically, the likelihood ratio derivative The effectiveness of the estimation method applied to the reliability sensitivity analysis and the proposed bias technique are effective in reducing the variance of the derivative estimation. For the considered example system, the proposed biased Monte Carlo method is given for each of the quantities of interest It is well estimated that the variance of each estimate is reduced by at least 6 compared to the original Monte Carlo method Magnitude.