计算故障先验概率的最大熵方法

为了解决故障先验概率估算不准的问题,提出了基于最大熵的故障先验概率的计算模型.该模型以相关的先验信息作为最大概率估计的约束条件,并通过拉格朗日函数,将故障先验概率估算问题转化成无约束优化问题.为了实现对无约束优化问题的快速求解,提出了一种基于最速下降法和牛顿法的混合梯度算法;并且,针对大规模系统中故障变量过多的情况,依据系统分解的原则,将高维故障空间分解为多个低维故障空间,给出了低维故障空间求解的快速计算方法.通过最大熵方法和故障平均间隔(MTTF,Mean Time To Failure)方法的结果比较,证明最大熵方法更具准确性.

Maximum entropy method for fault prior probabilities

To solve precision problem of fault prior probabilities,the calculation model of fault prior probabilities based on maximum entropy theory was proposed.Through this model,which could make full use of the given prior information as the constraints of maximum likelihood estimation and based on Lagrange function,the calculation problem of fault prior probabilities was transformed to non-constrained optimization problem.The non-constrained optimization problem was solved rapidly,based on the gradient method mixed by steepest decent method and Newton method.When the faults were overabundant in large scale system,the highly multidimensional fault space could be decomposed by the principle of decomposition of system.The fast calculation method of fault prior probabilities was given in lowly multidimensional space.With the comparison of the result calculated by the maximum entropy method and the MTTF(mean time to failure) method respectively,the maximum entropy method was proved to be more precise.