摘要
概率符号有向图(probabilistic signed digraph,PSDG)模型通过在传统定性符号有向图(signed digraph,SDG)的模型结构中引入节点和支路的概率信息,改善了传统定性SDG故障诊断的性能,提高了故障诊断的分辨率。然而,在PSDG模型中,节点的概率分布通常是在给定其父节点条件下的条件概率分布,建模时所需要的先验条件概率参数的个数与其父节点的个数成指数关系,定义如此数量巨大的先验条件概率参数无疑会极大地增加对大规模系统建模的难度。为了解决对象先验知识不完备的情况下PSDG建模过程中先验条件概率参数的设置问题,本文提出了一系列获取未知条件概率参数的估计方法:针对父节点影响状态相同的情况,提出了扩展Noisy-OR门理论的估计方法;针对父节点影响状态相异的情况,提出了近似估计方法和极值估计方法。文中对这些估计方法进行了理论分析,证明了采用这些方法的可行性。应用这些估计法方法使得建模需要确定的先验条件概率参数的数量从节点个数的指数关系降为线性关系,极大地降低了建立大规模PSDG模型的复杂性和工作量。通过对某石化公司气体分馏装置建立PSDG模型进行故障诊断实例研究,在使用本文提出的估计方法后,建模所需事先确定的先验概率参数数量急剧降低,诊断结果与实际发生的故障相符,进一步证明了该估计方法的有效性。
The fault diagnosis approach based on probabilistic signed digraph （PSDG） can improve the performance and the fault resolution of the traditional qualitative signed diagraph （QSDG） approach, by introducing the probabilistic parameters of nodes and branches into the original SDG model structure. However, in a PSDG model, the probability distribution of a node is the conditional probability distribution under the condition of its parent nodes, so that, the number of apriori conditional probabilistic parameters which should be attached：to a node will show an exponential relationship with the number of its parent nodes. For a sufficiently large system with numerous nodes, eliciting so many apriori conditional probabilistic parameters will be too cumbersome to afford. Therefore, based on PSDG model, a series of approacfies are proposed to estimate the unknown apriori conditional probabilistic parameters for PSDG modeling with the incomplete knbwledge of the target process. For the case of the same influence from the parent nodes, an evaluating approach is proposed by extending the idea of Noisy-OR gate; and for the case of the different influence, the approximate and the extreme evaluating approaches are proposed. The presented approaches are also analyzed theoretically and the feasibility is proved. It has shown that the number of the apriori conditional probabilistic parameters in the PSDG can be decreased to be linear with the number of model nodes instead of exponential number by the proposed approaches, which reduces the complexity and workload in PSDG modeling greatly and effectively. The proposed approaches are illustrated on a gas fractionation unit of a petrochemical company. Using the proposed approaches, the number of the apriori conditional probabilistic parameters defined for the PSDG model of the unit is reduced remarkably, and the diagnostic results are consistent with the real faults, which shows the validity of the proposed method.
出处
《计算机与应用化学》
CAS
CSCD
北大核心
2011年第12期1497-1500,共4页
Computers and Applied Chemistry
基金
国家自然科学基金资助项目(60874049)
科技部国家高技术研究发展计划(863)资助项目(2007AA04Z193).
关键词
概率符号有向图
先验条件概率
故障诊断
probabilistic signed digraph, apriori conditional probabilistic, fault diagnosis
