计算故障先验概率的最大熵方法

孟晓风; 季宏; 王国华; 钟波

计算故障先验概率的最大熵方法

北京航空航天大学仪器科学与光电工程学院, 北京 100083

详细信息

作者简介:
孟晓风(1955-),男,重庆人,教授,mengxf@buaa.edu.cn.

中图分类号: TP 18
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- 被引次数: 0
出版历程
- 收稿日期: 2006-04-30
- 网络出版日期: 2006-11-30

Maximum entropy method for fault prior probabilities

School of Instrument Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

摘要: 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.
- 熵 /
- 最大概率估计 /
- 拉格朗日函数 /
- 梯度法
Abstract: 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.
- entropy /
- maximum likelihood estimation /
- Lagrange multipliers /
- gradient methods

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参考文献(1)

[1] Somnath Deb, Krishna R P, Vijay R, et al. Mufti-signal flow graphs:a novel approach for system testability analysis and fault diagnosis[J]. IEEE Aerospace and Electronics Magazine,1995, 10 (5):14-25 [2] Vijaya R, Mojdeh S, Krishna R P. Test sequencing problems arising in test planning and design for testability[J]. IEEE Transactions on Systems, Man and Cybernetics—Part A:Syatems and Humans, 1999,29(2):153-163 [3] 杨世凤,付连昆,陈新宇,等.设备故障诊断最优搜索策略的求解[J].振动、测试与诊断, 2004,24(2):117-120 Yang Shifeng, Fu Liankun, Chen Xinyu, et al. Solution to optimal searching of equipment fault diagnosis[J]. Journal of Vibration, Measurement & Diagnosis,2004,24(2):117-120(in Chinese) [4] 韩光臣,孙树栋,王军强,等.复杂系统模糊概率故障图模型研究[J].中国机械工程,2005,16(9):801-804 Han Guangchen, Sun Shudong, Wang Junqiang, et al. Probability research on fault graph model of complex system based on fuzzy probability[J]. China Mechanical Engineering, 2005, 16(9):801-804(in Chinese) [5] 齐怡,沈士团,李驿华,等.故障诊断专家系统中诊断决策方法的研究[J].航空学报, 2003,24(2):147-151 Qi Yi, Shen Shituan, Li Yihua, et al. Study of decision making method diagnostic expert system[J]. Acta Aeronautica et Astronautica Sinica, 2003, 24(2):147-151(in Chinese) [6] Fang Tu, Krishna R P, Somnath Deb, et al. Computationally efficient algorithms for multiple fault diagnosis in large graph-based systems[J]. IEEE Trans on SMC, 2003, 33(1):73-85 [7] Abbas A E. Entropy methods for joint distributions in decision analysis . IEEE Transactions on Engineering Management, 2006,53(1):146-159 [8] 陈珽.决策分析[M].北京:科学出版社,1987:15-17 Chen Ting. Decision analysis[M]. Beijing:Science Press, 1987:15-17(in Chinese)

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