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1. 空军工程大学 航空航天工程学院, 西安 710038;
2. 95503部队, 重庆 402360

Diagnostic strategy building method based on MDP
LIANG Yajun1, XIAO Mingqing1 , SONG Haifang1, YANG Zhao1, LIANG Peng2
1. Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China;
2. Unit 95503, Chongqing 402360, China
Received: 2015-05-05; Accepted: 2015-09-02; Published online: 2015-12-23 16:33
Corresponding author. Tel.: 13909285251 E-mail: xmqing@sohu.com
Abstract: Aiming at the problem that by the traditional method, it is difficult to get the global optimal diagnostic strategy of the complicated test system in fault detection for ignoring the uncertainty factors in the test execution and lacking of the long cycle optimization mechanism, a new diagnostic strategy building method based on Markov decision processes (MDP) is proposed. The process of fault detection and isolation is expressed as a Markov process; the unlimited discount model of the utility integrated criterion function is structured through the discount factor and objective weights; the global optimal diagnostic strategy is obtained with the policy iteration algorithm. The example shows that the test uncertainty factors are well considered, stable optimal strategy of overall situation can be achieved by this method, and the fast fault detection and isolation in the engineering practice can be guided effectively as well.
Key words: diagnostic strategy     Markov decision processes (MDP)     fault detection     policy iteration algorithm     strategy optimization

1 MDP理论模型

MDP的核心要素包括:状态、行动、转移概率及报酬。考虑到实际工程应用中,故障诊断的决策时刻总是离散的,故本文所讨论的MDP都是离散时间的,即离散时间MDP(Discrete Time Markov Decision Processes,DTMDP)。

MDP模型可由以下五元组确定:

MDP的最终目标是在策略空间Π中找出期望的最优策略π*满足式(2)。马氏策略的最优策略及最优函数的存在性已被证明[14],这里不再说明。

2 MDP故障诊断原理和策略模型 2.1 故障诊断原理

2.2 基于MDP的故障诊断策略模型

F1={f1,f2,…,fm}(m≥1)为系统的初始故障状态模糊集,由故障“推理机”可得图 1所示的系统故障诊断策略树,所有可能的系统故障状态模糊集依次记为F1,F2,…,则有系统故障状态空间S={F1,F2,…,Fk}(k≥1);所有检测项目t1,t2,…,td(d≥1)构成测试集T或行动集A(i),即A(i)=T={t1,t2,…,tn}(n≥1)。

 图 1 系统故障诊断策略树 Fig. 1 System fault diagnosis strategy tree

2.3 模型求解

1) 任取πΠ

2) 求解效用函数

3) 改进每个状态对应的行动,使其满足

4) 如果π*,则停止,V(s,π)=V(s,π*)为最优值函数,并返回π;否则,策略更新为π=π*,返回步骤2)。

3 诊断策略构建实例

 FT t1 t2 t3 t4 t5 p(fn) f1(射频接口) 0 0 0 0 0 0.01 f2(燃气推进器) 0 1 0 0 1 0.02 f3(发射电路盒) 0 0 1 1 0 0.05 f4(发射控制电源盒) 1 0 0 1 1 0.03 f5(挂弹信号组件) 1 1 0 0 0 0.09 f6(同步机构) 1 1 1 1 0 0.10 pnp 0.81 0.92 0.87 0.89 0.75 rc 1 1 1 1 1

1) pnp为测试tn能确定检测、反映出导弹发射架故障fm的概率,也就是系统故障状态发生转移的概率。因为在实际战地转场、内外场等恶劣的测试环境中存在多种外界因素,都会对测试效果造成一定的影响。

2) 考虑到测试设备的硬件架构已经搭建完成,不再讨论经济花费,所以表 1中的测试费用为测试时间成本的统计估计值,并作为费用报酬准则。

1) 确定折扣因子β。根据测试系统的可能检测周期,以及对诊断策略最优性的选取,折扣因子越接近1则策略长周期内的最优性越好,本例中确定0.80、0.95,并对比不同之处。

2) 确定准则权重。分析策略构建关键因素对测试效率、可靠性的影响,结合测试专家意见,给出测试费用和故障状态信息量的权重系数均为α=0.5;当检测偏向发生变化时,只需增加或减小权重值。

3) 根据表 1所示内容,按图 1所示构建出诊断策略树,可推出系统所有可能的故障状态模糊集,如表 2所示,进而得到故障状态空间S={F1,F2,…,F27}，且系统的可用行动集A(i)={t1,t2,…,t5}。

 故障状态 子故障 故障状态 子故障 F1 f1f2f3f4f5f6 F15 f3 F2 f1f2f3 F16 f4 F3 f4f5f6 F17 f5f6 F4 f1f3f4 F18 f4f5 F5 f2f5f6 F19 f6 F6 f1f2f4f5 F20 f5 F7 f3f6 F21 f4f6 F8 f1f2f5 F22 f1f4 F9 f3f4f6 F23 f1 F10 f1f3f5f6 F24 f3f4 F11 f2f4 F25 f2f5 F12 f1f3 F26 f1f5 F13 f2 F27 f3f6 F14 f1f2

4) 根据表 2内容,结合表 1中所示的系统故障状态转移概率,可确定在采取测试t1后系统的状态转移概率矩阵:

5) 根据表 1内容及式(3),可获得该测试系统3个报酬函数:

① 由表 1可知,测试费用报酬函数rc(in,an)=rc(an),anT,与系统所处状态无关,只取决于采取的测试行动。

② 由式(5)和状态转移概率矩阵,求得信息量报酬函数:

③ 已知准则权重α=0.5,综合a、b,进而得到综合报酬函数:

6) 式(9)代入式(6),得到该测试系统故障诊断策略构建的效用准则函数方程组:

7) 由于系统状态空间较大,本实例模型求解使用策略迭代算法,利用MATLAB中的MDP决策工具包编程可得结果,如图 2图 3所示。图 3为2个折扣因子下各故障状态的效用准则值,可以看出由于本例的检测周期较短,2个折扣因子下的策略趋势是一致的。

 图 2 最佳决策 Fig. 2 The best decisions
 图 3 最佳策略效用准则值 Fig. 3 Utility values of criteria of the best strategy

 图 4 系统故障诊断树 Fig. 4 Fault diagnosis tree of system
 图 5 不同权重α下的最佳决策 Fig. 5 The best decisions under different α
 图 6 不同权重α对应的策略效用准则值(β=0.95) Fig. 6 Utility values of criteria under different α (β=0.95)

4 结 论

1) 该方法能够充分考虑测试通过中的不确定性因素的影响,提高诊断结果的准确性与可靠性。

2) 可实现长周期动态寻优,生成全局最优诊断策略。

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#### 文章信息

LIANG Yajun, XIAO Mingqing, SONG Haifang, YANG Zhao, LIANG Peng

Diagnostic strategy building method based on MDP

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(4): 844-850.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0277