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1. 海军航空工程学院 研究生管理大队, 烟台 264001;
2. 海军航空工程学院科研部, 烟台 264001

Diagnosis method of simultaneous fault with incomplete information
SUN Weichao1 , XU Aiqiang2 , LI Wenhai2
1. Graduate Management Brigade, Naval Aeronautical Engineering Institute, Yantai 264001, China ;
2. Department of Scientific Research, Naval Aeronautical Engineering Institute, Yantai 264001, China
Received: 2015-06-30; Accepted: 2015-09-18; Published online: 2016-01-08 15:17
Foundation item: Pre Research Fund for Weapons and Equipment of PLA (9140A27020214JB14436)
Corresponding author. Tel.: 0535-6635836 E-mail: xuaq6342@yahoo.com.cn
Abstract: Test information is often incomplete in the fault diagnosis process of equipment. And simultaneous fault diagnosis process is more difficult at the same time. In response to this situation, the current methods of fault diagnosis with incomplete test information and of simultaneous fault diagnosis are studied firstly. Then we define incomplete fault diagnosis decision system to describe incomplete test information. And it defines incomplete boundary rough entropy to measure the level of uncertainty in the system and assign the importance of each attribute. Meanwhile, the method to calculate frequency of attributes' value under incomplete condition is proposed. In order to diagnose simultaneous fault, the paper constructs the diagnosis model under DSmT framework, and proposes a new combination rule of interval-value belief to overcome the shortcomings of previous methods. Finally, the validity and applicability of the method are proved by two equipment fault diagnosis examples.
Key words: simultaneous fault diagnosis     DSmT theory     interval-value belief combination     rough set theory     boundary rough entropy

1 不完备故障信息表示与特征提取 1.1 相容关系下不完备并发故障诊断决策系统

SB(x)表示对象集{yU|(x, y)∈SIM(B)}，对于集合B而言，SB(x)是与x不可区分的对象的最大集合，fb(x)表示在属性b下与x不可区分的对象的最大集合。

SIM(B)={SB(x)|xU}表示对U的一种分类，则U/SIM(B)中的元素称为相容类。U/SIM(B)中的相容类一般不构成U的划分，其构成U的覆盖，∪U/SIM(B)=U

1.2 不完备并发故障诊断决策系统中属性的重要度计算

 (1)

IDS中的不完备边界粗糙熵的定义式(1)同时考虑了由相容关系SIM(B)在对U进行分类时，导致不确定的2个方面因素。式(1)等号右端第1项表示决策表中的对象集合在相容关系SIM(B)下相对于决策类产生的粗集边界所引起的知识不确定；式(1)等号右端第2项刻画了在相容关系SIM(B)下产生的知识块大小引起的不确定。

 (2)

 (3)
1.3 不完备并发故障诊断决策系统中的属性值频率计算

2 并发故障诊断模型与信度合成 2.1 DSmT框架下并发故障诊断模型

DSmT作为信息融合算法中一个新的分支，有效地对D-S证据理论进行了扩展。在DSmT中，Θ={θ1, θ2, …, θn}作为所考虑融合问题的辨识框架，其是包含n个完备命题的有限集合。在DSmT框架下，定义超幂集DΘ，其是由Θ中的命题，以及其通过并、交运算组成的所有符合命题的集合。可表示为：①∅, θ1, θ2，…，θnDθ；②如果A, BDθ，那么ABDθABDθ；③除了①和②中包含的命题，再无其他命题属于Dθ

2.2 基于先验知识的区间信度合成规则

 (4)

 (5)

2个区间证据合成时，CDIP方法定义如下。

 (6)

3 基于CDIP规则的并发故障诊断方法

1)选取装备故障信息，构建不完备并发故障诊断决策系统IDS=(U, C∪{d}, V, f)，*∈V

2)对IDS中数据进行预处理。根据测试指标正常区间，按照“高于”、“低于”和“属于”该区间将测试数据进行离散化。

3)使用粗糙集方法对决策表进行约简，获得约简结果B。

4)若得到的约简结果不唯一，计算不完备边界粗糙熵EIB(Bi)，选取值最小的约简结果Bi

5)分别计算每一条测试属性的重要度s(ai)，通过计算ωai得到每条证据的权重。

7)构建DSm模型，在DSm框架下通过CDIP规则对区间证据进行组合。通过合成后的区间信度赋值对故障进行判断，给出诊断结果。

4 数值实验

4.1 运放电路并发故障诊断实例

 图 1 仪表放大器电路原理 Fig. 1 Principle of instrumentation amplifier circuit

 编号 Vs最大输入/mV Vs最小输入/mV 共模抑制比/dB 电路工作温度/℃ 最大增益/dB 故障模式 1 19.5 0.61 89 50.5 119 F1 2 10.1 1.03 20 65.1 108 F1 3 13.9 * 102 105.9 140 F1 4 17.8 0.90 117 90.4 106 F1 5 * 1.12 73 93.6 117 F1 6 14.4 0.48 120 77.4 103 F2 7 18.2 0.77 51 81.2 84 F2 8 18.5 0.01 93 * 40 F2 9 13.3 0.53 105 110.0 76 F2 10 * 0.49 81 66.3 81 F2 11 17.6 1.07 68 72.1 93 F1∩F3 12 18.0 0.96 * 58.6 101 F1∩F3 13 12.7 1.50 44 55.9 88 F1∩F3 14 11.9 1.91 62 61.7 79 F1∩F3 15 16.5 1.00 110 88.3 96 F1∩F3 注：*—缺失的测试数据。

 编号 C1 C2 C3 C4 C5 故障模式 1 2 1 1 1 2 F1 2 0 2 0 1 2 F1 3 1 * 1 0 2 F1 4 1 1 1 0 2 F1 5 * 2 1 0 2 F1 6 1 0 1 1 1 F2 7 2 1 0 1 0 F2 8 2 0 1 * 0 F2 9 1 1 1 0 0 F2 10 * 0 1 1 0 F2 11 1 2 0 1 1 F1∩F3 12 1 1 * 1 1 F1∩F3 13 1 2 0 1 1 F1∩F3 14 0 2 0 1 0 F1∩F3 15 1 1 1 0 1 F1∩F3

 i Ci mi(F1) mi(F2) mi(F1∩F3) 2 012 [0，0.250][0.333，0.429][0.400，0.500] [0.750，1.000][0.286，0.333]0 0[0.286，0.333][0.500，0.600] 5 012 001.000 0.8000.2000 0.2000.8000

 方法 T1={0, 2} m(F1) m(F2) m(F1∩F3) m(F1∪F2∪F3) 区间DSm规则 [0，0.250] [0，0] [0，0] [0.750，1.000] CDI2方法 [0.500，0.719] [0.281，0.500] [0，0] CDI5方法 [0.500，0.679] [0.321，0.500] [0，0] 本文方法 [0.652，0.786] [0.214，0.348] [0，0] 方法 T1={1, 2} m(F1) m(F2) m(F1∩F3) m(F1∪F2∪F3) 区间DSm规则 [0.333，0.429] [0，0] [0.286，0.333] [0.286，0.333] CDI2方法 [0.556，0.632] [0.041，0.055] [0.327，0.388] CDI5方法 [0.584，0.650] [0.064，0.083] [0.286，0.333] 本文方法 [0.617，0.676] [0.038，0.050] [0.286，0.333] 方法 T1={1, 1} m(F1) m(F2) m(F1∩F3) m(F1∪F2∪F3) 区间DSm规则 [0，0] [0.057，0.067] [0.495，0.610] [0.352，0.419] CDI2方法 [0.067，0.080] [0.147，0.173] [0.751，0.781] CDI5方法 [0.042，0.058] [0.168，0.195] [0.755，0.781] 本文方法 [0.031，0.046] [0.166，0.186] [0.776，0.795] 方法 T1={2, 2} m(F1) m(F2) m(F1∩F3) m(F1∪F2∪F3) 区间DSm规则 [0.400，0.500] [0，0] [0.500，0.600] [0，0] CDI2方法 [0.400，0.500] [0，0] [0.500，0.600] CDI5方法 [0.400，0.500] [0，0] [0.500，0.600] 本文方法 [0.400，0.500] [0，0] [0.500，0.600]

4.2 激励发生电路并发故障诊断实例

 图 2 旋转变压器激励发生电路原理 Fig. 2 Princiople of rotating transformer excitation generating circuit

 编号 信号频率/Hz 信号幅值/V 输入电压/V 频率稳定度/% +15 V电压/V -15 V电压/V 电路工作温度/℃ +5 V电压/V +10 V电压/V 故障模式 1 1 620 13.8 3.0 5.0 * -13.6 * 5.8 10.1 F1 2 * 9.0 3.3 9.3 18.9 -12.7 105 5.5 * F1 3 1 630 13.2 * 7.9 15.1 -15.9 70 * 9.0 F1 4 1 600 13.8 3.0 3.9 16.8 -16.5 72 6.6 11.9 F1 5 1 640 14.0 2.1 * 14.0 * * 6.0 * F1 6 1 630 * 4.1 7.2 13.9 -16.2 80 5.0 9.3 F1 7 1 440 13.1 * 14.0 17.2 -13.1 89 5.6 10.6 F1 8 1 260 13.6 2.6 2.9 15.5 * 91 6.1 10.3 F2 9 1 020 12.9 2.6 4.4 17.0 -14.5 69 4.9 * F2 10 * 13.0 2.8 * 13.8 -13.4 88 5.0 10.0 F2 11 1 580 14.2 2.5 12.9 14.2 -15.9 102 6.1 10.8 F2 12 1 530 13.8 * 8.0 16.2 -16.9 85 5.0 10.1 F2 13 1 690 10.9 1.1 10.5 * -13.6 86 6.9 9.4 F2 14 1 600 14.5 2.1 4.1 15.0 -19.0 72 * * F2 15 * 11.7 2.6 8.9 12.2 -11.3 91 5.6 8.4 F3 16 1 610 14.6 2.8 17.2 * -10.9 * 4.3 9.5 F3 17 1 660 9.8 2.5 11.5 10.0 -17.9 * 4.6 * F3 18 1 650 12.9 1.9 5.4 * -16.7 93 5.7 9.8 F3 19 1 650 13.0 * 3.3 13.2 * 70 * 9.1 F3 20 1 620 * 2.2 8.3 18.4 -17.7 74 6.0 * F3 21 2 640 12.1 2.0 8.2 13.5 -16.9 77 6.1 9.9 F3 22 1 730 13.9 2.1 14.4 * -15.0 * 5.8 10.3 F4 23 * 14.2 2.4 6.5 13.2 -18.2 80 4.1 10.6 F4 24 1 690 13.1 2.8 3.1 * -17.8 * * * F4 25 1 810 * 3.3 * 16.7 -16.9 75 5.6 11.0 F4 26 1 670 12.5 3.0 9.4 15.5 -17.3 * 3.0 * F4 27 1 700 14.0 * * 14.3 * 70 5.1 10.1 F4 28 * 13.1 1.8 2.5 12.0 -19.0 88 6.0 9.8 F4 注：*—缺失的测试数据；F1~F4—频率控制模块故障、幅值调理及驱动能力调节模块故障、电源模块故障及正弦信号产生模块故障。

 编号 C1 C2 C3 C4 C5 C6 C7 C8 C9 故障模式 1 1 1 2 1 * 1 * 2 1 F1 2 * 0 2 1 2 2 0 1 * F1 3 1 1 * 1 1 1 1 * 0 F1 4 0 1 2 1 2 1 1 2 2 F1 5 1 1 0 * 1 * * 2 * F1 6 1 * 2 1 1 1 1 1 0 F1 7 0 1 * 0 2 2 0 2 2 F1 8 0 1 1 1 1 * 0 2 1 F2 9 0 0 1 1 2 1 1 1 * F2 10 * 0 1 * 1 2 0 1 1 F2 11 0 1 1 0 1 1 0 2 2 F2 12 0 1 * 1 1 0 1 1 1 F2 13 2 0 0 0 * 1 0 2 0 F2 14 0 1 0 1 1 0 1 * * F2 15 * 0 1 1 0 2 0 2 0 F3 16 1 2 1 0 * 2 * 0 1 F3 17 2 0 1 0 0 0 * 1 * F3 18 1 0 0 1 * 0 0 2 1 F3 19 1 0 * 1 0 * 1 * 0 F3 20 1 * 1 1 2 0 1 2 * F3 21 1 0 0 1 1 0 1 2 1 F3 22 2 1 0 0 * 1 * 2 1 F4 23 * 1 1 1 0 0 1 0 2 F4 24 2 1 1 1 * 0 * * * F4 25 2 * 2 * 2 0 1 2 2 F4 26 2 0 2 1 1 0 * 0 * F4 27 2 1 * * 1 * 1 1 1 F4 28 * 1 0 1 0 0 0 2 1 F4

 i Ci mi(F1) mi(F2) mi(F3) mi(F4) 1 0 [0.182，0.375] [0.455，0.750] [0，0.125] [0，0.222] 1 [0.308，0.500] [0，0.100] [0.385，0.600] [0，0.182] 2 [0，0.125] [0.091，0.250] [0.091，0.250] [0.500，0.778] 2 0 [0.083，0.182] [0.231，0.300] [0.417，0.545] [0.083，0.182] 1 [0.313，0.400] [0.235，0.286] [0，0.067] [0.313，0.400] 2 [0，0.500] [0，0] [0.333，1.000] [0，0.500] 3 0 [0.100，0.333] [0.182，0.375] [0.182，0.375] [0.182，0.375] 1 [0，0.167] [0.286，0.455] [0.286，0.455] [0.143，0.273] 2 [0.444，0.750] [0，0.143] [0，0.143] [0.200，0.429] 5 0 [0，0.167] [0，0.167] [0.333，0.714] [0.222，0.571] 1 [0.176，0.308] [0.294，0.462] [0.063，0.214] [0.188，0.357] 2 [0.300，0.666] [0.100，0.333] [0.111，0.429] [0，0.286]

 方法 T1={2, 1, 2, 1} m(F1) m(F2) m(F3) m(F4) m(F1∩F2) m(F3∩F4) 区间DSm规则 [0，0.012] [0，0.005] [0，0.001] [0.006，0.048] [0.010，0.161] [0.003，0.109] CDI2方法 [0.143，0.370] [0.062，0.180] [0.002，0.063] [0.144，0.475] [0.091，0.483] [0.019，0.293] CDI5方法 [0.111，0.463] [0.028，0.177] [0，0.028] [0.152，0.604] [0.074，0.481] [0.007，0.268] 本文方法 [0.105，0.451] [0.028，0.173] [0，0.028] [0.157，0.630] [0.069，0.474] [0.008，0.283] 方法 T1={2, 1, 0, 0} m(F1) m(F2) m(F3) m(F4) m(F1∩F2) m(F3∩F4) 区间DSm规则 [0，0.003] [0，0.002] [0.015，0.106] [0，0.005] [0，0.055] [0.030，0.420] CDI12 [0.016，0118] [0.057，0.185] [0.218，0.553] [0.029，0.132] [0.012，0.243] [0.141，0.590] CDI15 [0.012，0.141] [0.079，0.274] [0.117，0.618] [0.008，0.134] [0.021，0.276] [0.094，0.618] 本文方法 [0.012，0.150] [0.074，0.251] [0.120，0.621] [0.008，0.132] [0.023，0.286] [0.095，0.620] 方法 T1={1, 0, 1, 0} m(F1) m(F2) m(F3) m(F4) m(F1∩F2) m(F3∩F4) 区间DSm规则 [0，0.003] [0，0.004] [0，0.004] [0.006，0.067] [0，0.053] [0.031，0.391] CDI12 [0.089，0.235] [0.074，0.207] [0.018，0.125] [0.150，0.442] [0.012，0.249] [0.150，0.552] CDI15 [0.089，0.294] [0.069，0.243] [0.001，0.123] [0.046，0.442] [0.021，0.260] [0.132，0.660] 本文方法 [0.084，0.279] [0.064，0.235] [0.001，0.130] [0.046，0.454] [0.019，0.254] [0.143，0.679] 方法 T1={1, 1, 2, 2} m(F1) m(F2) m(F3) m(F4) m(F1∩F2) m(F3∩F4) 区间DSm规则 [0.013，0.100] [0，0.001] [0，0.002] [0，0.009] [0.017，0.265] [0.003，0.138] CDI12 [0.213，0.543] [0.047，0.135] [0.004，0.109] [0.067，0.267] [0.090，0.492] [0.021，0.379] CDI15 [0.175，0.610] [0.017，0.140] [0.001，0.147] [0.057，0.358] [0.062，0.478] [0.020，0.432] 本文方法 [0.174，0.613] [0.018，0.133] [0.002，0.167] [0.051，0.343] [0.060，0.478] [0.023，0.450]

5 结论

1)可以有效地对不完备信息，以及在DSmT框架下对并发故障进行表示。

2)通过对测试信息中的特征进行提取，度量其对决策的重要程度。

3)在对区间证据进行合成时，有效地融入了证据特征，可以获得较之前区间合成方法更为精确的合成结果。

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#### 文章信息

SUN Weichao, XU Aiqiang, LI Wenhai

Diagnosis method of simultaneous fault with incomplete information

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(7): 1449-1460
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0433