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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

Avionic devices fault diagnosis based on fusion method of rough set and D-S theory
SUN Weichao1, LI Wenhai2 , LI Wenfeng1
2. Department of Scientific Research, Naval Aeronautical Engineering University, Yantai 264001, China
Abstract:In order to solve the conflict of multi-sources information in the fault diagnosis process of avionics electric equipment, a method based on rough set theory and evidence theory for fault diagnosis was proposed. Because both rough set theory and evidence theory had advantages in dealing with uncertainty problems. The method proposed converted diagnostic data to mass function which was needed in evidence theory in order to fuse results with rough set theory. Meanwhile, the method defined boundary rough entropy, got dynamic weight parameters which reflected the significance of every information source used in fusion process with the entropy and improve the rule for conflicting evidence combination. The experiment shows that the method improves the fusion results' accuracy of diagnostic information effectively and has a good practical value in process of avionics electric fault diagnosis.
Key words: boundary rough set entropy     rough set     D-S evidence theory     conflicting evidence fusion     fault diagnosis

D-S证据理论作为决策级信息融合算法因其具有对不确定信息表示、度量与组合的能力,在多属性决策问题中得到广泛的应用.为了解决数据存在冲突的问题,目前针对证据理论的改进也在不断进行,主要集中于两方面,通过改变冲突部分的分配方式对组合规则进行改进[16]以及通过对各证据权重的计算对证据本身进行修正[17, 18, 19].故障诊断作为一种多属性决策问题,是D-S证据理论的主要应用方向之一.文献[20]将其用于齿轮箱的故障诊断并引入信息熵对证据进行修正,文献[21]在故障诊断过程中通过对证据权重进行动态修正得到更为精确的结果;而更为常见的是D-S证据理论与其他算法的联合应用,与粗糙集不同的是,证据理论在其中负责诊断结果的融合.文献[22]将神经网络的输出作为证据进行合成,对涡轮机故障进行诊断;文献[23]用SVM构建分类器,对于多个分类器的结果使用D-S证据理论进行合成;文献[24]在对旋转机械进行并发故障诊断时用人工免疫算法对故障数据进行聚类,避免证据合成时焦元过多造成的计算困难.

1 故障诊断决策模型 1.1 基于粗糙集的数据处理

1) PSI(R)({d})=PSI(C)({d}).

2) 不存在rR,使得PSI(R-{r})({d})=PSI(R)({d})成立.

1.2 基于证据理论的冲突融合

D-S合成方法可以表述为,假设辨识框架Θ下的两个证据Ev1Ev2,其相应的基本信任分配函数为m1m2,焦元分别为AiBj,则D-S合成规则为

2 航空电子装备故障诊断方法 2.1 基于边界粗糙熵的决策重要度计算

BnR(Yi)=Yi-Yi,所以BnP(Yi)⊆BnQ(Yi).    证毕

XPlU/I(P),XQkU/I(Q).

E2B(P)≤E2B(Q).

EB(R)=E1B(R)+E2B(R),故EB(P)≤EB(Q).    证毕

2.2 基于决策重要度的冲突证据合成方法

2.3 基于CECS的航空电子装备故障诊断方法

1) 采集装备测试数据,选取故障信息,构建粗糙集诊断决策表L={U,C∪{d},V,f}.

2) 对决策表中数据进行预处理.根据测试指标正常区间,按照“高于”、“低于”、“属于”该区间将测试数据进行离散化.

3) 按照粗糙集方法对决策表进行约简,获得约简结果R.

4) 若得到约简结果不唯一,通过式(2)计算边界粗糙熵EB(Ri),选取值最小的约简结果Ri.

5) 根据式(1)计算Ri中的每条属性的值频率p[fa(xi)],构建证据的基本概率赋值函数mi.

6) 根据式(6)计算e(Ri)得到证据源Ri的群体可信度,并通过式(4)计算w(ai)得到每条证据的权重.

7) 通过CECS算法对证据进行组合.

CECS算法针对选定的证据群,为了界定可分配部分比例,引入群体可信度e(Ri),通过步骤6)计算每个证据的支持度w(ai)来决定冲突信息在证据间的分配比例,在证据合成的过程中将其作为权重因子进行证据修改.通过以上步骤,CECS算法使得故障诊断结果具有更大的可信性和合理性.

3 故障诊断实例 3.1 高度表故障分析

3.2 高度表故障诊断

 编号 C D C1 C2 C3 C4 C5 1 1 0 1 0 0 d1 2 1 0 0 0 0 d1 3 2 0 2 2 0 d1 4 0 0 1 1 1 d1 5 1 2 0 0 2 d1 6 0 0 1 2 0 d1 7 2 1 0 0 2 d2 8 1 1 1 0 0 d2 9 1 2 2 1 0 d2 10 1 0 0 0 1 d2 11 2 2 1 0 0 d2 12 1 0 2 1 0 d2 13 2 0 2 0 1 d3 14 0 0 2 0 0 d3 15 2 1 2 1 0 d3 16 0 2 2 1 1 d3 17 2 2 2 0 0 d3 18 1 2 0 0 0 d3

R1中的每一个属性Ci作为一条证据,而将不同的故障模块di作为辨识框架.在不同的属性值下会得到证据不同的基本信任分配函数,这些基本概率分配函数如表 2所示.

 属性 Ci mi(d1) mi(d2) mi(d3) i=1 0 0.5 0 0.5 1 0.375 0.5 0.125 2 0.167 0.333 0.5 i=2 0 0.556 0.222 0.222 1 0 0.667 0.333 2 0.167 0.333 0.5 i=3 0 0.286 0.428 0.286 1 0.6 0.2 0.2 2 0.167 0.333 0.5 i=4 0 0.272 0.364 0.364 1 0.2 0.4 0.4 2 1 0 0

 特征 m1 m2 m3 m4 s(ai) 0.608 0.830 0.719 0.763 w(ai) 0.208 0.284 0.246 0.262

 测试样本 合成方法 D-S方法 Yager[25]方法 文献[26]方法 文献[27]方法 基于证据距离方法[28] 本文方法 T1={2,0,2,2} m(d1) 1 0.016 0.481 0.249 0.234 0.282 m(d2) 0 0 0.218 0.109 0.130 0.115 m(d3) 0 0 0.301 0.150 0.179 0.156 m(Θ) 0 0.984 0 0.492 0.457 0.457 T2={0,1,1,2} m(d1) 0 0.525 0.263 0.299 0.275 m(d2) 0 0.217 0.109 0.095 0.128 m(d3) 0 0.258 0.130 0.141 0.132 m(Θ) 1 0 0.498 0.465 0.465 T3={2,1,1,0} m(d1) 0 0 0.253 0.126 0.131 0.132 m(d2) 0.572 0.016 0.396 0.206 0.216 0.226 m(d3) 0.428 0.012 0.351 0.132 0.198 0.190 m(Θ) 0 0.972 0 0.486 0.452 0.452 T4={2,2,2,2} m(d1) 1 0.005 0.378 0.164 0.141 0.210 m(d2) 0 0 0.249 0.106 0.158 0.131 m(d3) 0 0 0.373 0.159 0.278 0.196 m(Θ) 0 0.995 0 0.571 0.463 0.463

Yager合成方法[25]将冲突的部分全部分配在辨识框架上,由融合结果可以看出,证据源为4个时,效果并不理想,且该方法在处理低冲突证据时的效果好于处理高冲突证据的效果,当处理样本T2中的高冲突证据时,Yager合成方法将全部信任都赋予辨识框架上,导致方法失效.

 方法 样本 w(a1) w(a2) w(a3) w(a4) 本文方法 T1~T4 0.208 0.284 0.246 0.262 基于证据距离方法 T1 0.278 0.276 0.278 0.168 T2 0.286 0.169 0.322 0.223 T3 0.270 0.230 0.218 0.282 T4 0.298 0.298 0.298 0.106

4 结 论

1) 在粗糙集框架内实现故障诊断决策模型构建.

2) 对冗余故障信息进行约简,所提出的边界粗糙熵可以有效衡量每条测试项目对于决策的重要程度,提升了后期融合精度.

3) 在冲突证据的合成应用中,有效集成了证据的先验知识,得到诊断结果的准确度要好于目前存在的证据合成方法.

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#### 文章信息

SUN Weichao, LI Wenhai, LI Wenfeng

Avionic devices fault diagnosis based on fusion method of rough set and D-S theory

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(10): 1902-1909.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0030