案例检索——EMC-CBR故障诊断研究（三）

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案例检索的核心任务就是计算新案例和案例库中的案例的相似度，而相似度要由案例的故障特征和系统结构确定。

（1）案例属性之间的距离

由于系统结构直接影响着EMI的大小，即便两个设备具有相同的物理布局但采用不同的元件或材料，其EMC的效果也是不同的，因此两个案例之间的“系统结构”之间的距离不仅和谓词相关，而且要考虑到谓词函数的参数——谓词往往表示结构布局，而参数往往表示材料或元件。因此，在计算案例属性之间的距离时，对于案例属性中的谓词和参数要赋予不同的权值。

设case-i的某个属性(故障特征或系统结构)有m个谓词，case-j对应的该属性有n个谓词，且二者相同的谓词个数为k，其中min(m,n)≥k。若该属性中，谓词权重为<!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter" /> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0" /> <v:f eqn="sum @0 1 0" /> <v:f eqn="sum 0 0 @1" /> <v:f eqn="prod @2 1 2" /> <v:f eqn="prod @3 21600 pixelWidth" /> <v:f eqn="prod @3 21600 pixelHeight" /> <v:f eqn="sum @0 0 1" /> <v:f eqn="prod @6 1 2" /> <v:f eqn="prod @7 21600 pixelWidth" /> <v:f eqn="sum @8 21600 0" /> <v:f eqn="prod @7 21600 pixelHeight" /> <v:f eqn="sum @10 21600 0" /> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect" /> <o:lock v:ext="edit" aspectratio="t" /> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:17.25pt; height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image001.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1273088713"> </o:OLEObject> </xml><![endif]-->，参数权重为<!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style='width:15.75pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image003.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1273088714"> </o:OLEObject> </xml><![endif]-->，<!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style='width:60pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image005.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1273088715"> </o:OLEObject> </xml><![endif]-->，则定义两案例在该属性的距离为

<!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style='width:126pt;height:48pt' o:ole="" filled="t"> <v:fill color2="black" /> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image007.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1273088716"> </o:OLEObject> </xml><![endif]-->

其中， <!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style='width:17.25pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image009.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1273088717"> </o:OLEObject> </xml><![endif]-->为case-i、case-j中第<!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style='width:9.75pt;height:14.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image011.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1273088718"> </o:OLEObject> </xml><![endif]-->h个相同的谓词的参数之间的匹配程度，有

<!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style='width:128.25pt;height:38.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image013.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1273088719"> </o:OLEObject> </xml><![endif]-->

该定义只考虑了相同的谓词以及相同谓词对应的参数之间的关系，两案例相同的谓词越多，则这两个案例之间的距离越短。

（2）案例的相似度

设d₁<!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style='width:12.75pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image015.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032" DrawAspect="Content" ObjectID="_1273088720"> </o:OLEObject> </xml><![endif]-->为两案例“故障特征”属性的距离，<!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image017.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033" DrawAspect="Content" ObjectID="_1273088721"> </o:OLEObject> </xml><![endif]-->d₂为两案例“系统结构”属性的距离，由于0<=d₁<!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style='width:12.75pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image015.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034" DrawAspect="Content" ObjectID="_1273088722"> </o:OLEObject> </xml><![endif]-->,<!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style='width:47.25pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image019.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035" DrawAspect="Content" ObjectID="_1273088723"> </o:OLEObject> </xml><![endif]-->d₂<=1，则可以定义两案例的相似度为：

<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036" DrawAspect="Content" ObjectID="_1273088724"> </o:OLEObject> </xml><![endif]-->

其中，<!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style='width:27.75pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image023.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038" DrawAspect="Content" ObjectID="_1273088725"> </o:OLEObject> </xml><![endif]-->SIM₁、<!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style='width:29.25pt;height:17.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image025.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->SIM₂<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039" DrawAspect="Content" ObjectID="_1273088726"> </o:OLEObject> </xml><![endif]-->分别为两案例“故障特征”属性、“系统结构”属性对应的相似度，且

<!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style='width:66pt;height:18pt' o:ole="" filled="t"> <v:fill color2="black" /> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image027.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037" DrawAspect="Content" ObjectID="_1273088727"> </o:OLEObject> </xml><![endif]-->，<!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style='width:33pt;height:15.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image029.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->i=1,2<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040" DrawAspect="Content" ObjectID="_1273088728"> </o:OLEObject> </xml><![endif]-->

案例库中和目标案例相似度最大的案例，就是最佳匹配案例。当然，有可能出现即便是最佳匹配案例和目标案例的相似度也比较小的情况。可以为了保证最终结果的正确性，设定一个相似度的阈值，低于该阈值的相似度的案例不能作为最终结果使用，必须利用专家系统对结果进行修正。