Knowledge Rep resentation for Incomp lete Fault D iagnosis Based on Flow Graphs

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1 JOURNAL OF HARB IN UN IVERSITY OF SC IENCE AND TECHNOLOGY Vol114 No13 Jun. 2009,, (, ) :,. Paw2 lak,.,,,. : ;;; : TP206 : A : (2009) Knowledge Rep resentation for Incomp lete Fault D iagnosis Based on Flow Graphs HUAN G W en2tao, XU Zhi2m ing, WANG W ei2jie ( School ofmechatronics Engineering, Harbin Institute of Technology, Harbin , China) Abstract: In view of the disadvantages existing in the current fault2diagnosis2know ledge rep resentation methods due to the incomp letion of the fault diagnosis inform ation, a m ethod using flow graph to rep resent the incomp lete fault2diagnosis2know ledge is investigated on the basis of the one p roposed by Paw lak. The definitions of comp lete and incomp lete fault2diagnosis2decision2flow2graph is p resented. A graphic m ethod app licable for containing incom2 p lete fault2diagnosis2inform ation in the fault2diagnosis2know ledge is established. The confidence and the coverage are emp loyed as the evaluating indicators of decision rules imp licit in the incomp lete fault2diagnosis2decision2flow2 graph, which p rovides the foundation of fault2diagnosis2know ledge acquisition based on the flow graph. For conven2 ience of exp lanation, an examp le for the fault diagnosis of an electronic circuit is given. Key words: fault diagnosis; incomp lete information; flow graphs; know ledge exp ression 1, [ 1 ],,,., ;, [ 2 ],,,, [ 3 ], : : ( ) ;( ) : (1974),,.

2 3,: 43 ( ). [ 4 ].,, [ 5-6 ],,.,.,,,., : ;.,,. - -,,,,,.,.,,,., Z. Pawlak ( Flow Graphs) [ 7-9 ],.,..,,,. 2,. < U, M, D, V M, V D >. am, V a, dd, V d,.,,, 3TP 1 TP 2 TP 3, 1., U = { u 1, u 2, u 3, u 4, u 5, u 6, u 7 }7, M = { TP 1, TP 2, TP 3 }3, V TP1 = {L, N, H}, V TP2 = {L, N, H, 3 }, V TP3 = { TL, L, N, H }3, 3, D = { d}, V d. = { Y, N } 1 U TP 1 TP 2 TP 3 d u 1 L L L N u 2 L L TL N u 3 H H L N u 4 L N TL Y u 5 L N L Y u 6 N H H N u 7 N 3 N N 3 ( Flow Graphs)Z. Pawlak2002. G = (N, B,), N -, B Α N N (),: B R +.,. G = (U, M, D, N, R, N, R ), U ; M D, M = { m 1, m 2, m m }, D = { d}; m i m i : V m i = { m i ( u ) ϖ { u U } },, d : V d = { d ( u) ϖ uu },

3 44 14 : (m i : V m ij m i M, V m ij V m i ),, V m ij m i j ;, : dd, V d j V d ), N ΑM M, ; R ΑM D, ; N : N 2 U, N (m i : V m ij, m i + 1 : V m i + 1, k ) = { uu (m i ( u) = V m ij ) (m i + 1 ( u) =V m i + 1, k ) } (1) R : R 2 U, R (m m : V mm j, d: V dk ) = { uu (m m ( u) =V m m j ) ( d ( u) =V dk ) } (2) G, ML DL, G,., G,.,,,. G,, N (m i : V m ij, m i + 1 : V m i + 1, k )., R (m m : V m m j, d: V dk ). G,,, m i : 3 m i M,,,.,. N R m i : 3 m i M,,., 3 N : N 3 2 U, 3 N (m i : V m ij 3, m i + 1 : V m i + 1, k 3 ) = { uu (m i ( u) = 3 ) (m i + 1 ( u) = 3 ) } (3) m i : V m ij 3 m i + 1 : V m i + 1, k 3 m i : V m ij 3 m i + 1 : V m i + 1, k 3, ; 3 R : R 3 2 U, 3 R (m m : V m m j 3, d: V dk ) = { uu (m m ( u) = 3 ) ( d ( u) =V dk ) } (4) (m m : 3 ) ( d: V dk )., 1, 1. 4,., m i M, V m i, dd, V d,., 3, m j M, u i U m j ( u i ) = 3, V m j \ { 3 }. 1, u 7 TP 2 L N H, 1 3 (),.

4 3,: 45,. 5 G. : DR: [ (m 1 : V m 1, k ), (m m : V m m, n ), ) ] (5),,,., DR 3 : (m 1 : V m 1, k ),, (m i : V m 1, l 3 ),, (m m : V m m, n ), ) (6) DR 3 (m 1 : V m 1, k ),, m i : V m 1, l 3 ).,, (m m : V mm, n ),,. G, DR 3 : [ (m 1 : V m 1, k ),, m i : V m 1, l 3,, (m m : V m m, n ), ) ] m - 1 N R (DR 3 ) = ( N (m i : V m i, k, m i + 1 : V m i + 1, n ) ) card (DR 3 i = 1 N m p : V m p, q 3 R (m m : V mm, k d: V d j ) (7) ) = card{ N R [ (m 1 : V m 1, k ),, (m i : V m 1, l 3 ),, (m m : V m m, n ), ) ] } (8) (7) (8),. cer(dr 3 ) = card [ N R (DR 3 ) ] card[ N R (R l 3 ) ] cov (DR 3 ) = card[ N R (DR 3 ) ] card[ N R ) ] (9) (10) : R l 3 = ( m 1 : V m 1, k ),, m i : V m 1, l 3,, (m m : V m m, n ) ; card[ N R (R l 3 ) ]0; card{ N R ) } 0., card [ N R (DR 3 ) ] DR 3,DR 3, card [ N R (R l 3 ) ]DR 3, card{ N R ) }DR 3. DR 3 DR 3, DR 3 ; DR 3 DR 3, DR 3.,.,. 6, ; ;,,,,,.,,.,.,,,,. (50)

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