14 3 20096 JOURNAL OF HARB IN UN IVERSITY OF SC IENCE AND TECHNOLOGY Vol114 No13 Jun. 2009,, (, 150001) :,. Paw2 lak,.,,,. : ;;; : TP206 : A : 1007-2683 (2009) 03-0042- 04 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 150001, 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 ], : 2009-03 - 21 : (200802131078) ;(20070410888) : (1974),,.
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 },
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 (),.
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)
50 14 : [ 1 ] L IVAN IM, KA ISER K, J IA W. Scheduling Hard and Soft Real - Time Communication in a Controller area Network [ J ]. Control Engineering Practice, 1999, 7 (12) : 1515-1523. [ 2 ],,. CAN [ J ]., 2007, 21 (5) : 51-54. [ 3 ] SHENGM IN C, MENG W. Analysis of Schedulability of CAN Based on RM A lgorithm [ C ] / /Vehicular Electronics and Safety. ICVES. IEEE International Conference, Dec. 2007: 1-4. [ 4 ],,,. CAN [ J ]., 2006, 26 (6) : 1301-1303. [ 5 ],,. CAN [ J ]., 2008, 27 (1) : 65-69. [ 6 ] PβREZ P, BENET G., BLANES F. Communication Jitter Influ2 ence on Control Loop s U sing Protocols for D istributed Real - Time System s on CAN Bus [ C ] / /Proc. Of IFAC SIC ICA, Aveiro, Por2 tugal, July 2003. [ 7 ] CAVAL IER I S, STEFANO A D i, BELLO L. Lo. CAN A ssessment in Time - Critical Cyclic App lications through Petri Net Model [ C ] / / Industrial Electronics, Control, and Instrumentation, Pro2 ceedings of the 1996 IEEE IECON 22nd International Conference, 1996, 2: 922-927. [ 8 ] BURCHARD A, L IEBEHERR J, Oh YF, Son SH. New Strategies for A ssigning Real - time Tasks to Multip rocessor System s [ J ]. IEEE Transaction On Computers, 1995, 44 (12) : 1429-1442. [ 9 ] HAAS P J. Stochastic Petri Nets: Modelling, Stability, Simulation [M ]. Sp ringer - Verlag, NewYork, 2002. ( : ) (45) : [ 1 ],. [ C ] / / 1995,, 1995: 9-34. [ 2 ],,. [ J ]., 2006, 42 ( ) : 135-138. [ 3 ] VENKAT Venkatasubramanian, RAGHUNATHAN Rengaswamy, KEW EN Yin, et al. A Review of Process FaultDetection and D iag2 nosis Part I: Quantitative Model2based Methods [ J ]. Computers and Chem ical Engineering, 2003, 27 (3) : 293-311. [ 4 ],,,. [ J ]., 2003, 39 (9) : 1-10. [ 5 ],,,. [M ]. :, 1993. [ 6 ] ZHA IL ian2yin, KHOO L i2pheng, FOK Sai - 2heong. Knowledge Acquisition and Uncertainty in Fault D iagnosis: a Rough Sets Per2 spective[ C ] / / T. Evangelos, F. Giovanni ( eds. ). Data M ining and Knowledge D iscovery App roaches Based on Rule Induction Techniques, Sp ringer US, 2006, 6: 359-394. [ 7 ] PAWLAK Z. Theorize with Data U sing Rough Sets[ J ]. Proceed2 ings - IEEE Computer Society s International Computer Software and App lications Conference, 2002: 1125-1128. [ 8 ] PAWLAK Z. Flow Graphs and Intelligent Data Analysis[ J ]. Fun2 damenta Informaticae, 2005, 64 (1-4) : 369-377. [ 9 ] PAWLAK Z. Decision Trees and Flow Graphs [ C ] / / Lecture Notes in Computer Science ( Rough Sets and Current Trends in Computing - 5th International Conference), 2006: 1-11. ( : )