Application of Rough Set Theory to EMI diagnosis

1 Cheng-Lung Huang

2 Te-Sheng Li

2 Ting-Kuo Peng

1 Cheng-Nan Shih

1The Department of Information Management, Huafan University and 2Department of Industrial Engineering and Management, Ming Hsin University of Science and

Technology

(Revised July 18, 2003; Accepted September 22, 2003)

(EMI, Electromagnetic Interference)

EMI

EMIEMI

EMI

(RST, Rough Set Theory) RST

RST

EMIRST

Abstract: Electromagnetic emissions are radiated from every part of motherboards of personal

computers, and thus electromagnetic interference (EMI) occurs. EMI has a bad effect on the

367 - 385

Journal of Management & Systems Vol. 11, No. 3, July 2004

pp. 367-385

368

surrounding environment because EMI may cause malfunctions or fatal problems of other digital

devices. EMI engineers diagnose EMI problems of motherboard from the electromagnetic noise data

measured by the Spectrum Analyzer. It is time consuming to find out the sources (PS2, USB, VGA, etc.)

of electromagnetic noise. Rough set theory (RST) is a new mathematical approach to data analysis.

This paper constructs an EMI diagnostic system based on RST. There are the following steps: Data

Collection, Data Preprocessing, Descretization, Attribute Reduction, Reduction Filtering, Rule

Generation, Rule Filtering, Classification, and Accuracy Calculation. Historical EMI noise data,

colleted from a famous motherboard company in Taiwan, are used to generate diagnostic rules. The

result of our research (average diagnostic accuracy of 80%) shows that RST model is a promising

approach to EMI diagnostic support system.

Keywords: Data Mining, Rough Set Theory, Attributes Reduction, Electromagnetic Interference

1.

EM I (Electromagnetic Interference) (Morgan, 1994; Mills, 1993)

(Archambeault, 2002)

()

EMI (IBMNECHPDellFujitsu)

EMI

EMIEMIEMI

EMI (

USB)

EMI

369

EMI

(Data

Mining)EMI

EMI1EMI

EMI (EMC, Electromagnetic

Compatibility)

(RST, Rough Set Theory) (Pawlak

1982, 1994, 1995; Kusiak, 2001) EMIEMI

EMI

2RST3

4

EMI EMI

EMI

D ata M in ing

EMI

EMC

Y es

N o

1 EMI

370

2.

2.1

Data Mining

(Han, 2000) (Classification) (Prediction)

(Association) (Clustering

(Sushmita, 2002; Kusiak,

2000; Kusiak, 2001; Bayardo, 1999; Hui, 2000; McKee, 2002; Ben-Arieh, 1998; Yoshida, 1999)

Gardner (2000) SOM (Self-Organizing

Map Neural Networks) (Rule Induction)

(90) Kruskal-Wallis

(Wafer Map) (Chen 2000; Lee, 2001; Skinner, 2002)

EMI

2.2

(Rough Set Theory, RST) Z. Pawlak1982

(Pawlak, 1982) (Vagueness and imprecise)

(Pawlak, 1991)RST

RST (1) (2)

(3) (Pawlak, 1982; Kusiak, 2001)RST

(Dimitras, 1999; Kusiak, 2001; Ahna, 2000; McKee, 2002)

RSTRSTRSTEMI

(1) (Information System)

(Decision Table) (Information Table)S= (Pawlak, 1991), U (Universe)U={x1, x2,, x10}A (Attributes)

A={a1, a2, a3}={,,}VVa1a1Va1={,,}(Information Function) VAUf :

371

UxAaVaxf a ,,),(

(Decision Attribute) (Condition Attributes)

(2) (Indiscenibility Relation) S=P AP Uyx , Ind(P)

x y

Paayfaxf = ),,(),( Ind(P)P

(Elementary Sets))(][ PIndix

(3) (Approximation of Sets)

(Lower Approximation)(Upper Approximation)RSTXU UX AP XP

}][|{ )( XxUxPX PIndii =

xixiX

PX XP (P-Lower Approximation)

XP

}0][|{ )( = XxUxPX PIndii

xixiX

PX XP (P-Upper Approximation)XU (Boundary) PXPXPNX =

BX = BXXXU4

(Undefinable Sets): 1) PX UPX X U (Roughly definable in U)

2) PX UPX = X U (Externally undefinable in U)

3) =PX UPX X U (Internally undefinable in U)

4) =PX UPX = X U (Totally undefinable in U)

1)(0),(/)()( = XPXcardPXcardX PP

(4) (Reduction of Attributes) )()( iaAIndAInd = aiai (Dispensable in A)

aiai

372

S ( ) P A ,...,,{ 21 XX =

UXXXUXX ijiin == ,,}, U (Classification) Xi(Classes)

( ) d =P

},...,,{ 21 nPXPXPX },...,,{ 21 nPXPXPXP = (Quality of Classification)

)(/)()(1

UcardPXcardn

iiP

=

=

P AP PA )(P P

R APR

)()( PR = P )(PRED

(Minimal Subsets of Attributes)

(Core)

)()( PREDPCORE =

RST

(Discernibility Matrix) (Walczak, 1999)2.3

(5) ( Decision Rules)

2.3

2.3 RST

RST8

(1) A={Diploma, Experience, French, Reference } =

{a1, a2, a3, a4}, D={Decision}={d}

2

Diploma{MBA, MCE, MSc} = {1, 2, 3}

Experience{High, Medium, Low} = {1, 2, 3}

French{Yes, No} = {1, 2}

Reference{Excellent, Good, Neutral} = {1, 2, 3}

Decision{Accept, Reject} = {1, 2}

373

1 ()

U Diploma Experience French Reference Decision x1 MBA Medium Yes Excellent Accept

x2 MBA Low Yes Neutral Reject

x3 MCE Low Yes Good Reject

x4 MSc High Yes Neutral Accept

x5 MSc Medium Yes Neutral Reject

x6 MSc High Yes Excellent Accept

x7 MBA High No Good Accept

x8 MCE Low No Excellent Reject

2

U a1 a2 a3 a4 d x1 1 2 1 1 1

x2 1 3 1 3 2

x3 2 3 1 2 2

x4 3 1 1 3 1

x5 3 2 1 3 2

x6 3 1 1 1 1

x7 1 1 2 2 1

x8 2 3 2 1 2

Xd=1 = {x1,x4,x6,x7}Xd=2 = {x2,x3,x5,x8}

3x1x2

a2a4a2a4

{x1,x4,x6,x7}

-

(Boolean function) a1a221 aa

a1 and a2(a1, a2) (a1 + a2) (a1 or a2)

(a1+a2+a3)a2=a2, a2(a1+a2+a3)(a1+a3)(a1+a3) = a2(a1+a3)=a2a1+a2a3

374

3 A

x1 x2 x3 x4 x5 x6 x7 x8 x1 x2 a2, a4 x3 a1,a2,a4 - x4 - a1,a2 a1,a2,a4 x5 a1, a4 - - a2 x6 - a1,a2,a4 a1,a2,a4 - a2,a4 x7 - a2,a3,a4 a1,a2,a3 - a1,a2,a3,a4 - x8 a1,a2,a3 - - a1,a2,a3,a4 - a1,a2,a3 a1,a2,a4

)(Df A =(a2, a4) (a1,a2,a4)( a1, a4)( a1,a2,a3)( a1,a2)( a1,a2,a4)( a2,a3,a4)( a1,a2,a4)

( a1,a2,a4)( a1,a2,a3)( a2)( a1,a2,a3,a4)( a2,a4)( a1,a2,a3,a4)( a1,a2,a3)( a1,a2,a4)

=( a1, a4) a2=a1a2+a2a4

a1a2+a2a4a1a2a2a4

a1a2a2a4a1a2

a3a44

4 (a1a2)

U Diploma (a1) Experience (a2) Decision(d)

x1 1 2 1

x2 1 3 2

x3 2 3 2

x4 3 1 1

x5 3 2 2

x6 3 1 1

x7 1 1 1

x8 2 3 2

4

{a1,a2}5 (

)

375

5 a1a2

x1 x2 x3 x4 x5 x6 x7 x8 x1 a2 a1,a2 - a1 - - a1,a2 x2 a2 - a1,a2 - a1,a2 a2 - x3 a1,a2 - a1,a2 - a1,a2 a1,a2 - x4 - a1,a2 a1,a2 a2 - - a1,a2 x5 a1 - - a2 a2 a1,a2 - x6 - a1,a2 a1,a2 - a2 - a1,a2 x7 - a2 a1,a2 - a1,a2 - a1,a2 x8 a1,a2 - - a1,a2 - a1,a2 a1,a2

)(1 Df =a2(a1,a2)a1(a1,a2)=a1a2 )(2 Df =a2(a1,a2)(a1,a2)a2=a2 )(3 Df =(a1,a2)(a1,a2)(a1,a2)(a1,a2)=a1+a2 )(4 Df =(a1,a2)(a1,a2)a2(a1,a2)=a2 )(5 Df =a1a2a2(a1,a2)=a1a2 )(6 Df =(a1,a2)(a1,a2)a2(a1,a2)=a2 )(7 Df =a2(a1,a2)(a1,a2)(a1,a2)=a2 )(8 Df =(a1,a2)(a1,a2)(a1,a2)(a1,a2)=a1+a2

66x2, x4, x6,

x7,x1, x5x3x8a1=2a2=3

d=2x2a2=3 d=2x3x8

a1(-)a1

6 (-) (a1a2)

U Diploma (a1) Experience (a2) Decision x1 1 2 1 x2 - 3 2 x3 - 3 2 x4 - 1 1 x5 3 2 2 x6 - 1 1 x7 - 1 1 x8 - 3 2

376

64 ()

1) Experience = 1(High) Decision = 1 (Accept)

2) Experience = 3(Low) Decision = 2 (Reject)

3) Experience = 2(Medium) and Diploma = 1(MBA) Decision = 1 (Accept)

4) Experience = 2(Medium) and Diploma = 3(MSc) Decision = 2 (Reject)

a2a47884()

1) Experience = 1(High) Decision = 1 (Accept)

2) Experience = 3(Low) Decision = 2 (Reject)

3) Experience = 2(Medium) and Reference = 1(High) Decision = 1 (Accept)

4) Experience = 2(Medium) and Reference = 3(Low) Decision = 2 (Reject)

7 (a2a4)

U Experience (a2) Reference (a4) Decision (d) X1 2 1 1 X2 3 3 2 X3 3 2 2 X4 1 3 1 X5 2 3 2 X6 1 1 1 X7 1 2 1 X8 3 1 2

8 (-) (a2a4)

U Experience (a2) Reference (a4) Decision(d) X1 2 1 1 X2 3 - 2 X3 3 - 2 X4 1 - 1 X5 2 3 2 X6 1 - 1 X7 1 - 1 X8 3 - 2

377

3. RSTEMI

3.1

EMI (Spectrum Analyzer)EMI

2 (Frequency) 30MHz1GHz1MHz

()dBdB

MHzdB

30MHz~230MHz30dB231MHz~1GHz37dB

EMIEMI

2

Freq.(MHz)EMIWarning Mark

X!

EMI

2 EMI

378

3.2 EMI

RSTEMI3 (Data Collection)

(Data Preprocessing) (Discretization) (Attribute

Reduction) (Reduction Filtering) (Rule Generation)

(Rule Filtering) (Classification) (Accuracy Calculation)

(Diagnostic System)

3 RST EMI

(1)

EMI

111 (9)

EMI415134 281 (2)

Port (4)

: A (Printer, Ps2, Com) B (VGA) C (LAN, USB, Audio, Game)

(3)

10

1. 4.3.

5.

6. 7.8. 10.

9.

2.

379

9

Chipset 3 3 3 a1

IO Chipset I/O(Printer,Com,PS2) 7 3 7 a2

Audio 3 2 3 a3

Memory 2 2 2 a4

PCB-size 2 2 2 a5

CPU-slot CPU 5 3 5 a6

USB USB 2 2 2 a7

LAN LAN 4 4 4 a8

VGA VGA 4 3 4 a9

Failure-Level EMI Noise 3 3 3 a10

Frequency-Level 8 5 3

a11

Failure-Area EMI 3 3 3 d

4 ABC

(4)

30-1G MHzEMIdB (30-230 MHz)

(230-1G)

Area A

Area B

380

(Johnson, 1974; Vinterbo, 2000)

(Fitness function)

Rosetta (2001)

2Set

{Chipset, Audio, Memory, PCB-size, CPU-slot, LAN, Failure-Level, Freq-Level}

{Chipset, Audio, PCB-size, CPU-slot, LAN, VGA, Failure-Level, Freq-Level}

3Set

{Chipset, VGA, Failure-Level, Freq-Level}

{Chipset, Memory, LAN, Failure-Level, Freq-Level}

{Chipset, PCB-size, LAN, Failure-Level, Freq-Level}

(5)

{Chipset, Audio, Memory, PCB-size,

CPU-slot, LAN, Failure-Level, Freq-Level} {Chipset, VGA,

Failure-Level, Freq-Level}

(6)

16622

Chipset (Via) AND Audio (CMI9738) AND Memory (SDRAM) AND PCB-size (Micro-ATX) AND

CPU-slot (Socket478) AND LAN (None) AND Fail-Level (C) AND Freq-Level(2) => Fail-area (A)

ChipsetViaAudioCMI9738Memory

SDRAMPCB-sizeMicro-ATXCPU-slotSocket478LAN None

Fail-LevelCFreq-Level2A

(Chipset, Audio,)EMI (Freq-Level)

(Fail-Level)EMIA (Printer, Ps2Com)

(7)

(8)

(Slowinski, 1994)

1) (Deterministic Logical Rule)

381

2) ()

()

3) (Non-deterministic Logical Rule)

()

4)

(9)

90.39%71.64% (1011)

10

A C B A 72 3 0 96% C 23 179 0 88.61% B 0 1 3 75%

75.79% 97.81% 100% 90.39%

11

A C B A 46 12 0 79.31% C 18 42 0 70% B 4 4 8 50%

67.65% 72.41% 100% 71.64%

(10)

EMIEMIEMI

EMI

81%

(90%72%)

EMI

(1)

382

3.3

(Decision Tree)

EMIEMI

ID3 (Quinlan, 1986) C4.5 (Quinlan, 1993)

C5.0 (http://www.rulequest.com/)C5.0

EMI

(Testing Set)

(Training Set)12C5.0

77%11 (12) RST

RST (84)

RST

12

RST 8 4 88.4% 70.6% 79.5%

11 11 85.4% 68.7% 77%

4.

EMIEMI

RSTEMIEMI

EMI

RST

(1)~(9)

(Hybrid System)

383

(

) RST

5.

NSC-92-2213-E-211-012

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