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利用可拓工程法於蒸汽渦輪發電機組之振動故障診斷

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(1)

ӀϡΞ٤̍඀ڱٺᄐՠ഻዇൴࿪፟௡̝ॎજ߇ᅪ෧ᕝ

ͳ؜ዂ Ղқᓏ ߸୻ᚗ

઼ϲ๔ৈԫఙጯੰ࿪፟ր

ၡ! ࢋ

ώኢ͛੫၆൴࿪ᇄᄐՠ഻዇൴࿪፟௡ॎજ߇ᅪĂ೩΍˘इͽۏ̮ሀݭ׶Ξ ٤ᙯᓑבᇴࠎૄᖂ۞Ξ٤߇ᅪ෧ᕝڱĄࢵАĂॲፂனಞ၁ീྤफ़ޙϲ൴࿪፟௡

ॎજ߇ᅪ۞ۏ̮ሀݭĂ֭Ӏϡ˘௡າ۞Ξ٤ᙯᓑבᇴࢍზ߇ᅪྤफ़׶߇ᅪࣧЯ

̝ᙯᓑޘĂ൴࿪፟௡۞ॎજ߇ᅪΞགྷϤᙯᓑޘۡତ෧ᕝ΍ֽĄࠎរᙋώ͛ٙ೩

͞ڱ̝၁ϡّĂώࡁտͽ઼̂̚ౙ˘ֱ࿪ᇄ၁ീྤफ़ࠎ၆෪ĄീྏඕڍពϯĂ ώ͛ٙ೩̝͞ڱ࠹༊ዋЪᑕϡٺ၁ᅫ۞߇ᅪ෧ᕝր௚Ą

ᙯᔣෟĈ߇ᅪ෧ᕝăॎજ߇ᅪăΞ٤͞ڱăۏ̮ሀݭĄ

APPLICATION OF EXTENSION ENGINEERING METHOD TO

VIBRATION FAULT DIAGNOSIS OF STEAM TURBINE GENERATOR SETS

Mang-Hui Wang Heng-Sheng Lee Chin-Pao Hung

Department of Electrical Engineering National Chin-Yi Institute of Technology

Taichung, Taiwan 411, R.O.C.

Key Words: fault diagnosis, vibration fault, extension theory, matter- element model.

ABSTRACT

In this paper, a novel extension fault diagnosis method (EFDM), based on the matter-element model, and an extended correlation function is presented for vibration fault diagnosis of steam turbine generators. First, the matter-element models of the vibration fault are built according to diagnostics derived from practical diagnostic records. Then, vibration faults in steam turbine generators can be directly identified by degrees of relation.

Applications of this new method to generator sets in China have given promising results.

˘ă݈! ֏

၆࿪˧ր௚҃֏Ă൴࿪፟௡ߏ࠹༊ࢦࢋ۞న౯âό

൴࿪፟௡൴Ϡ߇ᅪĂ̙ҭົֹ൴࿪ᇄ൴Ϡྯְ፟߇Ăᚑࢦ ॡࠤҌົጱ࡭࿪˧ֻᑕ̚ᕝĂซֹ҃̍થຽயϠλ̂۞ຫ εĄЯѩĂ၆࿪˧̳Φ҃֏Ăਕૉӈॡ෧ᕝ΍൴࿪̰፟ొ

۞߇ᅪߏ˘Іܧ૱ࢦࢋ۞̍үĂтѩΞឰჯ࣒̍඀रਕӈ ॡଳפᑕតନ߉ٕטؠԆච۞ჯ࣒ࢍ൪Ăͽഇ೩چ࿪˧ր

௚ྻᖼ̝ΞያޘĄ

˘ਠ̂ݭ۞ᄐՠ഻዇൴࿪፟௡ߏϤᄐՠ഻዇፟ă൴࿪

፟׶፬Ⴣ፟ٙၹј۞Ă҃ᄐՠ഻዇፟௡۞ਕณ็ਖ਼ืᖣϤ

็જคాତĄ˘ਠ҃֏Ă൴࿪፟௡дϒ૱ېڶ˭ĂߏϤ࠹

༊િ׽۞็જคాତĂҭߏϤٺ፟ୠਕᖼೱј࿪ਕॡٙ૲

ֽ۞Ԯ˧Ăົጱ࡭็જค୊ᖼॡயϠॎજүϡ[1-4]Ą͔੓

ॎજ۞ࣧЯ࠹༊ኑᗔĂּт፟ୠคֹٚϡ̙ሒٕ̙ዋЪ۞

ማ໣ڵĂٕ࢑ྶณ࿅̂ඈЯ৵ĂӮѣΞਕౄј൴࿪፟௡ய

(2)

Ϡॎજ[5,6]ĄЯѩĂ൴࿪፟௡߇ᅪॡĂܮΞᖣϤॎજܫཱི

۞ᐛᙉјЊซҖ̶ᙷᏰᙊĂӈΞԱ΍Ξਕ۞߇ᅪࣧЯĄ

࿅ Ν ѣ ᙯ ߇ ᅪ෧ ᕝ ۞ ͞ ڱ ࠹༊ к Ă ּ т ૞छ ր ௚ (expert systems)[5]ăᙷৠགྷშྮăሀቘទᏭڱ݋(fuzzy logic approaches)[3] ׶ ሀ ቘ ৠ གྷ შ ྮ (fuzzy neural networks ć FNN)[2]ඈԫμĂЋဦԯ૞छགྷរٕ߇ᅪീྏ۞၁ּጯ௫੓

ֽĂͽפ΃ˠ̍෧ᕝ۞৿ᕇĄࡁտඕڍពϯĂᙷৠགྷშྮ

Ξͽଂ੊ቚྤफ़̚ᒔפགྷរĂТॡΞͽጯ௫Ꮾˢ׶Ꮾ΍̝

มܧቢّ۞ᙯᓑّĂ఺჌পᕇΞͽҹڇ૞छր௚ٙயϠ۞

৿ᕇĄҭߏĂᙷৠགྷშྮυืפ଀֖ૉ۞੊ቚྤफ़̖ਕགྷ Ϥጯ௫଀זྵჟቁ۞ඕڍĄѩγĂᙷৠགྷშྮ۞ࢨטߏ൑

ڱயϠୃّࢗ۞Ꮾ΍Ăдଯந˯ӧᙱޘྵ੼Ą૞छր௚׶

ሀቘទᏭڱ݋ඈଳϡ૞छགྷរ۞͞ڱĂ಼̏̂೩چ߇ᅪ෧ ᕝ̝໤ቁதĂ֭ͷ̏གྷјΑᑕϡٺ߇ᅪ෧ᕝᅳા̝̚Ą൒

҃Ă఺ֱ͞ڱώ֗ݒѣ˘ֱ̙ΞᔖҺ۞৿ᕇĂּт૞छགྷ រפ଀ӧᙱĂྤफ़ऱՀາ̙ٽ׶ർវ၁னྵࠎӧᙱඈયᗟĄ

ࠎҹڇ˯ࢗ͞ڱ̝৿ᕇֹ̈́෧ᕝ̍׍Հਕ၁ϡ̼Ăώ

͛೩΍˘इΞ٤߇ᅪ෧ᕝڱઇ̂ݭᄐՠ഻዇൴࿪፟௡۞ॎ

જᑭീĄΞ٤நኢߏ̂ౙጯ۰ች͛ࠎ˞ྋՙ͹މ៍Ϭ࠼ય ᗟٺ 1983 ѐٙଯጱ۞நኢ[9,10]ĂΞ٤ጯநኢ۞׌̂͹ค ߏۏ̮நኢ׶Ξ٤ะЪநኢĂӀϡۏ̮ሀݭ(matter-element model)ೡࢗੈिĂΞͽซҖณត׶ኳត۞ტЪ̶ژĄЯѩ ΞТॡࡁտณ׶ኳ׌۰၆યᗟ۞ᇆᜩ඀ޘĂֹֹϡ۰ਕ၆ ր௚পᇈ̝ৌ၁ّ଀זՀԆፋ۞ੈि[11,12]Ąώ͛೩΍૟

Ξ٤நኢᑕϡд൴࿪፟௡߇ᅪ෧ᕝ˯ĂࢵАĂӀϡனಞ၁

ീ̝९ּࡔᐂޙϲ߇ᅪᙷݭ۞ۏ̮ሀݭ[1]ĂГӀϡϒఢ̼

ᙯᓑבᇴზ΍ޞീ൴࿪፟௡Ъ׶Ч߇ᅪᙷݭ̝ᙯᓑޘĂซ

҃ΞͽۡତԱ΍߇ᅪېڶĄ౵ޢĂώ͛ͽ઼̂̚ౙߙ൴࿪

ᇄ၁ീ̝ྤफ़ซҖ෧ᕝീྏĂ෧ᕝඕڍពϯĂώ͛ٙ೩̝

͞ڱቁ၁ܧ૱ዋЪྋՙ൴࿪፟௡߇ᅪ෧ᕝ۞યᗟĄ

˟ăΞ٤நኢᖎ̬

Ξ٤நኢߏӀϡۏ̮ᖼೱ͞ёྋՙ͹މ៍Ϭ࠼۞ય ᗟĂΞ٤ะЪ૟ሀቘะЪଂ(0,1)ؼҩז(−∞, )[9]ĄЯѩĂ ιΞͽؠཌྷኢા̚Їңྤफ़۞ะЪࣃĄѩγĂΞ٤ะЪந ኢΞ҂ᇋ˘࣎ᕇᄃ׌ડม၁ᅫҜཉ(Ҝࣃ)̝ᙯܼĂтڍҜ ࣃд-1 ̝˭Ăពϯѩᕇ̙֭дѩะЪ̝̚ćࡶߏ̬ٺ 0 ז -1 ̝ม݋ჍΞ٤ાĂΞͽܑϯѩᕇд఺࣎ะЪቑಛγĂҭ ѣΞਕᛳٺ఺ะЪ۞˘ొЊćะЪࣃ̂ٺ 0 ॡĂ݋ܑϯѩ ᕇቁ၁д఺࣎ะЪቑಛ̝̰ĄΟ׏ะăሀቘะᄃΞ٤ะඈ

఺ˬ჌ะЪ۞পّͧྵтܑ˘ٙϯĂ҃ѣᙯٺΞ٤நኢ۞

࠹ᙯؠཌྷ૟д˭˘࣎̈༼̚ઇྎ௟۞̬௜Ą 1. ۏ̮۞ૄώநኢ

дΞ٤நኢ̚Ăۏ̮Βӣ˞ˬ࣎ૄώ۞ࢋ৵Ąనְۏ R ۞ЩჍࠎ NĂপᇈࠎ cĂ׎ᙯٺপᇈ c ۞ณࣃࠎ vĂ݋ೡ

ְࢗۏ۞ૄώ̮ٕ˘ჯۏ̮ࠎĈ

ܑ˘ ˬ჌̙Тᙷݭ۞ᇴጯะЪ

ͧྵีϫ Ο׏ะ ሀቘะ Ξ٤ะ ࡁտ၆෪ ᇴࣃតณ ᄬ֏ّតณ Ϭ࠼યᗟ

˘ਠሀݭ ᇴጯሀݭ ሀቘᇴጯሀݭ ۏ̮ሀݭ בᇴୃࢗ ᖼொבᇴ ะЪבᇴ ᙯᓑבᇴ

পّୃࢗ ໤ቁ ሀቘ Ξ٤

ะЪቑಛ CA(x){ }0,1 µA(x)[ ]0,1 KA(x)(−∞,)

R = (N, c, v) (1)

ࡶԧࣇ઄నְۏ R = (N, C, V)ߏ˘࣎׍ѣкჯ۞ۏ

̮Ăְ҃ۏѣ n ࣎পᇈॡĂΞͽϡ৏ੱ C = [c1,c2,...,cn]

΃ܑĂ׎၆ᑕ۞ณࣃ̶Ҿͽᇴࣃ৏ੱ V = [v1,v2,...,vn

ܑĂ݋кჯۏ̮۞ܑϯёࠎĈ

=

=

=

n n v c

v c

v c N

V C N

, , , , )

, ,

( 2 2

1 1 2

1

R R R R

n

L L

L (2)

ٕᖎ̼ј ) , , (N CV

R= (3)

ۏ̮Ri=(N,ci,vi)(i=1, 2,…,n)ߏ R ۞ௐ i ࣎̄ۏ̮Ă

˘ְ࣎ۏΞਕѣధк۞পᇈĂ̙҃Т۞ۏ̮Ξਕົѣ࠹Т

۞পᇈ׶ᇴࣃĄΞ٤நኢ۞ૄώؠநт˭ٙϯĈ ؠந 1. నְۏѣధк۞পᇈĂ׎ؠཌྷࠎĈ

N (N, c, v) {(N,c1,v1) (, N,c2,v2) (,K, N,cn,vn)} (4)

׎̚Ă௑ཱི “ ” ΃ܑΞ٤Ą

ؠந 2. న˘ְֱۏѣ࠹Т۞পᇈĂ׎ؠཌྷࠎĈ

! (N, c, v) {(N1,c,v1) (, N2,c,v2) (,K, Nn,c,vn)} (5)

ؠந 3. న̙࠹Т۞ְۏѣ࠹Т۞পᇈࣃĂ׎ؠཌྷࠎĈ (N, c, v) {(N1,c1,v) (, N2,c2,v) (,K, Nn,cn,v)} (6)

ֹϡۏ̮ሀݭĂԧࣇΞͽೡࢗኳณᄃۏ̮ኳณ̝ม

۞ᙯܼĂซ҃ޙϲ˘࣎າ۞ᇴጯ៍هĄ 2. Ξ٤ะЪநኢ

(˘) Ξ٤ะЪ۞ؠཌྷ

న ኢ ા U ̚ Ї ˘ ̮ ৵ x ͷxU Ă ݋ ѣ ˘ ၁ ᇴ

(−∞)

, ) (x

K ᄃ̝၆ᑕĂ݋Ξ٤ะЪ A~

̝ؠཌྷࠎĈ

{( , ) , ( ) ( , )}

~= x y xU y=K x −∞

A (7)

׎̚ y=K(x)ࠎ A~

۞ᙯᓑבᇴĂK(x)ࠎ x ̝ᙯᓑޘĂ׎

ቑಛࠎ-∞ ז ∞Ă׎Ξ٤ะЪ A~

д U ኢા̚ΞܑϯјĈ

(3)

K(x)

x

a b

bp ap

1

-1

ဦ 1 Ξ٤ᙯᓑבᇴ

+

=A J A

A~ o

(8)

׎̚

{( , ) , = ( )>0}

+=

x K y U x y x

A (9)

{( , ) , = ( )=0}

= x y x U y K x

Jo (10)

{( , ) , = ( )<0}

=

x K y U x y x

A (11)

дё(9)׶(10)̚ĂA Ⴭࠎ A+ ~

۞ϒાćA Ⴭࠎ A ~

۞࢑

ાćJ ۞ొЊ݋Ⴭࠎ Ao ~

۞࿬ࠧ[9]Ą (˟) ෼۞ؠཌྷ

న x ࠎ၁ા(−∞,)˯Ї˘ᕇĂXo= a,b ࠎ˘၁ા˯

Ї˘ડมĂ݋ᕇ x ᄃડมX ۞෼ؠཌྷࠎĈ o

2 ) 2

,

( a b b a x

X

x o = +

ρ (12)

(ˬ) Ҝཉࣃ(Ҝࣃ)

дΞ٤ะ̚ੵᅮ҂ᇋᕇᄃડม۞ҜཉᙯܼγĂགྷ૱ื

҂ᇋ˘࣎ᕇ၆׌ડม̝ҜཉᙯܼĄనXo= a,b Ă

p

p b

a

X = , ĂͷXo∈ Ă݋ᕇ x ᙯٺX Xo,X ۞Ҝࣃ ࠎĈ

X x

X x

o o

= 1

) , ( ) , ) ( , ,

( o x X x Xo X

X x

D ρ ρ

(13)

(α) ܐඈᙯᓑבᇴ

Xo= a,bĂX= ap,bp ĂXo∈ ͷ൑̳ВბᕇĂX

݋ܐඈᙯᓑבᇴࠎ

) , , (

) , ) (

( Dx X X X x x

K

o

ρ o

= (14)

ᙯᓑבᇴΞࢍზ x ᕇᛳٺX ̝ᙯᓑ඀ޘĂ༊o K(x)0

ܑϯ x ᛳٺX ۞඀ޘĂo K(x)<0Ⴭࠎ x ̙ᛳٺX ۞o

඀ޘĄӀϡΞ٤ᙯᓑבᇴΞࢍზ x ᕇᛳٺX ̝඀ޘĂo Ξ٤ᙯᓑבᇴтဦ 1 ٙϯĄ༊K(x)0ܑϯ x ᛳٺX o

ဦ 2 ᄐՠ഻዇൴࿪፟௡ϯຍဦ

۞඀ޘć༊K(x)<0Ⴭࠎ x ̙ᛳٺX ۞඀ޘć༊o 0

) ( 1< <

K x ॡĂჍࠎΞ٤ાĂܑϯтڍېၗԼតॡĂ x ѣ፟ົјࠎѩะЪ۞˘ొЊĄ

ˬăώ͛೩΍̝ॎજ߇ᅪ෧ᕝ͞ڱ

ဦ 2 ࠎ˘ᄐՠ഻዇൴࿪፟௡۞ᖎ̼ሀݭĂ׎̚Βӣˬ

̂ొЊĈ഻዇ă൴࿪፟׶፬Ⴣ፟ĄՏ࣎ొЊ࠰Ϥ็જคా

ତĂઇࠎ፟ୠਕณ̝็ਖ਼ಫ̬Ą൴࿪፟дϒ૱ፆү˭Ăॎ

જଐԛ࠹༊ᘦؠͷॎ಼ྵ̈ćҭߏࡶѣ߇ᅪ൴Ϡă፟ୠΑ த൴ϠλតٕயϠᇶၗᜩᑕॡĂ׎ॎજੈཱི̝ॎ಼˵ົᐌ

̝Լត[13,14]ĄЯѩĂΞͽᖣϤॎજੈཱིᐛᙉ̶ژٙ೩ֻ

̝Ꮨگॎ಼ซҖ߇ᅪ෧ᕝĄώ͛ٙ೩΍۞͞ڱॲፂ͛ᚥ̝

၁ീྤफ़[1]Ăଂॎજ߇ᅪੈཱི̚߄Ᏼ΍׏ݭ۞˝჌পᇈࣃ (̶Ҿࠎ 0.01f~0.39f, 0.40f~0.49f, 0.5f, 0.51f~0.99f, f, 2f, 3f~5f, oddf ׶ >5f ඈ˝჌Ꮨگ̝ॎ಼)ઇࠎ߇ᅪ෧ᕝր௚̝

ᏮˢܫཱིĂ׎̚ f ࠎ൴࿪፟୊ᖼᐛதĂoddf ࠎ؈ѨᏘگӣ ณĄࢵАĂԧࣇӀϡ఺ֱ၁ീ̝ྤफ़ޙϲॎજ߇ᅪ჌ᙷ۞

ۏ̮ሀݭĂ൒ޢ൴࿪፟௡̝߇ᅪᙷݭΞᖣϤΞ٤ᙯᓑבᇴ ซҖ̶ᙷ׶ᏰᙊĄ

1. ൴࿪፟௡ॎજ߇ᅪ෧ᕝ۞ۏ̮ሀݭ

ॲፂ၁ീྤफ़߇ᅪ჌ᙷΞ̶јα჌[1]ĂΩనؠ˘௡൴

࿪፟ր௚дϒ૱˭̝ۏ̮ሀݭĂ݋ፋ࣎߇ᅪ෧ᕝ̝ۏ̮ሀ ݭΞፋநтܑ˟ٙϯĄְۏ R ߏᛳٺ఺̣჌߇ᅪݭၗ۞ۏ

̮Ăܑ˟̚F ={F1,F2,F3,F4,F5}ࠎ׎߇ᅪะĂF ̶Ҿ΃i

ܑௐ i ࣎߇ᅪݭၗĄ׎ࣃાቑಛߏֶፂՏ࣎পᇈ̮၆ᑕ̝

གྷ׏ાనؠĂ׎Ᏼؠ͞ڱΞӀϡ၁ീྤफ़̚Ч߇ᅪᙷݭٙ

၆ᑕপᇈณࣃ۞˯ă˭ࢨࣃࢎؠĄΩγГᏴؠ˘ۏ̮ೡࢗ

Чॎજᐛᙉ౵̝̂टధณ̝˯˭ࢨٕ༼ાĂ׎నؠт(15) ёٙϯĈ

>

=

=

08 0 0

13 0 0

13 0 0 5

3

16 0 0 2

85 0 0 1

20 0 0 99

0 51 0

54 0 0 5

0

27 0 0 49

0 40 0

12 0 0 39

0 01 0

) , , (

. , f ,

. ., odd f,

. ., f, f~

. ., f,

. ., f,

. , f, . f~

.

. , f, .

. , f, . f~

.

. , f, . f~

. , F

V C F R

p

p p

p (15)

(4)

ܑ˟ ൴࿪፟௡ॎજ߇ᅪ۞ۏ̮ሀݭ ߇ᅪ

ᙷݭ ۏ̮ሀݭ

F1Ĉ

̙πᏊ

>

=

00596 0 00322 0

04958 0 01962 0

04958 0 01962 0 5

3

09388 0 05299 0 2

84174 0 75780 0 1

01846 0 01049 0 99 0 51 0

00993 0 00131 0 5

0

00267 0 00122 0 49 0 40 0

05129 0 00256 0 39

0 01

1 0

1

. , . f ,

. , . odd f,

. , . f, f~

. , . f,

. , . f,

. , . f, . f~

.

. , . f, .

. , . f, . f~

.

. , . f, . f~

. , F

R

F2Ĉ ༥ ᇠ ᇝ

>

=

07864 0 05200 0

02518 0 01288 0

05657 0 04653 0 5

3

02107 0 01725 0 2

61279 0 56365 0 1

17401 0 12527 0 99 0 51 0

02175 0 00523 0 5

0

01598 0 00545 0 49 0 40 0

11805 0 03012 0 39

0 01

2 0

2

. , . f ,

. , . odd f,

. , . f, f~

. , . f,

. , . f,

. , . f, . f~

.

. , . f, .

. , . f, . f~

.

. , . f, . f~

. , F

R

F3Ĉ

ෘ৳

>

=

03770 0 02230 0

12893 0 07667 0

12893 0 07667 0 5

3

15624 0 14974 0 2

63413 0 54074 0 1

00723 0 00566 0 99

0 51 0

00553 0 00281 0 5

0

00344 0 00178 0 49

0 40 0

01320 0 00178 0 39

0 01

3 0

3

. , . f ,

. , . odd f,

. , . f, f~

. , . f,

. , . f,

. , . f, . f~

.

. , . f, .

. , . f, . f~

.

. , . f, . f~

. , F

R

F4Ĉ ڵ ቯ ॎ

>

=

00791 . 0 00510 . 0

02777 . 0 02069 . 0

02777 . 0 02069 . 0 5

3

09657 . 0 03498 . 0 2

09938 . 0 05216 . 0 1

19642 . 0 07214 . 0 99 0 51 0

53938 . 0 39201 . 0 5

0

26129 . 0 14473 . 0 49 0 40 0

02475 . 0 00482 . 0 39 0 01

3 0

3

, f ,

, odd f,

, f, f~

, f,

, f,

, f, . f~

.

, f, .

, f, . f~

.

, f, . f~

. , F

R

F5: ϒ૱

>

=

0007 0 0 0

0005 0 0 0

0002 0 0 0 5

3

0005 0 0 0 2

84 0 75 0 1

0005 0 0 0 99

0 51 0

0003 0 0 0 5

0

0009 0 0 0 49

0 40 0

0005 0 0 0 39

0 01

5 0

5

. , . f ,

. , . odd f,

. , . f, f~

. , . f,

. , . f,

. , . f, . f~

.

. , . f, .

. , . f, . f~

.

. , . f, . f~

. , F

R

߇ᅪ෧ᕝ۞ۏ̮ሀݭޙϲޢĂӈΞซҖ൴࿪፟௡̝߇ ᅪ෧ᕝĄ˘ਠ҃֏Ă༼ા۞ᏴؠߏֶЧ࣎གྷ׏ા̝౵̂˯

˭ࢨᏴؠĂ׎Ᏼؠቑಛ่ົᇆᜩᙯᓑבᇴΞ٤ા̝ቑಛĄ

ֶώ͛ീྏགྷរ଀ۢĂ׎၆߇ᅪ෧ᕝ໤ቁதᇆᜩ̙̂Ăд

৿ͻ̂ณീྏྤफ़˭ĂΞᏴؠ૟ٙѣགྷ׏ા۞˯˭ࢨᕖᆧ ࡗ 10%ĂӈΞ଀ז΄ˠ႕ຍ۞ඕڍĄ

2. Ξ٤߇ᅪ෧ᕝڱ

ώ͛ٙ೩΍۞Ξ٤߇ᅪ෧ᕝڱ̏གྷјΑгӀϡ࿪ཝ హវޙၹ΍˘इ൴࿪፟௡۞߇ᅪ෧ᕝր௚Ą׎߇ᅪ෧ᕝႊ

ზڱ݋т˭Ĉ

Վូ 1ĈАޙϲՏ࣎߇ᅪᙷݭ۞ۏ̮ሀݭ

! 12 5

9 9

8 8

7 7

6 6

5 5

4 4

3 3

2 2

1 1

,..., , i

V c

V c

V c

V c

V c

V c

V c

V c

V , c F

R

i i i i i i i i i i

i =

= (16)

׎ ̚Vij= aij,bij ࠎ Ч প ᇈะ ̝ གྷ ׏ા Ă֭ ੃

pj pj

pj a b

V = , ࠎЧপᇈะ̝ณાٕ༼ાĄ׎Տ࣎

߇ᅪᙷݭགྷ׏ાΞϤീྏྤफ़ᒔ଀[1]Ăώࡁտॲ ፂՏ˘჌ॎજ߇ᅪᐛᙉቑಛ̝˯ă˭ࢨࣃనؠགྷ

׏ાVij = aij,bij ۞ࣃĂ׎ፋநтܑ˟ٙϯĄ Վូ 2Ĉ ૟ޞീ൴࿪፟௡۞ॎજܫཱིۏ̮ᖎܑ̼ϯј˭

ёĈ

>

=

=

9 8 7 6 5 4 3 2 1

5 3

2 1

99 0 51 0

5 0

49 0 40 0

39 0 01 0

) (

t t t t t t t t t t

t t t

v f ,

v odd f,

v f, f~

v f,

v f,

v f, .

f~

.

v f, .

v f, . f~

.

v f, . f~

. , F

,C,V F

R (17)

׎̚Ăv ࠎޞീ፟௡ௐ i ࣎পᇈ̝ณࣃĄ ti Վូ 3ĈӀϡώ͛ٙ೩΍̝߇ᅪᙯᓑבᇴĂࢍზޞീ൴࿪

፟௡̝߇ᅪᙯᓑޘĈ

, ,



=

ij tj ij tj pj tj

ij tj

ij tj ij

ij tj

tj ij

V V v

v V v

V v

V v V

V v v

K

) if , ( ) , (

) , (

) if , (

) (

ρ ρ

ρ ρ

(18)

׎̚i=1,2,...,5 ; j=1,2,...,9

2

ij ij ij

a

V b

= (19)

ဦ 3 ӈߏώ͛ٙ೩΍̝Ξ٤ᙯᓑבᇴĄ׎̚Ă༊

1 ) (

0K v ॡĂ࠹༊ٺ็௚۞ሀቘะЪĂΞϡͽณޘ v ᛳ ٺV ۞඀ޘć҃ij K(v)<0۞ొЊΞϡٺณޘ v ̙ᛳٺV ̝ ij

(5)

K(v)

v aij bij

bpj apj

1

-1

ဦ 3 ώ͛ٙ೩̝Ξ٤ᙯᓑבᇴ

඀ޘĂ఺࣎ొЊ˵ߏΞ٤ะЪ׶ሀቘะЪ౵̂۞मளćд ሀቘะЪ̚఺࣎ొЊߏ՟ѣؠཌྷ۞ĂٕߏӮͽ 0 ܑϯĄ Վូ 4ĈֶЧᙯᓑבᇴࣃ၆߇ᅪ෧ᕝ̝ࢦࢋّనؠᝋࢦ

9 2 1, i , , i

i W W

W L Ăдώયᗟ̚ЯࠎՏ࣎পᇈౌ࠹

༊ࢦࢋĄЯѩĂώ͛פ׎πӮࣃĂӮ૟Чপᇈࣃ

̝ᝋࢦࣃࠎ 1/9Ą

Վូ 5ĈࢍზЧ߇ᅪᙷݭ̝ᙯᓑޘλi

9 12 5

1

,..., , i K W

j ij ij

i = =

= ,

λ (20)

Վូ 6ĈࢍზЧ߇ᅪᙯᓑޘ࠹၆ࣃĂֹՏѨ۞߇ᅪ෧ᕝࣃ ӮдIJ1Ď-1ij̝มĄ

2 12 5

min max

max

min , i , ,...,

i i =

=

λ λ λ λ

λ λ (21)

׎̚

{ }i

i

λ λ max

5 max 1

= (22)

{ }i

i

λ λ min

5 1

min= (23)

Վូ 7Ĉቁؠ൴࿪፟௡ࠎң჌߇ᅪĂ׎߇ᅪ෧ᕝ۞ڱ݋т

˭ٙϯĈ

IF (λk′ =1) THEN (F =t Fk) (24) λk′ =1 ݋ҿᕝޞീ൴࿪፟௡߇ᅪ̝͹ࢋ჌ᙷࠎ

F Ă׎΁߇ᅪᙷݭ̝Ξਕّ݋ֶ׎ᙯᓑޘ̂̈ՙk

ؠâਠᙯᓑޘ෸̂۰ĂຍᏜ඾ྍ߇ᅪݭၗ൴Ϡ

̝፟த෸̂ć̝ͅĂ݋෸̈Ą

步驟 8:ࡶٙѣ൴࿪፟௡࠰̏෧ᕝԆலĂ݋ඕՁćӎ݋ྯ

аҌՎូ 2ĂซҖ˭˘࣎൴࿪፟௡̝߇ᅪ෧ᕝĄ Ӏϡώ͛ٙ೩̝͞ڱĂ׎͹ࢋᐹᕇߏᖣϤ߇ᅪᙯ ᓑޘΞͽۡତԱ΍൴࿪፟௡׶Чॎજ߇ᅪݭၗ̝

ᙯᓑ඀ޘĄࡶֹϡ็௚۞ᙷৠགྷშྮдጯ௫Ԇ˘

௡ቑּޢĂ˫ѣ˘ඊາྤफ़ॡĂ૟ᅮࢋࢦາઇጯ

௫ᄃ੊ቚĂ̖ਕѣड़гՀາྤफ़ऱć࠹ͅ۞Ăώ

͞ڱ݋̙ᅮࢋጯ௫ٕአፋЇңણᇴࣃĂΪืགྷϤ ዋ༊۞నؠ˯˭ࢨᇴࣃĂӈΞޝटٽг྿ז෧ᕝ

۞ϫ۞ĂΩγдՀາྤफ़͞ࢬĂΪᅮՀજొЊᇴ ࣃӈΞ྿јĂ༼࠷˞ధкր௚Հາॡٙਈ෱۞ॡ มĂ಼̂ࢫҲ෧ᕝր௚ჯ᜕̝јώĄ

αă၁̶ּژᄃ੅ኢ

Ϥٺ઼̰ѣᙯ൴࿪፟௡ॎજ߇ᅪ۞੃ᐂྵᙱפ଀Ăࠎ ᙋځώ͛ٙ೩͞ڱ۞၁ϡّĂώࡁտপҾ͔ϡ 14 ඊ̂ౙ˘

ֱ൴࿪ᇄ၁ീ̝ᄐՠ഻዇൴࿪፟௡۞߇ᅪྤफ़[1]Ă׎ീྏ

ྤफ़ፋநтܑˬٙϯĄᏮˢྤफ़Β߁˝჌ᐛᙉܫཱི۞ॎ

಼Ă׎̚ f ܑϯ൴࿪፟ᖼ̄۞୊ᖼᐛதĄଂྤफ़̚଀ۢĂ ᄐՠ഻዇൴࿪፟௡߇ᅪ෧ᕝ۞ᙱ఍дٺ׍ѣሀቘّ׶ܧቢ

ّඈপّĂͽ࡭ٺޝᙱϡ็௚ဦԛᏰᙊநኢĂޙϲ߇ᅪࣧ

Яᄃ߇ᅪপᇈ̝ม۞ᙯᓑّĄ

ૄٺ߇ᅪ෧ᕝ۞ኑᗔّĂώ͛೩΍˘इΞ٤߇ᅪ෧ᕝ

͞ڱĂ֭૟ܑˬ۞ീྏྤफ़ྶˢซҖ෧ᕝĂ׎෧ᕝ۞ඕڍ тܑαٙϯĄϤܑα̚ΞᅅٽгҿҾ΍൴࿪፟۞߇ᅪᙷ ݭĄּтĂдௐ 1 ඊ൴࿪፟௡ྤफ़̚଀ۢĂ׎߇ᅪᙷݭF1

۞ᙯᓑޘ࠹༊ٺ 1(ٕ౵̂ࣃ)Ă݋ѩ߇ᅪᙷݭҿؠࠎF Ă1

ٕࠎᖼค̙πᏊ߇ᅪĄ࠹၆гĂдТ˘ඊྤफ़̚Ă׎΁߇ ᅪᙷݭ۞ᙯᓑޘࣃಶព଀࠹༊̈ĂЯѩԧࣇܮΞͽ˩̶ۺ ؠௐ 1 ඊ൴࿪፟ߏᛳٺௐ˘჌߇ᅪ(̙πᏊ)ᙷݭĂ఺׶၁ ᅫ۞߇ᅪᙷݭ࠹༊˘࡭ĄѩγĂώ͞ڱ̙֭Ϊࢨٺ෧ᕝ൴

࿪፟௡۞͹ࢋ߇ᅪᙷݭĂᔘΞͽӀϡ࠹၆ᙯᓑޘԱ΍׎΁

߇ᅪ჌ᙷ̝ΞਕّĂּтௐ 2 ඊ൴࿪፟௡ྤफ़ֽᄲĂ̙π Ꮚ߇ᅪ̝࠹၆ᙯᓑޘࣃࠎ 1Ă఺ܑϯ͹ࢋ߇ᅪߏᛳٺௐ˘

჌(̙πᏊ)ćΩγĂдТ˘ඊྤफ़̚Ăෘ৳߇ᅪ̝࠹၆ᙯ ᓑޘࣃࠎ 0.49Ă఺ܑϯෘ৳߇ᅪ̝ΞਕّϺ࠹༊੼Ă൴࿪

ᇄჯ᜕̍඀रӈΞӀϡ఺࣎޽ᇾĂซҖՀซ˘Վ۞ᑭߤĂ ͽႾീ൴࿪፟ߏӎѣෘ৳ன෪Ą࠹၆гĂௐ 2 ඊྤफ़۞߇ ᅪᙷݭಶ̙Ξਕᛳٺௐα჌(ڵቯዩᒜ)ĂЯࠎ׎ᙯᓑޘ౵

̈ࠎ-1Ąͧྵܑˬ׶ܑα̝ඕڍΞͽ࠻΍Ăώ͛ٙ೩΍̝

߇ᅪ෧ᕝڱ۞෧ᕝඕڍ׶၁ᅫ̝߇ᅪᙷݭӮ࠹༊˘࡭ĂΩ γߏώ̝͛͞ڱĂإΞซ˘Վ೩ֻѨࢋ߇ᅪᙷݭ̝Ξਕ

ّĂ఺჌ੈि၆னಞˠࣶߏ࠹༊ࢦࢋ۞ෞҤ޽ᇾĄ Ϥٺ൴࿪፟௡ซҖณീॡĂγдᒖဩٕˠࠎЯ৵̝ᇆ ᜩĂѣΞਕౄјณീੈཱི̝εৌٕᄱमĄࠎീྏώ͞ڱ̝

ट᏾ਕ˧Ăώࡁտ̶Ҿ૟൴࿪፟௡ॎજ߇ᅪᏮˢྤफ़ᐌ፟

ΐˢ±5%Ҍ±30%۞ᄱमĂͽͧྵώ͛ٙ೩̝͞ڱ۞ट᏾

ਕ˧Ă׎ඕڍтܑ̣ٙϯĄܑ̚ඕڍពϯĂώ͛ٙ೩۞Ξ ٤߇ᅪ෧ᕝڱĂ׎ट᏾ਕ˧ܧ૱ᐹ෸Ăдᄱम྿ז±10% ॡĂώ͞ڱ၆͹ࢋ߇ᅪ۞໤ቁத̪ਕ྿ 100%̝ᏰᙊதĄ

҃ ༊ ྤ फ़ ᄱ म ྿±20%׎ ၆ ͹ ࢋ ߇ ᅪ ̝ ໤ ቁ த ̪ ྿ 85.7%ć҃дໂޘೋ̼̝ᒖဩ˭ĂࡶᏮˢܫཱི྿±30%ॡĂ ၆͹ࢋ߇ᅪᙷݭإѣܕˣј̝໤ቁதĄଂͽ˯ඕڍΞۢĂ

(6)

ܑˬ ᄐՠ഻዇൴࿪፟௡ॎજ߇ᅪ၁ീྤफ़[1]

ᇹώ Ԕཱི

(0.01Ƃ 0.39)f1

(0.40Ƃ

0.49)f1 0.5f1 (0.51Ƃ

0.99)f1 1f1 2f1 (3Ƃ5)f1 odd f1 >5f1 ၁ᅫ߇ᅪ

჌ᙷ 1 0.00256 0.00122 0.00993 0.01826 0.81123 0.07904 0.04958 0.04958 0.00397 ̙πᏊ(F1) 2 0.05129 0.00267 0.00227 0.01846 0.7578 0.09388 0.03373 0.03373 0.00596 ̙πᏊ(F1) 3 0.00494 0.00162 0.00131 0.01049 0.84174 0.05299 0.01962 0.01962 0.00322 ̙πᏊ(F1) 4 0.118051 0.01598 0.00831 0.12527 0.56643 0.01725 0.04653 0.02356 0.07864 ༥ᇝ(F2) 5 0.03012 0.01275 0.02175 0.16904 0.61279 0.01977 0.05657 0.02518 0.052 ༥ᇝ(F2) 6 0.1167 0.00545 0.00523 0.17401 0.56365 0.02107 0.05358 0.01288 0.05344 ༥ᇝ(F2) 7 0.00344 0.00344 0.00553 0.00723 0.54074 0.15488 0.12893 0.12893 0.02687 ෘ৳(F3) 8 0.00178 0.00178 0.00323 0.00566 0.58058 0.15624 0.11422 0.11422 0.0223 ෘ৳(F3) 9 0.0132 0.00261 0.00281 0.00642 0.63413 0.14974 0.07667 0.07667 0.0377 ෘ৳(F3) 10 0.02475 0.18273 0.39201 0.19642 0.05736 0.09657 0.02254 0.02254 0.0051 ڵቯॎᒜ(F4) 11 0.00482 0.24 0.50575 0.07214 0.08549 0.03526 0.02535 0.02535 0.0059 ڵቯॎᒜ(F4) 12 0.02364 0.14473 0.53938 0.10211 0.05216 0.09117 0.02069 0.02069 0.00548 ڵቯॎᒜ(F4) 13 0.00755 0.26129 0.4818 0.0761 0.08415 0.03498 0.02331 0.02331 0.0055 ڵቯॎᒜ(F4) 14 0.01321 0.23394 0.488 0.06358 0.09938 0.03841 0.02777 0.02777 0.00791 ڵቯॎᒜ(F4)

ܑα ώ͛ٙ೩͞ڱ̝߇ᅪ෧ᕝඕڍ ᇹώ

Ԕཱི

̙πᏊ

࠹၆ᙯᓑޘ

༥ᇝ

࠹၆ᙯᓑޘ

ෘ৳

࠹၆ᙯᓑޘ

ڵቯॎᒜ

࠹၆ᙯᓑޘ

ϒ૱

࠹၆ᙯᓑޘ

၁ᅫ߇ᅪ

჌ᙷ 1 1 -0.286556 0.098743 -1 0.0002140 ̙πᏊ 2 1 0.1841345 0.497567 -1 -0.0005651 ̙πᏊ 3 1 -0.3033451 0.316456 -1 0.0000332 ̙πᏊ 4 0.240234 1 -0.01567 -1 0.0006354 ༥ᇝ 5 0.256567 1 0.0320876 -1 -0.0006453 ༥ᇝ 6 0.216345 1 0.235635 -1 -0.0004653 ༥ᇝ 7 -0.155676 -0.080698 1 -1 0.0003546 ෘ৳

8 -0.677324 -0.587098 1 -1 0.0045465 ෘ৳

9 0.2172345 0.0523456 1 -1 -0.0003445 ෘ৳

10 -1 -0.568333 -0.645458 1 0.0004532 ڵቯॎᒜ 11 -1 -0.745677 -0.462238 1 0.0014875 ڵቯॎᒜ 12 -1 -0.588567 -0.672349 1 0.0016785 ڵቯॎᒜ 13 -1 -0.703456 -0.435676 1 0.0028976 ڵቯॎᒜ 14 -1 -0.727456 -0.496566 1 0.0004765 ڵቯॎᒜ

ܑ̣ ट᏾ਕ˧ീྏ̝ඕڍ

ᄱमΐˢּͧ ώ͛ٙ೩͞ڱ̝Ᏸᙊத

±0% 100%

±5% 100%

±10% 100%

±15% 92.9%

±20% 85.7%

±25% 85.7%

±30% 78.6%

༊னಞྤफ़Я఼ੈăܫཱི఍நٕˠࠎЯ৵யϠ࠹༊̂۞ᄱ मॡĂώ͛ٙ೩΍̝͞ڱ̪ਕ౅࿅Ξ٤࠹၆ᙯᓑޘĂ೩ֻ

ჯ᜕̍඀रΞያ۞෧ᕝੈिĄ

̣ăඕ ኢ

ώኢ͛೩΍˘इӀϡΞ٤நኢઇ̂ݭᄐՠ഻዇൴࿪

፟௡߇ᅪ෧ᕝ۞͞ڱĂᄃ็௚۞߇ᅪ෧ᕝڱ࠹ͧྵĂώ͞

ڱ̙֭ᅮࢋኑᗔ۞ણᇴనؠ׶̴ܜ۞ጯ௫࿅඀ĂЯѩΞԣ

ిઇྤफ़ऱՀາĂซ಼҃̂ࢫҲనࢍ߇ᅪ෧ᕝր௚۞ॡ

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Secondly then propose a Fuzzy ISM method to taking account the Fuzzy linguistic consideration to fit in with real complicated situation, and then compare difference of the order of

Wang, Solving pseudomonotone variational inequalities and pseudocon- vex optimization problems using the projection neural network, IEEE Transactions on Neural Networks 17

In this paper, we build a new class of neural networks based on the smoothing method for NCP introduced by Haddou and Maheux [18] using some family F of smoothing functions.

Chen, The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem, Journal of Global Optimization, vol.. Soares, A new

Qi (2001), Solving nonlinear complementarity problems with neural networks: a reformulation method approach, Journal of Computational and Applied Mathematics, vol. Pedrycz,

Define instead the imaginary.. potential, magnetic field, lattice…) Dirac-BdG Hamiltonian:. with small, and matrix