ӀϡΞ٤̍ڱٺᄐՠ഻൴̝፟ॎજ߇ᅪ෧ᕝ
ͳዂ Ղқᓏ ߸ᚗ
઼ϲ๔ৈԫఙጯੰ፟ր
ၡ! ࢋ
ώኢ͛੫၆൴ᇄᄐՠ഻൴፟ॎજ߇ᅪĂ೩˘इͽۏ̮ሀݭΞ ٤ᙯᓑבᇴࠎૄᖂ۞Ξ٤߇ᅪ෧ᕝڱĄࢵАĂॲፂனಞ၁ീྤफ़ޙϲ൴፟
ॎજ߇ᅪ۞ۏ̮ሀݭĂ֭Ӏϡ˘າ۞Ξ٤ᙯᓑבᇴࢍზ߇ᅪྤफ़߇ᅪࣧЯ
̝ᙯᓑޘĂ൴፟۞ॎજ߇ᅪΞགྷϤᙯᓑޘۡତ෧ᕝֽĄࠎរᙋώ͛ٙ೩
͞ڱ̝၁ϡّĂώࡁտͽ઼̂̚ౙ˘ֱᇄ၁ീྤफ़ࠎ၆෪ĄീྏඕڍពϯĂ ώ͛ٙ೩̝͞ڱ࠹༊ዋЪᑕϡٺ၁ᅫ۞߇ᅪ෧ᕝրĄ
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˧ր҃֏Ă൴፟ߏ࠹༊ࢦࢋ۞న౯âό
൴፟൴Ϡ߇ᅪĂ̙ҭົֹ൴ᇄ൴Ϡྯְ፟߇Ăᚑࢦ ॡࠤҌົጱ˧ֻᑕ̚ᕝĂซֹ҃̍થຽயϠλ̂۞ຫ εĄЯѩĂ၆˧̳Φ҃֏Ăਕૉӈॡ෧ᕝ൴̰፟ొ
۞߇ᅪߏ˘Іܧ૱ࢦࢋ۞̍үĂтѩΞឰჯ࣒̍रਕӈ ॡଳפᑕតନ߉ٕטؠԆච۞ჯ࣒ࢍ൪Ăͽഇ೩چ˧ր
ྻᖼ̝ΞያޘĄ
˘ਠ̂ݭ۞ᄐՠ഻൴፟ߏϤᄐՠ഻፟ă൴
፟፬Ⴣ፟ٙၹј۞Ă҃ᄐՠ഻፟۞ਕณ็ਖ਼ืᖣϤ
็જคాତĄ˘ਠ҃֏Ă൴፟дϒ૱ېڶ˭ĂߏϤ࠹
༊િ۞็જคాତĂҭߏϤٺ፟ୠਕᖼೱјਕॡٙ
ֽ۞Ԯ˧Ăົጱ็જคᖼॡயϠॎજүϡ[1-4]Ą͔
ॎજ۞ࣧЯ࠹༊ኑᗔĂּт፟ୠคֹٚϡ̙ሒٕ̙ዋЪ۞
ማڵĂٕྶณ࿅̂ඈЯ৵ĂӮѣΞਕౄј൴፟ய
Ϡॎજ[5,6]ĄЯѩĂ൴፟߇ᅪॡĂܮΞᖣϤॎજܫཱི
۞ᐛᙉјЊซҖ̶ᙷᏰᙊĂӈΞԱΞਕ۞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]ඈԫμĂЋဦԯछགྷរٕ߇ᅪീྏ۞၁ּጯ௫
ֽĂͽפˠ̍෧ᕝ۞ᕇĄࡁտඕڍពϯĂᙷৠགྷშྮ
Ξͽଂቚྤफ़̚ᒔפགྷរĂТॡΞͽጯ௫ᏮˢᏮ̝
มܧቢّ۞ᙯᓑّĂপᕇΞͽҹڇछրٙயϠ۞
ᕇĄҭߏĂᙷৠགྷშྮυืפ֖ૉ۞ቚྤफ़̖ਕགྷ Ϥጯ௫זྵჟቁ۞ඕڍĄѩγĂᙷৠགྷშྮ۞ࢨטߏ
ڱயϠୃّ۞ᏮĂдଯந˯ӧᙱޘྵĄछր
ሀቘទᏭڱඈଳϡछགྷរ۞͞ڱĂ಼̏̂೩چ߇ᅪ෧ ᕝ̝ቁதĂ֭ͷ̏གྷјΑᑕϡٺ߇ᅪ෧ᕝᅳા̝̚Ą
҃Ăֱ͞ڱώ֗ݒѣ˘ֱ̙ΞᔖҺ۞ᕇĂּтछགྷ រפӧᙱĂྤफ़ऱՀາ̙ٽർវ၁னྵࠎӧᙱඈયᗟĄ
ࠎҹڇ˯͞ڱ̝ᕇֹ̈́෧ᕝ̍Հਕ၁ϡ̼Ăώ
͛೩˘इΞ٤߇ᅪ෧ᕝڱઇ̂ݭᄐՠ഻൴፟۞ॎ
જᑭീĄΞ٤நኢߏ̂ౙጯ۰ች͛ࠎ˞ྋՙމ៍Ϭ࠼ય ᗟٺ 1983 ѐٙଯጱ۞நኢ[9,10]ĂΞ٤ጯநኢ۞̂ค ߏۏ̮நኢΞ٤ะЪநኢĂӀϡۏ̮ሀݭ(matter-element model)ೡੈिĂΞͽซҖณតኳត۞ტЪ̶ژĄЯѩ ΞТॡࡁտณኳ۰၆યᗟ۞ᇆᜩޘĂֹֹϡ۰ਕ၆ րপᇈ̝ৌ၁ّזՀԆፋ۞ੈि[11,12]Ąώ͛೩
Ξ٤நኢᑕϡд൴፟߇ᅪ෧ᕝ˯ĂࢵАĂӀϡனಞ၁
ീ̝९ּࡔᐂޙϲ߇ᅪᙷݭ۞ۏ̮ሀݭ[1]ĂГӀϡϒఢ̼
ᙯᓑבᇴზޞീ൴፟ЪЧ߇ᅪᙷݭ̝ᙯᓑޘĂซ
҃ΞͽۡତԱ߇ᅪېڶĄޢĂώ͛ͽ઼̂̚ౙߙ൴
ᇄ၁ീ̝ྤफ़ซҖ෧ᕝീྏĂ෧ᕝඕڍពϯĂώ͛ٙ೩̝
͞ڱቁ၁ܧ૱ዋЪྋՙ൴፟߇ᅪ෧ᕝ۞યᗟĄ
˟ăΞ٤நኢᖎ̬
Ξ٤நኢߏӀϡۏ̮ᖼೱ͞ёྋՙމ៍Ϭ࠼۞ય ᗟĂΞ٤ะЪሀቘะЪଂ(0,1)ؼҩז(−∞, )[9]ĄЯѩĂ∞ ιΞͽؠཌྷኢા̚Їңྤफ़۞ะЪࣃĄѩγĂΞ٤ะЪந ኢΞ҂ᇋ˘࣎ᕇᄃડม၁ᅫҜཉ(Ҝࣃ)̝ᙯܼĂтڍҜ ࣃд-1 ̝˭Ăពϯѩᕇ̙֭дѩะЪ̝̚ćࡶߏ̬ٺ 0 ז -1 ̝มჍΞ٤ાĂΞͽܑϯѩᕇд࣎ะЪቑಛγĂҭ ѣΞਕᛳٺะЪ۞˘ొЊćะЪࣃ̂ٺ 0 ॡĂܑϯѩ ᕇቁ၁д࣎ะЪቑಛ̝̰ĄΟะăሀቘะᄃΞ٤ะඈ
ˬะЪ۞পّͧྵтܑ˘ٙϯĂ҃ѣᙯٺΞ٤நኢ۞
࠹ᙯؠཌྷд˭˘࣎̈༼̚ઇྎ۞̬Ą 1. ۏ̮۞ૄώநኢ
дΞ٤நኢ̚Ăۏ̮Βӣ˞ˬ࣎ૄώ۞ࢋ৵Ąనְۏ R ۞ЩჍࠎ NĂপᇈࠎ cĂᙯٺপᇈ c ۞ณࣃࠎ vĂೡ
ְۏ۞ૄώ̮ٕ˘ჯۏ̮ࠎĈ
ܑ˘ ˬ̙Тᙷݭ۞ᇴጯะЪ
ͧྵีϫ Οะ ሀቘะ Ξ٤ะ ࡁտ၆෪ ᇴࣃតณ ᄬ֏ّតณ Ϭ࠼યᗟ
˘ਠሀݭ ᇴጯሀݭ ሀቘᇴጯሀݭ ۏ̮ሀݭ בᇴୃ ᖼொבᇴ ะЪבᇴ ᙯᓑבᇴ
পّୃ ቁ ሀቘ Ξ٤
ะЪቑಛ CA(x)∈{ }0,1 µA(x)∈[ ]0,1 KA(x)∈(−∞,∞)
R = (N, c, v) (1)
ࡶԧࣇనְۏ R = (N, C, V)ߏ˘࣎ѣкჯ۞ۏ
̮Ăְ҃ۏѣ n ࣎পᇈॡĂΞͽϡੱ C = [c1,c2,...,cn]
ܑĂ၆ᑕ۞ณࣃ̶Ҿͽᇴࣃੱ V = [v1,v2,...,vn]
ܑĂкჯۏ̮۞ܑ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
۞পᇈᇴࣃĄΞ٤நኢ۞ૄώؠநт˭ٙϯĈ ؠந 1. నְۏѣధк۞পᇈĂؠཌྷࠎĈ
N (N, c, v) {(N,c1,v1) (, N,c2,v2) (,K, N,cn,vn)} (4)
̚Ăཱི “ ” ܑΞ٤Ą
ؠந 2. న˘ְֱۏѣ࠹Т۞পᇈĂؠཌྷࠎĈ
! (N, c, v) {(N1,c,v1) (, N2,c,v2) (,K, Nn,c,vn)} (5)
ؠந 3. న̙࠹Т۞ְۏѣ࠹Т۞পᇈࣃĂؠཌྷࠎĈ (N, c, v) {(N1,c1,v) (, N2,c2,v) (,K, Nn,cn,v)} (6)
ֹϡۏ̮ሀݭĂԧࣇΞͽೡኳณᄃۏ̮ኳณ̝ม
۞ᙯܼĂซ҃ޙϲ˘࣎າ۞ᇴጯ៍هĄ 2. Ξ٤ะЪநኢ
(˘) Ξ٤ะЪ۞ؠཌྷ
న ኢ ા U ̚ Ї ˘ ̮ ৵ x ͷx∈U Ă ѣ ˘ ၁ ᇴ
(−∞∞)
∈ , ) (x
K ᄃ̝၆ᑕĂΞ٤ะЪ A~
̝ؠཌྷࠎĈ
{( , ) , ( ) ( , )}
~= x y x∈U y=K x ∈ −∞∞
A (7)
̚ y=K(x)ࠎ A~
۞ᙯᓑבᇴĂK(x)ࠎ x ̝ᙯᓑޘĂ
ቑಛࠎ-∞ ז ∞ĂΞ٤ะЪ A~
д U ኢા̚ΞܑϯјĈ
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 ۞ొЊჍࠎ Ao ~
۞ࠧ[9]Ą (˟) ۞ؠཌྷ
న x ࠎ၁ા(−∞,∞)˯Ї˘ᕇĂXo= a,b ࠎ˘၁ા˯
Ї˘ડมĂᕇ x ᄃડมX ۞ؠཌྷࠎĈ o
2 ) 2
,
( a b b a x
X
x o = − + − −
ρ (12)
(ˬ) Ҝཉࣃ(Ҝࣃ)
дΞ٤ะ̚ੵᅮ҂ᇋᕇᄃડม۞ҜཉᙯܼγĂགྷ૱ื
҂ᇋ˘࣎ᕇ၆ડม̝ҜཉᙯܼĄనXo= a,b Ă
p
p b
a
X = , ĂͷXo∈ Ăᕇ 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
నXo= a,bĂX= ap,bp ĂXo∈ ͷ̳ВბᕇĂX
ܐඈᙯᓑבᇴࠎ
) , , (
) , ) (
( Dx X X X x x
K
o
ρ o
= (14)
ᙯᓑבᇴΞࢍზ x ᕇᛳٺX ̝ᙯᓑޘĂ༊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 ᄐՠ഻൴፟ϯຍဦ
۞ޘć༊K(x)<0Ⴭࠎ x ̙ᛳٺX ۞ޘć༊o 0
) ( 1< <
− K x ॡĂჍࠎΞ٤ાĂܑϯтڍېၗԼតॡĂ x ѣ፟ົјࠎѩะЪ۞˘ొЊĄ
ˬăώ͛೩̝ॎજ߇ᅪ෧ᕝ͞ڱ
ဦ 2 ࠎ˘ᄐՠ഻൴፟۞ᖎ̼ሀݭĂ̚Βӣˬ
̂ొЊĈ഻ă൴፟፬Ⴣ፟ĄՏ࣎ొЊ࠰Ϥ็જคా
ତĂઇࠎ፟ୠਕณ̝็ਖ਼ಫ̬Ą൴፟дϒ૱ፆү˭Ăॎ
જଐԛ࠹༊ᘦؠͷॎ಼ྵ̈ćҭߏࡶѣ߇ᅪ൴Ϡă፟ୠΑ த൴ϠλតٕயϠᇶၗᜩᑕॡĂॎજੈཱི̝ॎ಼˵ົᐌ
̝Լត[13,14]ĄЯѩĂΞͽᖣϤॎજੈཱིᐛᙉ̶ژٙ೩ֻ
̝Ꮨگॎ಼ซҖ߇ᅪ෧ᕝĄώ͛ٙ೩۞͞ڱॲፂ͛ᚥ̝
၁ീྤफ़[1]Ăଂॎજ߇ᅪੈཱི̚߄Ᏼݭ۞˝পᇈࣃ (̶Ҿࠎ 0.01f~0.39f, 0.40f~0.49f, 0.5f, 0.51f~0.99f, f, 2f, 3f~5f, oddf >5f ඈ˝Ꮨگ̝ॎ಼)ઇࠎ߇ᅪ෧ᕝր̝
ᏮˢܫཱིĂ̚ f ࠎ൴፟ᖼᐛதĂoddf ࠎ؈ѨᏘگӣ ณĄࢵАĂԧࣇӀϡֱ၁ീ̝ྤफ़ޙϲॎજ߇ᅪᙷ۞
ۏ̮ሀݭĂޢ൴̝፟߇ᅪᙷݭΞᖣϤΞ٤ᙯᓑבᇴ ซҖ̶ᙷᏰᙊĄ
1. ൴፟ॎજ߇ᅪ෧ᕝ۞ۏ̮ሀݭ
ॲፂ၁ീྤफ़߇ᅪᙷΞ̶јα[1]ĂΩనؠ˘൴
፟րдϒ૱˭̝ۏ̮ሀݭĂፋ࣎߇ᅪ෧ᕝ̝ۏ̮ሀ ݭΞፋநтܑ˟ٙϯĄְۏ R ߏᛳٺ̣߇ᅪݭၗ۞ۏ
̮Ăܑ˟̚F ={F1,F2,F3,F4,F5}ࠎ߇ᅪะĂF ̶Ҿi
ܑௐ i ࣎߇ᅪݭၗĄࣃાቑಛߏֶፂՏ࣎পᇈ̮၆ᑕ̝
གྷાనؠĂᏴؠ͞ڱΞӀϡ၁ീྤफ़̚Ч߇ᅪᙷݭٙ
၆ᑕপᇈณࣃ۞˯ă˭ࢨࣃࢎؠĄΩγГᏴؠ˘ۏ̮ೡ
Чॎજᐛᙉ̝̂टధณ̝˯˭ࢨٕ༼ાĂనؠт(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)
ܑ˟ ൴፟ॎજ߇ᅪ۞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 ᑡ
〉
〈
> 〈 〉
〉
〈 〉
〈
〉
〈
〉
〈 〉
〈
〉
〈 〉
〈
=
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~
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.
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R
F4Ĉ ڵ ቯ ॎ ᒜ
〉
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>
〉
〈 〉
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〈〈 〉
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=
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~
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R
F5: ϒ૱
〉
〈
>
〉
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〈
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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
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. , . f ,
. , . odd f,
. , . f, f~
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R
߇ᅪ෧ᕝ۞ۏ̮ሀݭޙϲޢĂӈΞซҖ൴̝፟߇ ᅪ෧ᕝĄ˘ਠ҃֏Ă༼ા۞ᏴؠߏֶЧ࣎གྷા̝̂˯
˭ࢨᏴؠĂᏴؠቑಛ่ົᇆᜩᙯᓑבᇴΞ٤ા̝ቑಛĄ
ֶώ͛ീྏགྷរۢĂ၆߇ᅪ෧ᕝቁதᇆᜩ̙̂Ăд
ͻ̂ณീྏྤफ़˭ĂΞᏴؠٙѣགྷા۞˯˭ࢨᕖᆧ ࡗ 10%ĂӈΞז΄ˠ႕ຍ۞ඕڍĄ
2. Ξ٤߇ᅪ෧ᕝڱ
ώ͛ٙ೩۞Ξ٤߇ᅪ෧ᕝڱ̏གྷјΑгӀϡཝ హវޙၹ˘इ൴፟۞߇ᅪ෧ᕝրĄ߇ᅪ෧ᕝႊ
ზڱт˭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༼ાĄՏ࣎
߇ᅪᙷݭགྷાΞϤീྏྤफ़ᒔ[1]Ăώࡁտॲ ፂՏ˘ॎજ߇ᅪᐛᙉቑಛ̝˯ă˭ࢨࣃనؠགྷ
ાVij = aij,bij ۞ࣃĂፋநтܑ˟ٙϯĄ Վូ 2Ĉ ޞീ൴፟۞ॎ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 ࠎޞീ፟ௐ i ࣎পᇈ̝ณࣃĄ ti Վូ 3ĈӀϡώ͛ٙ೩̝߇ᅪᙯᓑבᇴĂࢍზޞീ൴
̝፟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 ӈߏώ͛ٙ೩̝Ξ٤ᙯᓑבᇴĄ̚Ă༊
1 ) (
0≤K v ≤ ॡĂ࠹༊ٺ็۞ሀቘะЪĂΞϡͽณޘ v ᛳ ٺV ۞ޘć҃ij K(v)<0۞ొЊΞϡٺณޘ v ̙ᛳٺV ̝ ij
K(v)
v aij bij
bpj apj
1
-1
ဦ 3 ώ͛ٙ೩̝Ξ٤ᙯᓑבᇴ
ޘĂ࣎ొЊ˵ߏΞ٤ะЪሀቘะЪ̂۞मளćд ሀቘะЪ࣎̚ొЊߏ՟ѣؠཌྷ۞ĂٕߏӮͽ 0 ܑϯĄ Վូ 4ĈֶЧᙯᓑבᇴࣃ၆߇ᅪ෧ᕝ̝ࢦࢋّనؠᝋࢦ
9 2 1, i , , i
i W W
W L Ăдώયᗟ̚ЯࠎՏ࣎পᇈౌ࠹
༊ࢦࢋĄЯѩĂώ͛פπӮࣃĂӮЧপᇈࣃ
̝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 7Ĉቁؠ൴፟ࠎң߇ᅪĂ߇ᅪ෧ᕝ۞ڱт
˭ٙϯĈ
IF (λk′ =1) THEN (F =t Fk) (24) ࡶλk′ =1 ҿᕝޞീ൴፟߇ᅪ̝ࢋᙷࠎ
F Ă߇ᅪᙷݭ̝Ξਕֶّᙯᓑޘ̂̈ՙk
ؠâਠᙯᓑޘ̂۰ĂຍᏜྍ߇ᅪݭၗ൴Ϡ
̝፟த̂ć̝ͅĂ̈Ą
步驟 8:ࡶٙѣ൴፟࠰̏෧ᕝԆலĂඕՁćӎྯ
аҌՎូ 2ĂซҖ˭˘࣎൴̝፟߇ᅪ෧ᕝĄ Ӏϡώ͛ٙ೩̝͞ڱĂࢋᐹᕇߏᖣϤ߇ᅪᙯ ᓑޘΞͽۡତԱ൴፟Чॎજ߇ᅪݭၗ̝
ᙯᓑޘĄࡶֹϡ็۞ᙷৠགྷშྮдጯ௫Ԇ˘
ቑּޢĂ˫ѣ˘ඊາྤफ़ॡĂᅮࢋࢦາઇጯ
௫ᄃቚĂ̖ਕѣड़гՀາྤफ़ऱć࠹ͅ۞Ăώ
͞ڱ̙ᅮࢋጯ௫ٕአፋЇңણᇴࣃĂΪืགྷϤ ዋ༊۞నؠ˯˭ࢨᇴࣃĂӈΞޝटٽг྿ז෧ᕝ
۞ϫ۞ĂΩγдՀາྤफ़͞ࢬĂΪᅮՀજొЊᇴ ࣃӈΞ྿јĂ༼࠷˞ధкրՀາॡٙਈ۞ॡ มĂ಼̂ࢫҲ෧ᕝրჯ᜕̝јώĄ
αă၁̶ּژᄃኢ
Ϥٺ઼̰ѣᙯ൴፟ॎજ߇ᅪ۞ᐂྵᙱפĂࠎ ᙋځώ͛ٙ೩͞ڱ۞၁ϡّĂώࡁտপҾ͔ϡ 14 ඊ̂ౙ˘
ֱ൴ᇄ၁ീ̝ᄐՠ഻൴፟۞߇ᅪྤफ़[1]Ăീྏ
ྤफ़ፋநтܑˬٙϯĄᏮˢྤफ़Β߁˝ᐛᙉܫཱི۞ॎ
಼Ă̚ f ܑϯ൴፟ᖼ̄۞ᖼᐛதĄଂྤफ़ۢ̚Ă ᄐՠ഻൴፟߇ᅪ෧ᕝ۞ᙱдٺѣሀቘّܧቢ
ّඈপّĂͽٺޝᙱϡ็ဦԛᏰᙊநኢĂޙϲ߇ᅪࣧ
Яᄃ߇ᅪপᇈ̝ม۞ᙯᓑّĄ
ૄٺ߇ᅪ෧ᕝ۞ኑᗔّĂώ͛೩˘इΞ٤߇ᅪ෧ᕝ
͞ڱĂܑ֭ˬ۞ീྏྤफ़ྶˢซҖ෧ᕝĂ෧ᕝ۞ඕڍ тܑαٙϯĄϤܑα̚ΞᅅٽгҿҾ൴፟۞߇ᅪᙷ ݭĄּтĂдௐ 1 ඊ൴፟ྤफ़ۢ̚Ă߇ᅪᙷݭF1
۞ᙯᓑޘ࠹༊ٺ 1(ٕ̂ࣃ)Ăѩ߇ᅪᙷݭҿؠࠎF Ă1
ٕࠎᖼค̙πᏊ߇ᅪĄ࠹၆гĂдТ˘ඊྤफ़̚Ă߇ ᅪᙷݭ۞ᙯᓑޘࣃಶព࠹༊̈ĂЯѩԧࣇܮΞͽ˩̶ۺ ؠௐ 1 ඊ൴፟ߏᛳٺௐ˘߇ᅪ(̙πᏊ)ᙷݭĂ၁ ᅫ۞߇ᅪᙷݭ࠹༊˘ĄѩγĂώ͞ڱ̙֭Ϊࢨٺ෧ᕝ൴
፟۞ࢋ߇ᅪᙷݭĂᔘΞͽӀϡ࠹၆ᙯᓑޘԱ
߇ᅪᙷ̝ΞਕّĂּтௐ 2 ඊ൴፟ྤफ़ֽᄲĂ̙π Ꮚ߇ᅪ̝࠹၆ᙯᓑޘࣃࠎ 1Ăܑϯࢋ߇ᅪߏᛳٺௐ˘
(̙πᏊ)ćΩγĂдТ˘ඊྤफ़̚Ăෘ৳߇ᅪ̝࠹၆ᙯ ᓑޘࣃࠎ 0.49Ăܑϯෘ৳߇ᅪ̝ΞਕّϺ࠹༊Ă൴
ᇄჯ᜕̍रӈΞӀϡ࣎ᇾĂซҖՀซ˘Վ۞ᑭߤĂ ͽႾീ൴፟ߏӎѣෘ৳ன෪Ą࠹၆гĂௐ 2 ඊྤफ़۞߇ ᅪᙷݭಶ̙Ξਕᛳٺௐα(ڵቯዩᒜ)ĂЯࠎᙯᓑޘ
̈ࠎ-1Ąͧྵܑˬܑα̝ඕڍΞͽ࠻Ăώ͛ٙ೩̝
߇ᅪ෧ᕝڱ۞෧ᕝඕڍ၁ᅫ̝߇ᅪᙷݭӮ࠹༊˘ĂΩ γߏώ̝͛͞ڱĂإΞซ˘Վ೩ֻѨࢋ߇ᅪᙷݭ̝Ξਕ
ّĂੈि၆னಞˠࣶߏ࠹༊ࢦࢋ۞ෞҤᇾĄ Ϥٺ൴፟ซҖณീॡĂγдᒖဩٕˠࠎЯ৵̝ᇆ ᜩĂѣΞਕౄјณീੈཱི̝εৌٕᄱमĄࠎീྏώ͞ڱ̝
टਕ˧Ăώࡁտ̶Ҿ൴፟ॎજ߇ᅪᏮˢྤफ़ᐌ፟
ΐˢ±5%Ҍ±30%۞ᄱमĂͽͧྵώ͛ٙ೩̝͞ڱ۞ट
ਕ˧Ăඕڍтܑ̣ٙϯĄܑ̚ඕڍពϯĂώ͛ٙ೩۞Ξ ٤߇ᅪ෧ᕝڱĂटਕ˧ܧ૱ᐹĂдᄱम྿ז±10% ॡĂώ͞ڱ၆ࢋ߇ᅪ۞ቁத̪ਕ྿ 100%̝ᏰᙊதĄ
҃ ༊ ྤ फ़ ᄱ म ྿±20% ၆ ࢋ ߇ ᅪ ̝ ቁ த ̪ ྿ 85.7%ć҃дໂޘೋ̼̝ᒖဩ˭ĂࡶᏮˢܫཱི྿±30%ॡĂ ၆ࢋ߇ᅪᙷݭإѣܕˣј̝ቁதĄଂͽ˯ඕڍΞۢĂ
ܑˬ ᄐՠ഻൴፟ॎજ߇ᅪ၁ീྤफ़[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
ܑ̣ टਕ˧ീྏ̝ඕڍ
ᄱमΐˢּͧ ώ͛ٙ೩͞ڱ̝Ᏸᙊத
±0% 100%
±5% 100%
±10% 100%
±15% 92.9%
±20% 85.7%
±25% 85.7%
±30% 78.6%
༊னಞྤफ़Я఼ੈăܫཱིநٕˠࠎЯ৵யϠ࠹༊̂۞ᄱ मॡĂώ͛ٙ೩̝͞ڱ̪ਕ࿅Ξ٤࠹၆ᙯᓑޘĂ೩ֻ
ჯ᜕̍रΞያ۞෧ᕝੈिĄ
̣ăඕ ኢ
ώኢ͛೩˘इӀϡΞ٤நኢઇ̂ݭᄐՠ഻൴
፟߇ᅪ෧ᕝ۞͞ڱĂᄃ็۞߇ᅪ෧ᕝڱ࠹ͧྵĂώ͞
ڱ̙֭ᅮࢋኑᗔ۞ણᇴనؠ̴ܜ۞ጯ௫࿅ĂЯѩΞԣ
ిઇྤफ़ऱՀາĂซ಼҃̂ࢫҲనࢍ߇ᅪ෧ᕝր۞ॡ