Optimization of Shipborne Equipment System Reliability Based on Artificial Immune PSO Algorithm

Transcription

1 Joal of Physcs: Cofeece Sees PAPER OPEN ACCESS Opmzao of Shpboe Eqpme Sysem Relably Based o Afcal Imme PSO Algom To ce s acle: Sog-sh Shao ad M-zh Ra 8 J. Phys.: Cof. Se Ve e acle ole fo pdaes ad ehacemes. Ths coe as doloaded fom IP addess o 8//8 a 9:4

2 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 Opmzao of Shpboe Eqpme Sysem Relably Based o Afcal Imme PSO Algom SHAO Sog-sh RUAN M-zh College of aval achece ad ocea egeeg Naval Uvesy of Egeeg Wha 4333 Cha; Absac: Accodg o fzzy opmm seleco eoy e Ecldea dsace fom feasble poecs o e deal poec ad e ms-deal poec s egaded as evalao ceo fo esablshg e fzzy ml-ages opmzao model. I ca be ko a pacle sam opmzaopso algom s easy o ge local exemm ad e pacles lack dvesy ogh e aalyss of s cosgecy. The pacles velocy s coolled o mpove e defceces of s algom The eoy of afcal mme sysemais ad e mpoved pacle sam opmzao algom ae combed o p foad a e algom afcal mme pacle sam opmzaoai-pso. Ths meod s appled o e solo of sysem elably opmzao ad e smlao esl sho a s algom has bee capably of ee age seach ad e opmzao esl s moe easoable compaed o oe algoms.. Iodco Relably s a mpoa age of applcao pefomace fo shpboe eapo eqpme sysem. Ude e ccmsace of exsg mafacg caf ad echcal level ho o make e elably of hole sysem o be opmal ogh easoable allocao of sysem s elably s e poblem eed o be solved fo eqpme sysem opmzao. A e begg of sysem desg a mpoa ok s o deeme e elably age of evey compoe elemes based o e sysem elably []. If e compoe s elably s able o each e eqed level aoe meod of mpove sysem elably s o add eddacy eqpme e ppose of hch s make e compehesve agesages of beef ad cos as ell as e ages of oe aspecs of e hole sysem o be opmal e pocess of hch s scal opmzao of sysem elably. Accodg o e aalyss above e sysem elably opmzao s a poblem of mxed olea ml-ages opmzao. A pese may opmzao meods have bee sccessflly appled o solve s poblem. Fo example e geec algom s sed o e solo of sysem elably opmzao efeeces[] b e opmzao model s esablshed de e ccmsace of esoces esco o make e sysem elably o be opmal e esoces esco e model s gealy fleced by ma-made sbecve facos eefoe e opmzao esl go fom e model s acally o opmal mos cases. Ml-obecve decso-makg meod dscee vaables s pese efeeces[3] o selec e opmal elably vale of s lage ad complex sysem hoeve e pocess of solo s complcaed ad e esl s o pecse. The eddacy opmzao model fo ee-sae sysem ad s calclao meod s gve efeeces[4] hch e sysem eddacy s opmzed based o e case a e elably of sysem compoe s s ko hch s o cosse e fac. Coe fom s ok may be sed de e ems of e Ceave Commos Abo 3. lcece. Ay fe dsbo of s ok ms maa abo o e aos ad e le of e ok oal cao ad DOI. Pblshed de lcece by IOP Pblshg Ld

3 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 I s pape e fzzy ml-ages opmzao model of shpboe eqpme sysem elably allocao s se p Accodg o fzzy opmm seleco eoy. The afcal mme sysemais [5] ad e mpoved pacle sam opmzaopso [6] ae combed o p foad a e algom of mpoved afcal mme pacle sam opmzaoai-pso. I e calclao pocess of s algom e velocy of e pacles s coolled o make pacles have bee capably of ee age seach. Ths e algom s appled o e solo of shpboe eqpme sysem elably opmzao e fzzy ml-ages opmzao model of sysem elably allocao s egaded as e adapably fco of s algom fom hch e esl go s moe accae ad easoable.. Ml-ages opmzao model of shpboe eqpme sysem elably If oly cosde e age of elably e phase of sysem desg e poblem of sysem opmzao s easy o solve b s case s o exs e acal egeeg. I e pocess of sysem elably opmzao desadg e elaoshp beee evey opmzao ages s e bass fo sysem elably opmzao. I dffee opmzao ages e mos oday ages ae sysem elably cos ad expese egh ad volme. A A A Spae pa Spae pa Spae pa Spae pa Sppose a shpboe eqpme sysem s composed of s e elably ad e eddacy of evey ae R ad N especvely so e desg vaables of s sysem s: [ R R R N N N ]. Sysem elably: e sysem sho fg. ca be eqvale o seal s e calclao fomla of sysem elably s as follo: N R R Cos ad expese: e cos of e hole sysem s e sm cos of evey compoe s ad o ad sch eqpme hoeve e cos of e sysem s s closely elaed s elably. The hghe of e elably e lage of e cos e o ages sho e dec popoo elaoshp. Theefoe e ca ge a Fg. Relably sce of cea shpboe eqpme sysem c [ / l R s e o dsabled me of e ] accessoy e calclao fomla of e cos ad expese s: C N K N l R 3 Volme: e volme of e hole sysem s e sm volme of evey compoe s cosdeg e espace beee dffee s e volme calclao fomla shold be mlpled evso faco e cocee vale of hch deped o acal case so e calclao fomla of volme s: V v N 3 4 Wegh: Lke e volme e egh of e hole sysem s also e sm egh of evey compoe s cosdeg e egh of eddacy s ad e o sch eqpme shold be mlpled evso faco K K hch s e fco of N. So e calclao fomla of sysem egh s as follo:

4 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 W N K N 4 Fom e fomla above: K N exp N / 4 N N m R. The sysem opmzao poec s a bee poec hghe elably ad fee cos ad expese. I addo cosdeg e volme ad e cayg capacy of e ashp ae lmed eefoe e volme ad e egh shold be small ad lgh possble e phase of shpboe eqpme sysem desg. Accodg o e aalyss above e ml-ages opmzao model of shpboe eqpme sysem elably allocao s: 3. The fzzy ml-ages opmzao model max R m C mv mw R N v N N N l R exp N / 4 exp N / Meod of deal poec The deal poec s a spposed opmal poec ad e ms deal poec s a spposed os poec hch cold be go ogh choosg e opmal o e os age. These o poecs ae o exsed pacce oly cosdeed as e opmal o e os poec dealy. The ppose of sysem elably opmzao allocao s o fd e opmal poec amog dffee feasble allocao poecs e opmal poec s closes o e deal poec ad faes o e ms deal poec[7]. I ode o mease e appoach degee beee feasble poec ad e deal o ms deal poec sppose e opmzao ages of e poec ae m e deal poec s e ms deal poec s. [ x x x m] 6 [ x x x m] 3. The Ecldea dsace beee feasble poec ad e deal o ms deal poec Dffee ages have dffee dmeso o dmeso ad sadadzao eed o be doe fo e poecs syess vale max [ x ] so as o make se e same facos of evey age m ca be compaed each oe. Thee ae may meas of sadadzao e meod adoped s pape s as follos[8] x m x age of beef max x 7 max x x age of cos max x The ages syess vale x ca be asfomed o e coespodg degee elaed T o e opmal poec ogh e fomla7. [ ] s ecoded as e coespodg degee 3

5 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 veco elaed o e deal poec ad e T ] [ s ecoded as e coespodg degee veco elaed o e ms deal poec. Theefoe e Ecldea dsace beee e feasble poec ad e deal poec as ell as e ms deal poec ae shoed bello: d ] [ 8 d ] [ 9 As e fomla shoed above s e egh of e age. 3.3 The fzzy opmm seleco model Theoem: e fzzy opmm seleco model of sysem elably age allocao s m m x x Poof: accodg o ml-ages fzzy opmzao eoy e ages fco s esablshed as bello: c d d } ] [ { } ] [ { The fomla ca be asfomed o e olea pogammg poblem e fom of F / m de e esco a m. I ode o decease e mbe of ko facos ad e eqaos so as o make e poblem easy o solve e escos of ad ae o cosdeed. The Lagage fco esablshed s as bello: / m L Calclag e dffeeal coeffces of fomla above fo ad ad makg em o zeo e e fomla cold be go. Poof s ove. 4. Impoved afcal mme pacle sam opmzao algom 4. Theoy of afcal mme sysem Afcal mme sysemais s a ellge hch combes e fomao pocessg echqe calclao Meod. I das o ad se of bologcal mme sysem mechasm fo e developme of echcal meods o solve egeeg ad scefc poblems. Bologcal mme sysem s also a hghly evoloal bologcal sysem hch s desged o dsgsh beee osde hamfl ages ad e o ogas o emove paogec ogasms ad eeby maa e sably of ogasms. Isped fom bologcal mme sysem mechasm a applcao-oeed

6 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 compao model of e mme sysem-afcal Imme Sysem AIS s developed. Cloal seleco eoycs p foad by e Jee fsly e ma chaacescs of hch s a e mme cells ll do e clog polfeao de e smlao of ages sbseqely dvesy effeco cells sch as abodes ad memoy cells ae geeaed ogh geec mao. Cloal seleco coepas a affy mag pocess a s e pocess of age dvdals lo affy gadally asg e affy ad "mag" afe expeecg e opeao of eplcao polfeao ad mao based o e cloal seleco mechasm. So e affy mag s esseally a Daa seleco ad mao pocess. Cloal seleco s ealzed ogh e se of geec opeao sch as coss mao ad e coespodg cool mechasm fo e coloy. 4. Elemeay pacle sam opmzao algom The pacle sam opmzao algom PSO s p foad fsly by Keey e al 995 hch s a evolo algom a smlae e bd ad fsh sam s mgao ad gaeg aco e pocess of seekg fo food. Sppose ee s a coloy hch s composed of N pacles a ages seachg space dmesos e pacle s expessed as a dmesos veco x x x N e place of evey pacle s a poeal esl. The flgh speed of e pacle s also a dmesos veco hch s ecoded as V v v v. Sppose e opmal place a beg seached by e pacle so fa s p p p p ad e opmal place a beg seached by pacle sam so fa s pg pg pg pg s eal egh. Fomla ad fomla 3 ae called as e sadad eqao of PSO. v v c p x c p g x x x v 3 Clec e al s Reseach fd a compessed facos ca help o make se pacle sam opmzao algom covege moe apd speed ad e eeal speed eqao s sho by fomla 4. v v c p x c p g x 4 I e fomla 4 / 4 c 4 c c [ ] s adom mbe fom zeo o oe. c 4.3 Covegece aalyss of elemeay pacle sam opmzao algom The PSO algom s capably of seachg fo opmal pacle maly deped o e mal effec ad mpac beee pacles f sch mal effec ad mpac s emoved fom e algom e PSO algom s seachg capably ll become qe lmed[9]. The seachg capably of elemeay PSO algom deped o e compeo ad coopeao beee pacle sam so e pacles self lack mao mechasm oce e sgle pacle ge o e local exemm e pacles self ae dffcl o leap o of e esco. A e begg of calclao s algom s covege speed s apd ad s moo locs ggled e fom of se ave[] hoeve e speed of pacles beg o become slo o eve saga afe calclag some me. The pacle sam lose e capably of fe evolo he e speed of all pacles coloy s ealy o zeo e cold cosde a e algom has coveged. B may cases e algom has o coveged o ee age exemm o eve go e local exemm hch s called e pheomeo of pemay o sagao[]. The pacle sam s hgh-cogegaed ad 5

7 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 seosly lack dvesy he s pheomeo s akg place ad e pacle sam ll o leap o of e allyg po fo log me o foeve. Theefoe may meods fo mpovg pacle sam opmzao algom ae maly cealzed boosg e dvesy of pacle sam hch ca make pacle sam maa e capably of fe evolo e pocess of eave cclao. 4.4 Afcal mme pacle sam opmzao ad s ealzao seps Accodg o aalyss of e elemeay PSO algom s covegece ca be ko a ee ae o ma facos a make PSO algom o ge o local exemm o pemay. Oe s e pacle sam s dvesy e oe s e pacle sam s flgh speed. Expeme aalyss ells s e effecve meod fo avodg PSO algom o ge o pemay s o boos pacle sam s dvesy ad keep s dave flgh dg calclao o cclao pocess a s e pacle sam s flgh speed s o eqal o o close o zeo hch make pacles o seach adeqaely shk sae ad fly o of e gaeg place dspesg sae. Theefoe pacles ca seach a bgge space ad has bee capably of ee age seach. Elemeay PSO algom s mpoved ogh e opeao of coss ad mao afcal mme sysem o e cool o pacles flgh speed e basc meod s as follos. I e pocess of calclao o cclao f e compaably of e geeao pacle sam hch s made p of N pacles exceeds e alzed seg vale e coss ad mao opeao s doe o evey pacles of e geeao. affy / N affy s e mbe of pacles e same adapably coloy. If e pacles speed v of e geeao coloy s less a a cea vales vale ca be se accodg o e acal case speed cool opeao s doe o make pacles ee s flgh speed fo flyg o of covegece po specfc opeao s v a ad f v vom. a s speed cool paamee ad s adom mbe fom zeo o oe. The ealzao seps of AI-PSO algom ae: Sep: deeme e paamees of leag facos e maxmm cclao seps T ad e coloy scale ad e leag facos c c [ ] e esco c c 4. Sep: geeae e alzed coloy adomly ad alze e pacles speed ad poso se e cclao coe. Sep3: calclae e pacles opmal poso P. g P ad e hole pacle sam s opmal poso Sep: sg fomla 3 ad fomla 4 o ee pacles poso ad speed ad calclag evey pacle s adapably aff e adapably calclao meod s sho by fomla 5. k m x aff k 5 m x Sep5: calclae pacles compaably e coloy e pacles coloy ae caed o e coss o mao opeao some pobably f. Take e algom s code of s pape om as example e asfomao of coss ad mao opeaos ae sho belo. Coss opeaos Befoe coss: Afe coss: 6

8 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 Mao opeaos Befoe mao: Afe mao: Sep6: calclae e speed v of evey pacle e coloy f v s less a e seg vale opeao s caed o o cool e pacle s speed. Sep7: Deeme hee e emao codos ae sasfed f o asfe o sep 3 ad coes oese o ed e calclao. 5. Smlao esl ad s coclso Sppose a shpboe eqpme sysem s made p of fve sees s ad e alzed paamees of e sysem ae sho belo v R.9 N 5 The egh of e opmzao ages s ad e e deal poec ad e ms-deal poec of sysem elably opmzao ca be gaed accodg o e alzed paamees. The deal poec s e poec maxmm elably age ad a e same me mmm cos volme ad egh. Opposed o e deal poec e ms-deal poec s e poec mmm elably age ad maxmm cos volme ad egh. Ths e deal poec ad e ms-deal poec s sho belo The algom s alzed paamees smlao ae as follos: e scale of pacle sam N s 4 leag facos c.678 c.76 coss pobably P =.5 mao pobably c Pm. e maxmm cclao seps T. The pacles adapably of e fs ad e las geeao s sho fge. a Ialzed pacle sam b Pacle sam of e las geeao Fg. Dsbo of pacles adapably The algom s smlaed e mes e bes pacle seached e pocess of e mes opmzao s R N The 7

9 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 coespodg sysem elably ad e egh W s R.9454 cos ad expese C 56.3 volme V 76 s s s Fg.3 Pacle sam s bes adapably of dffee geeao I ode o expla e valdy of afcal mme pacle sam opmzao algom e algom s pefomace s compaed oe algom s hch clde elemeay pacle sam opmzao PSO ad afcal mme algom AIA. Dffee algoms maxmm adapably of evey geeao s sho fg.3 afe cclao seveal es of seps e opmal esl seached by e coloy of pacle sam opmzao ad afcal mme algom has eded o be sable oe ods e coloy s adapably s o mpoved as e cclao seps cease. Becase of coloy s dvesy ad e cool fo pacles speed AI-PSO algom s pacles ll go do slghly fom e ce opmal local exemm he e algom ed o ge o e pemae sae dg e hole cclao pocess ad e leap o of e local exemm ad seach aga. The holsc chage ed of coloy s adapably s mpoved as e cclao sep coes. Dffee algoms opmal calclao esls dg e mes smlao ae sho Tab. belo daa Tab. sho a AI-PSO algom s pacles ca seach a bgge solo space ad have a bee ee age seach capably compaed o oe o opmzao algoms ad e opmzao poec has a bee adapably ad s esl s moe easoable. Tab. Dffee algoms opmal calclao esls e mes smlao Opmzao ages Algoms PSO AIA AI-PSO N R R R R R R s C s V s W s

10 Fs Ieaoal Cofeece o Advaced Algoms ad Cool Egeeg IOP Pblshg IOP Cof. Sees: Joal of Physcs: Cof. Sees do :.88/ /87//7 affy Coclso I s pape e shpboe eqpme sysem s elably ml-age allocao model s esablshed based o fzzy opmm seleco afcal mme sysem mechasm s odced o PSO algom. Smlao esl ad e algom s pefomace aalyss sho a AI-PSO algom has bee ee age seach capably compaed o PSO ad AIA ad e opmzao poec has a bee adapably ad s esl s moe easoable. Hoeve e AI-PSO algom has also s defceces compaed o oe hesc algoms. Fo example somemes ca o ge sable esl. The occece pobably of s case s vey lo hch occs oce evey calclaos. Somemes e adapably of opmzao poec obaed fom AI-PSO algom s oly.967~.97 hoeve afe seveal smlaos o PSO ad AIA all of e opmzao poecs adapably ae hold fom.98 o.985 hch sho a AI-PSO algom s o sable eogh. Ths defcecy ca be avoded ogh calclao fo seveal mes e poblem of eqpme elably opmzao desg b some cases fo example e opeaoal poec decso makg bale occece of s case s faal. Becase of e saaeos chage of sao balefeld commade has o eogh me o opeae e pogam epeaedly fo e opmzao of comba poec. Theefoe ode o make e algom has moe exesve applcao aea e ex eseach s maly o e aspec of algom s sably. Refeeces [] Wag H Zhag Z W. Opmal appoome of sysem elably[j]. Theoy ad Pacce of Sysem Egeeg 88: [] Zhag T Z Teg C Ha Z G. Applcao of geec algoms o sysem elably opmzao[j]. Cool ad Decso 73: [3] D F E L LW. Ml-obecve decso-makg meod fo sysem elably opmzao dscee vaables[j]. Sysems Egeeg ad Elecocs 3 57: [4] Q R e L L L H e al. The eddacy desg ad opmzao fo a ee-sae sysem[j]. Sysems Egeeg ad Elecocs 3 58: [5] Wag H J Sh J F Ch Z. Imme algom ad smlao of flee a-mssle ob-shop schedle[j]. Joal of Sysem Smlao 8 4: [6] Bo L Lg Wag Y-H J e al. Impoved pacle sam opmzao combed chaos[j]. Chaos Solos ad Facals 5 55: 6-7. [7] Teg Z Zhag Qa J. Evalao of melayg plas based o deal plas[j]. ACTA ARMAMENTARII 7 8: [8] El-shakh M Y El-Keb A A. Maeace schedlg of geeao ad asmsso sysems sg fzzy evoloay pogammg [J]. IEEE Tas o Poe Sysems 3 8: [9] Zhag H Zhag T N She J H e al. Reseach o decso-makg of sce opmzao based o mpoved Te PSO[J]. Cool ad Decso 8 38: [] Kaava R Gagl R. Seg desg of compose beam sg gade ad pacle sam opmzao[j]. Compose Sces 7 84: [] Sh-Ka S Fa Ee Zahaa. A hybd smplex seach ad pacle sam opmzao fo cosaed opmzao[j]. Eopea J of Opeaoal Reseach 7 8: [] De Falco I Della Coppa A Taao E. Facg classfcao poblems Pacle sam opmzao[j]. Appled Sof Compg 7 73: