Classification of Power Signals Using PSO based K-Means Algorithm and Fuzzy C Means Algorithm

Transcription

1 Journal o Agrculur and L Scncs Vol. o. ; Jun 04 Classcaon o Powr Sgnals Usng PSO basd K-Mans Algorh and Fuzzy C Mans Algorh B. Mah S. Sabyasach S. Mshra Cnuron Insu o Tchnology CUTM Bhubanswar Inda Absrac Ths papr prsns a nw clusrng chnqu and parn classcaon o powr sgnal dsurbancs usng a odd vrson o S-Transor whch s oband by akng h Invrs Fourr ransor o S-Transor calld as odd - ransor TT-ransor. Th TT-ransor s a sgnal procssng chnqu whch s usd or vsual localzaon dcon and powr sgnal dsurbanc parn classcaon. Th TT-Transor a nw vw o localzng h aurs o a srs around a parcular pon on h axs. TT- Transor has good ably n gahrng rquncy; gahrs h hgh rquncy sgnals n dagonal poson o h spcru and supprssng h low rquncy sgnals. Th dagonal o TT-Transor rprsn a spl rquncy lrd vrson o h orgnal sgnal. Th nos can b sparad ro h cv sgnal whch can prov h sgnal-o-nos rao by usng TT-Transor. Th xracd aurs ar d as h npu o a Fuzzy C- Mans clusrng algorh FCA and K-Mans algorh or powr sgnal dsurbanc parn classcaon. To prov h parn classcaon o h uzzy C-ans and k-ans algorh h clusr cnrs ar updad usng parcl swar opzaon chnqu. Coparson o boh h algorh s ad or powr sgnal dsurbanc parn classcaon accuracy Kywords: FCA K-Mans powr sgnals S-Transor STFTWT I. Inroducon Th PQ ssus and rlad phnona can b arbud o h us o sold-sa swchng dvcs unbalancd and non lnar loads ndusral grad rcrs and nvrrs copur and daa procssng qupns c. whch ar bng ncrasngly usd n boh h ndusry and ho applancs. Ths dvcs nroduc dsorons n h phas rquncy and aplud o h powr sys sgnal hrby drorang PQ. Subsqun cs could rang ro ovrhang oor alurs and noprav procv qupn o powr nrush quas sac haronc dsorons and puls yp currn dsurbancs. Powr sgnal dsurbancs can also lad o powr nrrupons capacor swchng and crcu auls. Th classcaon o nonsaonary sgnals ay b dvdd no h sags o aur xracon dnsonaly rducon and parn rcognon. Furhror h dscrnav par o h sgnal s a ransn sgnal h poson o whch s unknown hn a ranslaon nvaran classr s rqurd. I s sn ha lnar rquncy rprsnaons lk h Shor T Fourr Transor [4] and h Wavl Transor [5 6] provd a powrul rawork or aur xracon localzng h hgh rquncy conn o h nonsaonary sgnals n rs o and n rquncy. Du o h hgh dnson o lnar -rquncy rprsnaons hr succss dpnds upon an xac or o dnsonaly rducon. Proranc o a classr s on o h os poran crron or choosng a parcular odl and h proranc o a classr shows s ably o accura classcaon. 95

2 Cnr or Proong Idas USA Drn xsng sgnal procssng chnqus such as Dscr Fourr Transor DFT Shor T Fourr Transor STFT Connuous Wavl Transor CWT Dscr Wavl Transor DWT S-Transor c. ar appld o nonsaonary powr dsurbancs sgnals or dcon localzaon and aur xracon. DFT s an xclln analyss nsrun wh a sall aoun o copuaons bu or non saonary sgnals DFT s nsnsv o odcaons n o hr spcru and vn o spl ranslaons. To hav and rquncy noraon sulanously STFT plays an poran rol by odulang a xd wndow wh sgnal bu als o gv varabl rsoluon. Wavl Transor WT uss a varabl wndow whch gvs good rquncy rsoluon and poor rsoluon a low rquncy and good rsoluon and poor rquncy rsoluon a hgh rquncy. Howvr h Wavl Transor s snsv o nos h WT[8] dos no ran h absolu phas noraon and h vsual analyss o h scal plos ha ar producd by h Wavl Transor s nrca. Boh h STFT and WT howvr sur ro a rad-o bwn and rquncy rsoluons. To oban absolu phas noraon and provd rsoluon S-Transor s usd whch cobns h good aurs o STFT[3] and WT. Th proprs o S-Transor ar ha has a rquncy dpndn rsoluon o -rquncy doan and nrly rr o local phas noraon. S-Transor uss a wndow whch s nvrsly proporonal o h rquncy and a Fourr Krnl. Th advanag o S-Transor s ha prsrvs h phas noraon o h sgnal and also provds a varabl rsoluon slar o Wavl Transor.In cas o S-Transor uss a Gaussan wndow and provds varabl rsoluon. S-Transor[6] localzs h ral and h agnary coponns o h spcru ndpndnly localzng h phas spcru as wll as h aplud spcru. Ths s rrrd o as absoluly rrncd phas noraon. Bu S-Transor surs ro poor concnraon o nrgy a hghr rquncy and hnc poor rquncy localzaon. Th nvrs Fourr ransor o h odd S-Transor gvs as TT-Transor whch gahrs h hgh rquncy sgnal coponns n h dagonal poson o h spcru and supprsss h low rquncy sgnal coponns. Agan h TT-Transor s appld o powr dsurbanc sgnals or aur xracon. Th xracd aurs ar d as npu o h PSO basd Fuzzy C Mans algorh and PSO basd K-Mans algorh or classcaon. Th PSO basd K-Mans algorh provds accura and provd classcaon rsuls. Ths papr prsns our scons such as scon II prsns h drvaon o TT-Transor Scon III prsns h proposd algorh and h rrnc and concluson s ollowd by scon IV. II. TT-Transor Th advanag o S-Transor s ha prsrvs h phas noraon o h sgnal and also provds a varabl rsoluon slar o wavl ransor. Howvr S-Transor surs ro poor concnraon o nrgy a hghr rquncy and hnc poor rquncy localzaon.tt-transor a nw vw o localzng h aurs o a srs around a parcular pon on h axs. Th TT-Transor [] s drvd ro h S-Transor ha s nvrs Fourr ransor o S-Transor.TT-Transor has good ably n gahrng rquncy; gahrs h hgh rquncy sgnals n dagonal poson o h spcru and supprssng h low rquncy sgnals. Ths lads o h da o lrng on h plan n addon o h rquncy plan. Only h dagonal o TT-Transor has bn usd or sgnal characrzaon. Th dagonal o TT-Transor rprsn a spl rquncy lrd vrson o h orgnal sgnal. Th nos can b sparad ro h cv sgnal whch can prov h sgnal-o-nos rao by usng TT-Transor. Th -rquncy analyss o a sgnal dpcs varaon o h sgnal s spcru wh. Th rcnly proposd S-Transor s a cobnaon o shor- Fourr ransor STFT and wavl ransor snc uss a wndow nvrsly proporonal o h rquncy and a Fourr Krnl. Th sandard S-Transor o a sgnal x s gvn by a convoluon ngral [0] as S 96 x. d whr s rquncy and ar varabls. Th sandard dvaon dlaon parar or wdh o wndow s a uncon o rquncy and n noral S- ransor s dn as

3 Journal o Agrculur and L Scncs Vol. o. ; Jun As h wdh o h wndow s dcad by h rquncy can asly b sn ha h wndow s wdr n h doan a lowr rquncs and narrowr a hghr rquncs. In ohr words h wndow provds good localzaon n h rquncy doan or low rquncs whl provdng good localzaon n doan or hghr rquncs. Th dsadvanag o h currn algorh s h ac ha h wndow wdh s always dnd as a rcprocal o h rquncy. A sgncan provn o S-Transor can b ralzd by dnng h sandard dvaon o h wndow as k 3 rsulng n a odd S-Transor as d x k S k. 4 Whr and conrol h wdh o h wndow. Choosng k= h quaon 3.4 can b wrn as d x S. 5 Th S-Transor can b wrn as a convoluon o wo uncons ovr h varabl d g p S 6 Or g p S 7 Whr x p 8 And g 9 L Bα b h Fourr ransor ro τ o α o h S-Transor Sτ. By h convoluon hor h convoluon n h τ doan bcos a ulplcaon n h α rquncy doan: ow dnng G P B 0 Whr Pα and Gα ar h Fourr ransor o pτ and gτ so w can wr X B Thus S-Transor s h nvrs Fourr Transor o h abov quaon d X S. and h odd S-Transor s gvn by d X S. 3 Th TT ransor s oband ro h nvrs Fourr ransor o h odd S-ransor as d S TT. 4

4 FREQUECY AMPLITUDE Cnr or Proong Idas USA Also nvrng h TT -Transor h orgnal sgnal x s oband as x TT d Dscr TT-Transor L x[ kt] k=0.- dno a srs corrspondng o x wh saplng nrval o T. Th dscr Fourr ransor s gvn by nk n X x kt T k0 As w know h S-Transor s gvn by S X. d Usng quaon 3.6 h S-Transor o a dscr srs xkt s gvn by lng n/t and τ pt whr T=/ Thus h dscr TT -Transor s gvn by TT ˆ pt kt n0 Sˆ pt n T. n k Th dscr TT-Transor conans dg cs snc s oband ro Ŝ. Th nvrson o Tˆ T s gvn by Xˆ k TT ˆ pt kt 8 p TRASIET O. OF SAMPLE POITS S-TRASFORM O. OF SAMPLE POITS Fg. Localzaon o Transn Sgnal Usng S-Transor 98

5 Journal o Agrculur and L Scncs Vol. o. ; Jun 04 III. Proposd Mhod Fg. Localzaon o Transn Sgnal Usng S-Transor and TT-Transor A.Parcl Swar Opzaon s an approach o probls whos soluons can b rprsnd as a pon n an n-dnsonal soluon spac. A nubr o parcls ar randoly s no oon hrough hs spac. A ach raon hy obsrv h "nss" o hslvs and hr nghbours and "ula" succssul nghbours hos whos currn poson rprsns a br soluon o h probl han hrs by ovng owards h. Varous schs or groupng parcls no copng s-ndpndn locks can b usd or all h parcls can blong o a sngl global lock. Ths xrly spl approach has bn surprsngly cv across a vary o probl doans. PSO was dvlopd by Jas Knndy and Russll Ebrhar n 995 ar bng nsprd by h sudy o brd lockng bhavour by bologs Frank Hppnr. I s rlad o voluon-nsprd probl solvng chnqus such as gnc algorhs. As sad bor PSO sulas h bhavors o brd lockng. Suppos h ollowng scnaro: a group o brds ar randoly sarchng ood n an ara. Thr s only on pc o ood n h ara bng sarchd. All h brds do no know whr h ood s. So wha's h bs sragy o nd h ood? Th cv on s o ollow h brd whch s nars o h ood. PSO larnd ro h scnaro and usd o solv h opzaon probls. In PSO ach sngl soluon s a "brd" n h sarch spac. W call "parcl". All o parcls hav nss valus whch ar valuad by h nss uncon o b opzd and hav vlocs whch drc h lyng o h parcls. Th parcls ly hrough h probl spac by ollowng h currn opu parcls.pso s nalzd wh a group o rando parcls soluons and hn sarchs or opa by updang gnraons. In vry raon ach parcl s updad by ollowng wo "bs" valus. Th rs on s h bs soluon nss has achvd so ar. Th nss valu s also sord. Ths valu s calld pbs. Anohr "bs" valu ha s rackd by h parcl swar opzr s h bs valu oband so ar by any parcl n h populaon. Ths bs valu s a global bs and calld gbs. Whn a parcl aks par o h populaon as s opologcal nghbors h bs valu s a local bs and s calld lbs. PSO s a populaon basd sochasc opzaon chnqu nsprd by socal bhavor o brd lockng. A concp or opzng nonlnar uncons usng parcl swar hodology PSO uss a populaon o ndvduals o sarch asbl rgon o h uncon spac. In hs conx 99

6 Cnr or Proong Idas USA Each candda soluon s calld PARTICLE and rprsns on ndvdual o a populaon aurs.. Th populaon s s o vcors and s calld SWARMs o aur daa pons. 3. Th parcls chang hr coponns and ov ly n a sarch spac. 4. Thy can valua hr acual poson usng h uncon o b opzd. 5. Th uncon s calld FITESS FUCTIO. 6. Parcls also copar hslvs o hr nghbors and a h bs o ha nghbors. 7. Each parcl rs o ody s currn poson and vlocy accordng o h dsanc bwn s currn poson and pbs and h dsanc bwn s currn poson and gbs. So Each parcl has Indvdual knowldg pbs s own bs-so-ar poson Socal knowldg gbs pbs o s bs nghbour Populaon-basd sarch procdur n whch ndvduals calld parcls chang hr poson sa wh. ndvdual has poson & ndvdual changs vlocy----- Parcls ly around n a uldnsonal sarch spac. Durng lgh ach parcl aduss s poson accordng o s own xprnc. and accordng o h xprnc o a nghborng parcl akng us o h bs poson ncounrd by sl and s nghbor. Th vlocy upda quaon s gvn by v wv c r pbs x c r gbs x and h poson upda quaon s gvn by x x v Whr w s h nra wgh whch nhancs h xploraon ably o parcls. Parars o PSO Th nubr o parcls :0 40 parcls. In hs cas 30 parcls ar consdrd nally o g good rsuls. Dnson o parcls :I s drnd by h probl o b opzd. Rang o parcls :I s also drnd by h probl o b opzd w can spcy drn rangs or drn dnson o parcls. Vax: Ths s don o hlp kp h swar undr conrol. w s h rang o h parcl as h Vax..g. X blongs [-0 0] hn Vax= 0. On anohr approach s Vax= UpBound LoBound/5 Vlocy can b ld o V ax Larnng/Acclraon acors : cand cusually qual o. Howvr ohr sngs wr also usd n drn paprs. Bu usually cquals o cand rangs ro [0 4]. Th soppng crra: Th axu nubr o raons h PSO xcu and h nu rror rqurn. PSO Procss. Inalz parcls wh rando poson and vlocy vcors.. Evalua nss or ach parcl s poson p. 3. I nssp br han nsspbs hn pbs= p. 3. S bs o pbss as gbs. 4. Upda parcls vlocy and poson 5. Sop: gvng gbs opal soluon. 6. I no Go o sp and rpa unl convrgnc or a soppng condon s sasd. 00

7 Journal o Agrculur and L Scncs Vol. o. ; Jun 04 Inra wgh For conrollng h growh o vlocs a dynacally adusd or consan nra wgh wr nroducd. Largr w -grar global sarch ably Sallr w -grar local sarch ably. By lnarly dcrasng W-gvs bs PSO proranc Th lnarly dcrasng nra wgh w s gvn by Whr k= sarch nubr I=axu nubr o raon Vlocy o h parcls k Vlocy o ach parcl s updad ro h knowldg o h prvous vlocy and W. Vax claps parcls vlocs on ach dnson and Vax s sauraon pon. Vax drns nnss wh whch rgons ar sarchd oo hgh can ly pas opal soluons oo low can g suck n local na Th locaon o ach parcl s hn changd n h nx sarch usng s updad vlocy noraon. Th nss valus o all parcls ar hn valuad and h ovrall bs locaon s slcd. Consrcon Facor. Clrc and Knndy proposd ha h consrcon acor s cv or h algorh o convrg. Consrcon acor guarans h convrgnc and provs h convrgnc vlocy. Th xprsson or vlocy has bn odd as v w w w w w 0 w0 k I prvous wgh 0 prsn wgh w 0.9 w v cr pbs x c r gbs x whr 4 c c 4 φ s s o 4.whch gvs c=c=.05 and =0.79 PSO algorh prors wll n h arly sag bu asly bcos praur n h local opa ara. Th vlocy s only rlad wh nra wgh and consrcon acor. I h currn poson o a parcl s dncal wh h global bs poson and h currn vlocy s a sall valu h vlocy n nx raon wll b sallr. Thn h parcl wll b rappd n hs ara whch lads o praur convrgnc. B Fuzzy C Mans Algorh In Fuzzy C ans clusrng [0] w drn h clusr cnr C and h brshp arx U and w hus drn dsnc clusrs. Fuzzy C Mans hod s basd on nzaon o h ollowng obcv uncon: J C u x c 9 0

8 Cnr or Proong Idas USA Whr = uzznss cocn u s h dgr o brshp o dnsonal asurd daa c s h n -dnsonal cnr o h clusr. c u. x u u C k x x c c k x n clusr x s h h o n - C K-Mans Clusrng Algorh Gvn a daa s o workload sapls a dsrd nubr o clusrs k and a s o k nal sarng pons h k- ans clusrng algorh nds h dsrd nubr o dsnc clusrs and hr cnrods []. A cnrod s dnd as h pon whos coordnas ar oband by copung h avrag o ach o h coordnas.. aur valus o h pons o h obs assgnd o h clusr []. Forally h Fas k-ans clusrng algorh ollows h ollowng sps.. Choos a nubr o dsrd clusrs k.. Choos k sarng pons o b usd as nal sas o h clusr cnrods. Ths ar h nal sarng valus. 3. Exan ach pon.. ob n h workload daa s and assgn o h clusr whos cnrod s nars o. 4. Whn ach pon s assgnd o a clusr rcalcula h nw k cnrods. 5. Rpa sps 3 and 4 unl no pon changs s clusr assgnn or unl a axu nubr o passs hrough h daa s s prord. Bor h clusrng algorh can b appld acual daa sapls.. obs ar collcd ro obsrvd workloads. Th aurs ha dscrb ach daa sapl n h workload ar rqurd a pror. Th valus o hs aurs ak up a aur vcor F F F M whr F s h valu o h h aur o h h ob. Each ob s dscrbd by s M aurs. For xapl ob rqurs 3MB o sorag and 0 sconds o CPU hn F F = 3 0. Th aur vcor can b hough o as a pon n M-dnsonal spac. Lk ohr clusrng algorhs k-ans rqurs ha a dsanc rc bwn pons b dnd []. Ths dsanc rc s usd n sp 3 o h algorh gvn abov. A coon dsanc rc s h Eucldan dsanc. Gvn wo sapl pons p and p ach dscrbd by hr aur vcors p = F F F M and p = F F F M h dsanc d bwn p and p s gvn by: d M F F I h drn aurs bng usd n h aur vcor hav drn rlav valus and rangs h dsanc copuaon ay b dsord snc aurs wh larg absolu valus nd o dona h copuaon []. To ga hs s coon or h aur valus o b rs scald n ordr o nz dsoron. Thr ar svral drn hods ha can b usd o scal daa. Th hod usd n hs papr s z-scor scalng. Z-scor scalng uss h nubr o sandard dvaons away ro h an ha h daa pon rsds. Th z-scor quaon s F * F whr F s h valu o h h aur o h h ob.. h daa pon μ s h an valu o h h aur and σ s h sandard dvaon o h h aur. Thus bor h algorh s appld h orgnal daa s s scald usng h z-scor scalng chnqu whr h aur an s subracd ro h aur valu and hn dvdd by h sandard dvaon o ha aur.. F s rplacd by s scald valu F *. Ths chnqu has h c o noralzng h workload aurs so ha no sngl aur donas n h clusrng algorh. 0 0

9 Journal o Agrculur and L Scncs Vol. o. ; Jun 04 Th nubr o clusrs o b ound along wh h nal sarng pon valus ar spcd as npu parars o h clusrng algorh. Gvn h nal sarng valus h dsanc ro ach z-scord scald sapl daa pon o ach nal sarng valu s ound usng quaon. Each daa pon s hn placd n h clusr assocad wh h nars sarng pon. w clusr cnrods ar calculad ar all daa pons hav bn assgnd o a clusr. Suppos ha C rprsns h cnrod o h h aur o h h clusr. Thn C n F n * whr F * s h h scald aur valu o h h ob assgnd o h h clusr and whr n s h nubr o daa pons n clusr. Th nw cnrod valu s calculad or ach aur n ach clusr. Ths nw clusr cnrods ar hn rad as h nw nal sarng valus and sps 3-4 o h algorh ar rpad. Ths connus unl no daa pon changs clusrs or unl a axu nubr o passs hrough h daa s s prord. PSO Clusrng Usng PSO clusrng s don and opal no. o clusrs ar slcd. Th cnr o h clusr ar chosn accordng o Eucldan dsanc and hn rnd by h Fuzzy C Mans Algorh. FCM dynacally drns no. o clusrs n h daa s. L S x... x... x s h swar o S-parcl such ha ndcas parcl. Th no. o clusr s gvn by c =axu nubr o clusrs d= npu dnson And = d And n ha s h nubr o clusrs usd by h clusrng soluon rprsnd by h global bs parcl yˆ such 3 Th cnrs C hav bn randoly nalzd as C = C C C. Inally ak h daa pons and h rando cnrs as h npu aurs.. Inalz h swar S. Randoly nalz o ach parcl n S such ha 3. For ach parcl v randoly choos h cnrod o h closs daa pon usng h Eucldan dsanc. v k [55] x 4. Apply PSO and upda vlocy and poson 5. Upda h cnr by Fuzzy C Mans algorh and K-Mans algorh 6. For ach daa pon h h corrspondng cnr was updad usng h orula. whr c l c n x k u. x u s u C y k k n c k x x c c k x 03

10 MEA Cnr or Proong Idas USA And wh K-Mans algorh as C n F n * 7. Rpa unl rnaon crra ar 8. Rpa sp-3 o sp-6 or ach daa pon and h opzd cnr was oband a h nd o raon. 9. Th opzd cnr was sn as arguns o h Fuzzy C Mans algorh. 0. Th Fuzzy C Mans algorh uss h opzd cnrs oband as arguns n ordr o achv h rqurd clusrng.. Th K-Mans algorh uss h opzd cnrs oband as arguns n ordr o achv h rqurd clusrng and copard wh K-Mans algorh. In h proposd work aurs such as nrgy sandard dvaon auocorrlaon an varanc and noralzd valus hav bn xracd ro h nonsaonary powr sgnals. Th ollowng dsurbancs hav bn consdrd or powr sgnal clusrng. Transn Sag wh haronc 3 Swll wh haronc 4 Flckr wh haronc 5 Monary nrrupon wh haronc 6 Volag noch 7 Haronc 8 Volag spk 9 Volag swll Classcaon o powr sgnals usng PSO basd Fuzzy C Mans algorh Transn Sag + haronc Swll + haronc 0.5 Flckr + haronc Mo. n. + haronc Volag noch Haronc 0 Volag spk Volag swll STADARD DEVIATIO Fg.3: Classcaon o Powr Sgnals Usng PSO basd Fuzzy-C Mans Algorh 04

11 MEA Journal o Agrculur and L Scncs Vol. o. ; Jun 04.5 Classcaon o powr sgnals usng PSO basd K-Mans algorh Fg.4: Classcaon o Powr Sgnals Usng PSO Basd K- Mans algorh Fg.3 shows h classcaon o powr sgnals usng PSO basd Fuzzy-C Mans algorh and s ound ha h powr dsurbanc sgnals ar classd bu h clusr parn vsualzaon s poorr. Fg.4 shows h classcaon o powr sgnals usng PSO basd K- Mans algorh and s ound ha h powr dsurbanc sgnals ar classd wh dsnc parns. Th classcaon accuracy s shown n h abl-. Tabl- Sl. Powr sgnal dsurbancs Accuracy n prcnag % o. PSO-Fuzzy C Mans PSO-K-Mans Transn Haronc och Sag Spk Sag+ Haronc Swll Flckr Sag+ Haronc % Accuracy Fro abl- s ound ha PSO K-Mans algorh gvs good prcnag o accuracy han h PSO-Fuzzy C Mans. In boh h algorh n h cas o sag s ound ha h classcaon accuracy s narly qual. Morovr h k-ans algorh s prrabl or h classcaon o h powr sgnals. I. Concluson and Rrnc -0.5 Transn Sag+haronc - Swll+haronc Flckr+haronc -.5 Mo. n. + haronc Volag noch - Haronc Volag spk Volag swll STADARD DEVIATIO Th nvrs Fourr ransor o odd S-Transor s known as TT-Transor whch s appld o xrac sascal aurs and vsual localzaon o powr dsurbanc sgnals. TT-Transor has ponal o localz h powr sgnal wavors br han h S-Transor as TT-Transor localzs h spcru dagonally. Th xracd aurs ar d as npu o a Fuzzy C Mans clusrng algorh FCAand K-Mans algorh or parn classcaon. To prov h parn classcaon a hybrd opzaon chnqu has bn appld whch s h hybrd o wo algorhs such as PSO - Fuzzy C Mans and PSO-K ans. or coparav assssn o powr sgnal dsurbanc parn classcaon accuracy. 05

12 Cnr or Proong Idas USA Parcl swar opzaon basd K-Mans algorh has achvd hghr parn rcognon accuracy n classyng varous powr sgnal dsurbancs han h PSO-Fuzzy C Mans classr. Fro h sulaon rsuls s ound ha h proposd algorh shows h br classcaon proranc han h xsng algorhs n powr sgnal dsurbanc parns classcaon. Rrncs C. R. Pnngar & L. Mansnha 03. A hod o - analyss: Th TT-ransor. Elsvr Scnc on Dgal Sgnal Procssng L. Cohn T-Frquncy Analyss. Prnc-Hall w Jrsy USA 995. L. Cohn T-Frquncy Dsrbuons A Rvw Procdng o IEEE Vol.77 o.7 July 989 pp E. O. Brgha Th Fas Fourr Transor And Is Applcaons Prnc-Hall Englwood Cls w Jrsy 988.F. S. Chn Wavl Transor In Sgnal Procssng Thory And Applcaons aonal Dns Publcaon o Chna 998. I. Daubachs Tn Lcurs On Wavls Phladlpha PA: SIAM 99. S. Malla A Wavl Tour O Sgnal Procssng LondonU.K.:Acadc998. Ingrd Daubchs Th Wavl Transor T Frquncy Localzaon and Sgnal Analyss IEEE Trans. On Inoraon Thory Vol.36 o.5 pp P. Rakov E. Sdc L.J. Sankov and J. Jang T Frquncy Sgnal Procssng Approachs wh Applcaons o Har Sound Analyss Copurs n Cardology Vol.33 pp R. Mchal Porno T Frquncy Rprsnaon o Dgal Sgnals and Syss Basd on Shor-T Fourr Analyss IEEE Transacons On Acouscs Spch And Sgnal Procssng Vol.Asp 8 o. pp Wang Y. S. Sound Qualy Esaon or onsaonary Vhcl oss Basd on Dscr Wavl Transor Journal o Sound and Vbraon Vol.3 pp P.S. Bradly and Usaa M. Fayyad: Rnng nal pons or k-ans clusrng. In Procdngs Fnh Inrnaonal Conrnc on Machn Larnng pags 9-99 San Francsco CA 998 Morgan Kauann. Khald Alsab Sanay Ranka and Vn Sngh: An Ecn k-ans clusrng algorh. In Procdngs o h Frs Workshop on Hgh Proranc Daa Mnng Orlando FL March 998. P. K. Dash B. K. Pangrah & G. Panda 003. Powr qualy analyss usng S-ransor. IEEE Transacons on powr dlvry Dorgo M. & Gabardlla L. M An colony sys: A cooprav larnng approach o h ravllng salsan probl. IEEE Transacons on Evoluonary Copuaon Dash P. K. Pangrah B. K. & Panda G Powr qualy analyss usng S-ransor. IEEE Transacons on powr dlvry L Jang Wnhu Yang A Modd Fuzzy C-Mans Algorh or Sgnaon o Magnc Rsonanc Iags Proc. VIIh Dgal Iag Copung: Tchnqus and Applcaons Sydny 0- Dc B. Bswal P. K. Dash S. Mshra B. Bswal P.K. Dash S. Mshra A Hybrd An Colony Opzaon Tchnqu For Powr Sgnal Parn Classcaon Elsvr Scnc Expr Syss Wh ApplcaonsVol.38 o.5 pp R. G. Sock wll L. Mansnha & R. P Low Localzaon o h coplx spcru: Th S-ransor. IEEE Transacons on Sgnal Procssng Mohad. Ahd Sah M. Yaany.al A Modd Fuzzy C-Mans Algorh For Bas Fld Esaon and Sgnaon o MRI Daa IEEE Trans. Md. Iag. Vol. o.3 pp C. T. Su C. F. Chang and J.P. Chou Dsrbuon work Rconguraon or loss rducon by An Colony sarch algorh Elcrc Powr Syss Rsarch Vol.75 o. -3 pp Aug O. J Oylad O. O Oladpupo I. C Obagbuwa Applcaon o k-mans Clusrng algorh or prdcon o Sudns Acadc Proranc Inrnaonal Journal o Copur Scnc and Inoraon ScuryVol. 7 o R. Pal K. Pal and J. C. Bzdk A Mxd C-Mans Clusrng Modl In IEEE In. Con. Fuzzy Syss pp. Span

13 Journal o Agrculur and L Scncs Vol. o. ; Jun 04 H. T C. Borgl C. Dorng and R. Krus Fuzzy Clusr Analyss Wh Clusr Rpulson prsnd a h Euro. Syp. Inllgn Tchnologs EUITE Tnr Span 00. H. T and R. Krus A Modcaon To Iprov Possblsc Fuzzy Clusr Analyss prsnd a h IEEE In. Con. Fuzzy Syss FUZZ-IEEE 00 Honolulu HI 00. H. T C. Borgl C. Dorng and R. Krus An Exnson To Possblsc Fuzzy Clusr Analyss Elsvr Scnc Fuzzy Ss Sys. Vol. pp E. E. Gusason and W. C. Kssl Fuzzy Clusrng Wh A Fuzzy Covaranc Marx n Proc. IEEE Con. Dcson and Conrol San Dgo CA pp D.L. Pha J.L. Prnc An Adapv Fuzzy C-Mans Algorh or Iag Sgnaon n h Prsnc o Innsy In hoogns. Parn Rcognon Lrs.Vol.0o.pp Mohad. Ahd Sah M. Yaany.al A Modd Fuzzy C-Mans Algorh For Bas Fld Esaon and Sgnaon o MRI Daa IEEE Trans. Md. Iag. Vol. o.3 pp L Jang Wnhu Yang A Modd Fuzzy C-Mans Algorh or Sgnaon o Magnc Rsonanc Iags Proc. VIIh Dgal Iag Copung: Tchnqus and Applcaons Sydny 0- Dc Mah H. J Bolln Irn Y.H. Gu Pr G. V. Axlbrg Eanoul Syvakaks Classcaon O Undrlyng Causs O Powr Qualy Dsurbancs: Drnsc Vrsus Sascal Mhods EURASIP Journal on advancs n sgnal procssng Vol.007 pp