The Prediction Algorithm Based on Fuzzy Logic Using Time Series Data Mining Method

The Predcon Algorhm Based on Fuzzy Logc Usng Tme Seres Daa Mnng Mehod I Aydn, M Karakose, and E Akn Asrac Predcon of an even a a me seres s que mporan for engneerng and economy prolems Tme seres daa mnng comnes he felds of me seres analyss and daa mnng echnques Ths mehod creaes a se of mehods ha reveal hdden emporal paerns ha are characersc and predcve of me seres evens Tme seres daa mnng eamnes he me seres n a phase space In hs paper, a predcon algorhm usng me seres daa mnng ased on fuzzy logc s proposed Earhquake predcon has een done from a synhec earhquake me seres y usng nvesgang mehod a frs sep ago Tme seres has een ransformed o phase space y usng nonlnear me seres analyss and hen fuzzy logc has een used o predcon opmal values of mporan parameers characerzng he me seres evens Truh of predcon algorhm ased fuzzy logc has een proved y applcaon resuls Keywords Even, fuzzy logc, me seres analyss, me seres daa mnng A I INTRODUCTION me seres daa s oaned a deermned me nerval from any sysem Daly prce change of a marke, curren and volage daa of an nducon moor and he populaon dsruon accordng o year n a counry may e consdered as a me seres Such a me seres conans evens of neres [1] One nnovae approach s o denfy crcal, me-ordered srucures, called emporal paern, whch are hdden n eq (1) and are characersc of neresng evens [] Tme seres analyss s fundamenal o engneerng, scenfc, and usness endeavors [3] Invesors are neresed n predcng fuure values from pas me seres daa A me seres eample has een gven n equaon (1) = {, = 1,, N} (1) In such a me seres, s me nde and N s he oal numer of oservaons Imporan evens are formed over he me For eample, an earhquake from a synhec sesmc me seres, nsananeous fall a sock prces and ncpen fauls n an nducon moor are consdered as an even for a me seres Tme seres s analyzed for predcon of hese evens Tradonal me seres analyss mehods such as Bo- I Aydn s wh Erzncan Unversy, Erzncan, Zp code 4600 Turkey (phone: 0090-533-48-56-9; fa: 0090-446-751-30-1; e-mal: lhanaydn@erzncanedur ) M Karakose s wh he Compuer Engneerng Deparmen, Unversy of Fra, Elazg, Zp code 3119 Turkey (e-mal: mkarakose@fraedur) E Akn s wh he Compuer Engneerng Deparmen, Unversy of Fra, Elazg, Zp code 3119 Turkey (E-mal: eakn@fraedur) Jenkns or Auoregressve Inegraed Movng Average (ARIMA) mehod can e used o model such me seres However, he ARIMA mehod s lmed y he requremen of saonary of me seres and normaly and ndependence of resduals An even characerzaon funcon g() can e employed o characerze he even n equaon (1) as shown n equaon () g ) = g(,,, ) () ( 1 1 Ths even characerzaon funcon changes accordng o he predcon am For eample, f represens oday s closng prce of a sock and our am s o predc he percenage change of omorrow s prce, hen he even characerzaon funcon can e defned as shown n equaon (3) The even characerzaon funcon s defned such ha s value a me nde correlaes hghly wh he occurrence of an even a some specfed me n he fuure [1] If earhquake predcon s waned o do one sep efore, he even characerzaon funcon n equaon (4) can e seleced +1 g( ) = (3) ( ) = + 1 g (4) Even characerzaon funcons a equaon (3) and (4) can e defned y dfferen ways for even predcons a dfferen me seres Before he even characerzaon funcon s deermned, he am s o selec hs funcon whch predcs mporan evens Ths s no rval ask due o nonlnear ehavors of mos me seres n he real world applcaons An mporan dsadvanage n me seres analyss s ha he me seres should e convered o saonary and perodc seres n order o analyze [4] As an emergng dscplne, daa mnng s he process of dscoverng hdden and useful nformaon from huge daa Daa mnng s defned as eracng useful and meanngful nformaon usng sasc, machne learnng, arfcal nellgence and paern recognon echnques from large daa ses [5] Daa mnng s he analyss of daa wh he goal of uncoverng hdden paerns Wess and Indurkhya [6] defned daa mnng as he search for valuale nformaon n large volumes of daa Tme seres daa mnng comnes daa mnng and nonlnear me seres analyss o analyze a me seres When daa mnng s appled o me seres daa, an even s consdered as an neresng paern Povnell [1] defnes me seres daa mnng as comnng of daa mnng, me seres analyss and genec 91

algorhm echnques He used he genec algorhm o dscover neresng paerns n a me seres y daa mnng Tme seres should e eamned n a phase space n order o ge neresng paern from The man goal n me seres daa mnng s o use me delay emeddng and phase space ased on Taken heorem [7] The phase space of a me seres n equaon (1) s generaed y usng me delay emeddng and emeddng dmenson n order o ge neresng paerns Elemens of form me lagged shape of orgnal me seres wh emeddng dmenson and me delay facor The phase space of he me seres n equaon (1) accordng o me delay facor and emeddng dmenson s presened n equaon (5) s a mar whose row vecor s a pon n he phase space = ( ( 1), ( ),, ) R (5) Where =1,,,k s me delay emeddng whch allows he phase space o e spanned over nonconsecuve melagged nsances For nsance, =3 and =3, he vecor s shown y =( -6, -3, ) Ths ransformaon preserves he nonlnear dynamcs of he orgnal me seres and he emporal paerns are represened y daa pons n he phase space [] The emporal paerns represenng he characersc of me seres are used o predcon of he mporan evens Ths mehod s successfully appled non-perodcal, nonlnear, and comple me seres Daa mnng s he process of dscoverng useful paern n daa ha are hdden and mporan paern I comes from several felds, ncludng sascs, daaase and machne learnng [5] I uses echnques such as cluserng, assocaon rules, and classfcaons models o denfy hdden and useful nformaon n large daaases Ohers who have appled daa mnng conceps o fndng paerns n me seres nclude Keogh and Smyh [8], [9] Ther approach uses a dynamc programmng mehod for algnng he me seres and a predefned se of emplaes Moon e al [10] proposed a new me susequence machng mehod They used he dual mach for me seres smlary Tme seres daa mnng has een used n a lo of felds such as cluserng and even predcon n leraure One of hese mehods s classfcaon and faul dagnoss n nducon moors [11], [1] Povnell [1] was suggesed an applcaon n order o even predcon In hs sudy, he dd dfferen applcaons such as earhquake predcon, sharp fall of sock prce A frs sep, he ransformed a me seres o phase space He seleced dfferen even characerzaon funcons for each applcaon Opmal emporal paern cluser wh radus r and emporal paern cener v was found y usng genec search algorhm Despe he novely of hs mehod, several prolems lmed s applcaons and mus o e addressed Frs, emporal paern cluser n hs sudy was defned y a rgd regon wh fed cener and radus Ths resrcon made hard o adus o he suaon when here s nose n phase space and ofen generaed hgh degree false-posve predcon The second dsadvanage s he compuaonal compley and saly The genec algorhm yelds heavy compung load The opmzaon resuls were ofen nconssen The choces of emeddng dmenson and me delay were always ased on user s eperence wh ral-and-error Feng e al [] suggesed new me seres daa mnng for denfyng emporal paerns In hs sudy, emporal paern cluser was chosen as a fuzzy se wh Gaussan shaped memershp funcon An effcen wo sep opmzaon sraegy was proposed o search he opmal emporal cluser n he phase space Tme delay emeddng and emeddng dmenson s chosen y muual nformaon and false neares neghor mehod, respecvely Graden descen opmzaon algorhm s chosen n order o fnd opmum emporal paern cluser Mullayer feedforward neural nework was performed on he D-sock predcon [13] The goal was predced ne day s closng prce change, wh he npu of oday as well as four prevous day s prce change In hs paper, proposed me seres daa mnng mehod s ased on fuzzy logc Ths mehod uses he fuzzy logc for earhquake and Lorenz seres predcon Therefore, even predcon doesn nclude comple mahemacal equaons and he predcon s smplfed The predcon s flele due o propery of fuzzy logc mehod Because emporal paern cluser s seleced as a fuzzy se, each of pon n emporal paern cluser elong o cluser wh a specfc memershp degree So he even predcon s predced accuraely The heavy load whch he genec algorhm yelds s removed Because user eperence aou even predcon s shown n phase space and augmened phase space easly, he fuzzy rules s also deermned, easly The paper s organzed as follows: Secon II provdes ref revew of me seres daa mnng usng phase space sraegy We nroduce and dscuss our applcaon resuls n secon III Concluson and fuure sudy are dscussed n secon IV II APPLICATIONS OF TIME SERIES DATA MINING Daa mnng s a echnque of dscoverng useful paern n daa ha are hdden and unknown n normal crcumsance Daa mnng conss of machne learnng, sascs and daaase desgn [] I uses mehods such as cluserng, classfcaon, assocaon rule mnng and proalsc graphcal dependency models o denfy hdden and useful nformaon from large daaases [], [3] Predcve daa mnng s a search for very srong paerns n g daa ha can generalze o accurae fuure decsons [] Daa mnng refers o eracng or mnng knowledge from large amouns of daa [5] Keogh e al [8] used pecewse lnear appromaon represenaon of me seres for cluserng, classfcaon and assocaon rule mnng of me seres daa They have eamned he frs eensve revew and emprcal comparson of me seres segmenaon algorhms from a daa mnng perspecve They have developed an effcen sequenal paern for denfyng frequen emporal paerns Falouus e al [14] have developed effcen me seres smlary search mehods namely susequence machng Povnell e al [15] have proposed a new sgnal analyss and classfcaon mehod ased on reconsruced phase space They have used sascal mehod o esmae of phase space Bayesan lkelhood and arfcal neural nework 9

have een used for classfcaon and compared wo echnques Feng e al [] have proposed fuzzy se and he Gaussan shaped memershp funcon o defne emporal paerns n me delay emeddng phase space The resulng oecve funcon represens no only he overall value of he even funcon, u also he wegh of he vecor n emporal paern cluser o whch conrues Graden descen opmzaon mehod has een used o search emporal paerns Furua e al [16] have appled sof compung echnques for earhquake acceleraon daa Applcaly and effcency of chaos predcon and neural nework mehod have een compared and eamned usng he me seres daa of earhquake acceleraon arge nformaon s eraced from me seres all daa mus e preprocessed and nal parameers are seleced In hs sage, he emeddng dmenson and me delay emeddng s deermned usng false neares neghor and muual nformaon echnques, respecvely Then me seres mus e ransformed o he phase space Afer even characerzaon funcon g( ) s defned, Eucldan dsance from nal pons of cener pons v of emporal cluser and cluser radus r are seleced as npus of predcon algorhm III PROPOSED PREDICTION ALGORITHM BASED ON FUZZY LOGIC USING TIME SERIES DATA MINING Tme seres daa mnng mehod esalshes a mehod ha uncovers hdden paerns n a me seres Mehods ased on he me seres daa mnng echnque are ale o successfully characerze and predc comple, non-perodc, rregular and chaoc me seres [1] The me seres daa mnng mehods overcome lmaons of radonal me seres analyss echnques y adapng daa mnng conceps for analyzng me seres Mehod used here s ased on me delay emeddng If he emeddng s performed correcly, he heorems nvolved guaranee ha he reconsruced dynamcs s opologcally dencal o he rue dynamcs of he sysem, and herefore ha he dynamcal nvarans are also dencal [17] The me seres whch s appled daa mnng should e eamned n a phase space Ths s an eremely powerful correspondence; mples ha conclusons drawn from he emedded or reconsrucon-space dynamcs are also rue of real dynamcs Tme delay emeddng and emeddng dmenson are mporan parameers n consung a reconsruced phase space or refly called phase space The phase space of a me seres gven n equaon (1) s a mar whose elemens are me lagged verson of he orgnal me seres daa as follows: = 1+ ( 1) + ( 1) N 1+ + N ( ) 1 N ( 1) Where, N s he orgnal me seres daa, N s numer of oservaons; s emeddng dmenson and s me delay I s mporan o pon ou ha each row vecor of s a sngle pon n he phase space Here, he me lag s deermned usng frs mnmum of muual nformaon echnque or auocorrelaon funcon and he emeddng dmenson can e esmaed usng false neares neghor mehod Block dagram of proposed predcon mehod ased on fuzzy logc s gven n Fg 1 Accordng o hs dagram, efore (6) Fg 1 The predcon algorhm scheme ased on fuzzy logc usng me seres daa mnng A Esmaon of Tme Delay Emeddng I mus e seleced an approprae me delay for phase space If s small compared o he nernal me scales of he sysem, successve elemens of he delay vecor are srongly correlaed All vecor of are hen clusered around he dagonal n he R, unless s very large [4] The wo mehods for esmang are he nformaon of auocorrelaon and muual nformaon Frs mehod s he auocorrelaon funcons For a me seres gven n equaon (1), me delay s esmaed y calculang auocorrelaon eween and as shown n equaon (7) C(, )= E( E{[ ) E( E( ) If we plo values versus he correspondng values a fed lag v earler, he auocorrelaon C quanfes how hese pons are dsrued If hey spread ou evenly over he plane, hen C s zero If hey end o crowd along he dagonal, hen C ecomes g from zero The auocorrelaon funcon akes he esmae of me nsance when he auocorrelaon funcon )] } (7) 93

frs crosses zero as he me delay The muual nformaon s compued y: M(,+ ) = p( ) ln p( ) p ln p (8), I s somemes advocaed ha one look for he frs mnmum of me delayed muual nformaon Ths s he nformaon we already possess aou he value +1 f we know The epresson we have o compue s ased on Shannon s enropy On he nerval eplored y he daa, we creae a hsogram for he proaly dsruon of he daa Denoe y p he proaly ha he sgnal assumes a value nsde he h n of hsogram, and le p ( ) e he proaly n n and s n n The frs mnmum of muual nformaon funcon marks as he me lag [4] B Esmaon of he Emeddng Dmenson When we sar o analyze a nonlnear me seres, we mus deermne he emeddng dmenson One way o esmae he emeddng dmenson s usng he neares neghor mehod [4] Ths means ha a -dmensonal phase space wll have he same opologcal properes as he orgnal phase space [] A phase space s a dmensonal merc space no whch a me seres s unfolded Takens [7] showed ha f Q s large enough, he phase space s homeomorphc o he sae space ha generaed he me seres Taken s Theorem provdes he heorecal usfcaon for reconsrucng sae spaces usng me-delay emeddng Taken s proved ha he sae space of an unknown sysem can e reconsruced If he emeddng s performed correcly, Takens Theorem guaranees ha he reconsruced dynamcs are opologcally dencal o he rue dynamcs of he sysem The algorhm of fndng false neares, neghor s descred as follows: For each daa pon whch s denoed y neares neghor s found y = arg mn n R, s, (9) Where s he Eucldean dsance eween he wo pons If he emeddng dmenson s changed from o +m, dsance eween he wo pons s calculaed y: If r = + m + m r eceed a gven hreshold v, hen (10) s marked as havng a false neares neghor Therefore, he emeddng dmenson s deermned y he fac ha he numer of daa pons r >v s zero n R Afer me delay emeddng and emeddng dmenson s deermned, he phase space mar s consued Anoher preparaon sage n he me seres daa mnng s deermned he even characerzaon funcon whch changes accordng o he applcaon In hs paper, ecause our am s he predcon of an earhquake from a synhec sesmc a me seres, he even characerzaon funcon s seleced as gven n equaon (4) To fnd he mporan even, he arge funcon mus also e deermned Such a arge funcon s descred n equaon (11) f ( v, r) = 1 (( M 1 M g( M = ), 1 M M g( g + g = ) 0) 0, 1 βn v < r f M N ohers β (11) Where g 0 s he smalles even value, N s oal numer of daa, β s rae of he mnmum cluser sze, r s cluser radus, v s cener pons of cluser, and M s oal numer of daa nsde cluser Dsadvanage of hs cluser s ha uses a crsp cluserng Radus of he cluser s crsp and each pon n he cluser s own same memershp degree Alernavely, he emporal paern cluser can e defned as fuzzy se: F = {(, µ ( ) R )} (1) F Where µ F ( ) he memershp s a funcon ndcang he degree of n F and s compued as n equaon (1) Accordng o hs new emporal paern cluser, he arge funcon s changed as equaon (14) v ( ) r F = e µ (13) N ma{ f ( v, r)} = ma µ F ( ) g( ) (14) = 1 Snce he fuzzy logc heory was descred y Prof L Zadeh, has een used many of feld of engneerng [18] Fuzzy logc s a prolem-solvng conrol sysem mehodology ha lends self o mplemenaon n sysems rangng from smple, small, emedded mcro-conrollers o large, neworked, mulchannel PC or worksaon-ased daa acquson and conrol sysems I can e mplemened n hardware, sofware, or a comnaon of oh I provdes a smple way o arrve a a defne concluson ased upon vague, amguous, mprecse, nosy, or mssng npu nformaon Fuzzy logc s approach o conrol prolems mmcs how a person would make decsons, only much faser Generally, fuzzy logc s que effecve mehod n sysems ha he mahemacal model s unknown or canno e esalshed The prolem soluon n fuzzy logc s hree seps: fuzzfer, nference mechansm, and defuzzfer Frs, he parameers of he sysem o e eamned are measured Then he npus are eposed o fuzzfer Knowledge ase o e oaned fuzzy rules eracs fuzzy values n order o usfcaon of he nspeced sysem In las sep, hese fuzzy oupu values are made ceran wh one of defuzzfer mehods and usfcaon of he sysem s made 94

IV APPLICATION RESULTS A The Sesmc Synhec Earhquake Eample The predcon algorhm ased on fuzzy logc s appled o a synhec sesmc me seres Mala package program s used n order o esmae an earhquake degree from synhec sesmc me seres Graphcs of synhec sesmc me seres s gven n Fg Fg 4 Augmened phase space of synhec sesmc me seres Fg Synhec sesmc me seres The frs npu of he fuzzy logc s radus of he emporal paern cluser and he second npu s Eucldan dsance of cluser cener pons from nal pons The oupu of fuzzy s shown he sze of he earhquake The memershp of fuzzy logc s gven n Fg 5 Afer synhec sesmc me seres s oaned, emeddng dmenson and me delay facor of phase space mus e deermned In hs sudy, emeddng dmenson s seleced as wo and me delay facor s seleced as one Accordng o hese parameers, consruced phase space s gven n Fg 3 Every par of adacen oservaons n he orgnal me seres forms a sngle pon n hs phase space The deermned radus and cener pons of emporal paern cluser ha predc he earhquake one sep ago s our arge n hs sudy usng me seres daa mnng Augmened phase space s gven n Fg 4 Our am s fnd he emporal paern ha wll show o e an earhquake The augmened phase space s a hree dmensonal phase space wh (, -1, +1 ) dmensons a) Memershp funcons for r ) Memershp funcons for v c) Memershp funcons of oupu D Fg 5 Inpu and oupu memershp funcons of fuzzy logc for synhec me seres phase space The consued rule ase accordng o hese memershp funcons s gven n Fg 6 The oupu graphc of predcon mehod ased on fuzzy logc and he applcaon resuls are gven n Fg 7 and Tale I, respecvely Fg 3 The phase space of synhec sesmc me seres Fg 6 Rule ase of predcon algorhm ased on fuzzy logc 95

Where σ, r and are model parameers of equaon 14, known as Prandl numer, Raylegh numer, and geomerc facor respecvely, see [6] for deals Fg 8 plos he Lorenz seres wh σ = 10 0, r=80 and =8/3 In hs applcaon he componen s chosen as oserved me seres wh 001 sep sze Fg 7 The earhquake predcon graphcs accordng o fuzzy npu values TABLE I THE APPLICATION RESULTS OF PREDICTION ALGORITHM BASED ON FUZZY LOGIC v r D 049 035 55 08 383 5 366 13 309 608 050 083 141 570 47 Earhquake sze accordng o radus and Eucldan dsance from nal pons of cener pons of emporal paern cluser s gven n Fg 7 If v s g and r s small, hen he degree of earhquake s small If v s small and r s small, hen he earhquake s g If he cener pons of he emporal paern cluser s 05 and 13 and radus of he emporal paern cluser s 13, hen he earhquake s mamum shown as n Fg 7 Therefore, Fuzzy logc could predc v and r parameers whch wll predc he earhquake one sep ago One of he advanages of hs mehod s o use daa mnng for analyss of me seres and such a sysem s modeled y fuzzy logc whou oo many comple mahemacal equaons As shown n Tale I, he opmum values of v and r s values of frs row and where sze of earhquake s 55 These parameers predc an earhquake one sep afer Fg 8 () componen of Lorenz seres Tme delay was deermned as =1 s and he emeddng dmenson =3 y muual nformaon and false neares neghor mehod, respecvely The esmaed muual nformaon for () componen of Lorenz seres s shown n Fg 9 and he emeddng dmenson s shown n Fg 10 Fg 9 Muual nformaon of () componen of Lorenz seres B Lorenz Seres Analyss A well known nonlnear me seres-lorenz seres s generaed y equaon (15), wh hree sae varales(, y, z): d = σ ( y ) d dy = r y z d dz = y z d (15) Fg 10 Mnmum Emeddng dmenson 96

The phase space of () has hree emeddng dmenson 3D dmensonal phase space s as shown n Fg 11 1 NB NS Z PS 05 PB -0-15 -10-5 0 5 10 15 0 c) Oupu memershp funcon for T Fg 1 Inpu and oupu memershp funcons of fuzzy logc for lorenz me seres phase space The rule ase for Lorenz me seres predcon s gven n Fg 13 The oupu surface of fuzzy s demonsraed n Fg 14 Fg 11 Phase space of () The mporance occurrence or even for hs seres was defned as o when he magnude of he predced ne pon s greaer han 15 g ( ) = + 1 15 > 0 (16) The goal of our approach s no denfy all even pons n he Lorenz me seres The algorhm akes an approach o denfy hose emporal paerns ha are lkely predcve of he evens The arge funcon f(v,r) was used o erac he fuzzy rules from phase spaces The memershp funcon of fuzzy logc s gven n Fg 1 Fg 13 Rule ase of predcon algorhm ased on fuzzy logc fro Lorenz me seres phase space a) Inpu memershp funcons for v Fg 14 The even predcon graphcs accordng o fuzzy npu values ) Inpu memershp funcon for z A as In Fg 14, he even s predced when dsance of cluser cener pons o nal pons s g and he as Z A s posve small V CONCLUSION Tme seres daa mnng s one of mporan ssues whch uses for me seres analyss and erac hdden, useful and neresng paerns from hem So hs mehod uses daa mnng for analyzng me seres, yelds a new approach o 97

me seres analyss When daa mnng whose man am s erac useful, neresng and hdden paerns from large daa ses s used n me seres daa, an earhquake predcon and he sudden fallng of sock prce s esmaed one sep efore One of advanage our approach, deec many evens Memershp funcons and fuzzy rules change ased on prolem Gaussan shaped fuzzy memershp funcon s used n order o deermne emporal paern clusers whou dependen of applcaons Thus he emporal paern can e defned a a smooh regon Genec search algorhm caches local mnma and yeld o heavy compung load The fuzzy emporal paern cluser represens emporal paerns more realscally n he me delay emeddng There s a poenal for furher developmen Alhough he Gaussan shaped memershp funcon s employed o represen he emporal paern and oecve funcon, oher dfferen funcons could e appled Also, some fuzzy opmzaon algorhm could e appled o dfferen me seres daa REFERENCES [1] R J Povnell, Tme Seres Daa Mnng: Idenfyng Temporal Paerns for Characerzaon and Predcon of Tme Seres Evens, PhD Dsseraon, Marquee Unversy, 180 p, 1999 [] Feng and H Huang, A Fuzzy-Se-Based Reconsruced Phase Space Mehod for Idenfcaon of Temporal Paerns n Comple Tme Seres, IEEE Trans on Knowledge and Daa Engneerng, Vol 17, No 5, pp 601-613, 005 [3] R J Povnell and Feng, Daa Mnng of Mulple Nonsaonary Tme Seres, n Proceedngs of Arfcal Neural Neworks n Engneerng, S Lous, Mssour, pp 511-516, 005 [4] H Kanz and T Schreer, Nonlnear Tme Seres Analyss, Camrdge: Camrdge Unversy Press, 388 p, 1997 [5] J Han and M Kamer, Daa Mnng: Conceps and Technques, San Francsco: Academc Press, 800 p,005 [6] SM Wess and N Indurkhya, Predcve Daa Mnng: A praccal Gude San Franssco: Morgan Kaufmann, 8 p, 1998 [7] F Takens, Deecng Srange Aracors n Turulence, presened a he Dynamcal Sysems and Turulence, Warwck, UK, 1981 [8] E Keogh and P Smyh, A Proalsc Approach o Fas Paern Machng n Tme seres Daaases, n proc Thrd In l Conf Knowledge Dscovery and Daa Mnng, 1997 [9] E Keogh, A fas and Rous Mehod for Paern Machng n Tme Seres Daaases, n proc Nnh In l conf Tools wh Arfcal Inellgence (TAI 97), pp 578-584, 1997 [10] Y S Moon and K Young Whang, W Kee Loh, Effcen me-seres susequence machng usng dualy n consrucng wndows, Informaon Sysems, Vol 6, pp 79-93, 001 [11] R Povnell, J Bangura, N Demerdash, and R Brown, Dagnoscs of Bar and End-Rng Connecor Breakage Fauls n Polyphase Inducon Moors Through a Novel Dual Track of Tme-Seres Daa Mnng and Tme-Seppng Coupled FE-Sae Space Modelng, IEEE Transacons on Energy Converson, Vol 17, No 1, pp 39-46, 00 [1] C, Yeh, R J Povnell, B Mrafzal and N A O Demerdash, Dagnoss of Saor Wndng Iner-Turn Shors n Inducon Moors Fed y PWM-Inverer Drve Sysems Usng a Tme-Seres Daa Mnng Technque, n proceedngs of Power Sysem Technology, pp891-896, 004 [13] M T Hagan, H B Demuh and M H Bale, Neural Nework Desgn, Boson: PWS Pulshng, 736 p, 1996 [14] C Falousos, M Ranganahan, and Y Manolopoulos, Fas Susequence Machng n Tme-Seres Daaases Proc Sgmod Record (ACM Specal Ineres Group on Managemen of Daa Conf), pp 419-49, 1994 [15] R J, Povnell and, Feng, A New Temporal Paern Idenfcaon Mehod for Characerzaon and Predcon of Comple Tme Seres Evens, IEEE Trans On Knowledge and Daa Engneerng, Vol 15, No, pp 339-35, 003 [16] H Furua and Y Nomura Tme Seres Predcon of Earhquake Inpu y usng Sof Compung, proc of he Fourh Inernaonal Symposum on Uncerany Modelng and Analyss (ISUMA 03), pp 351-356, 003 [17] E Bradley, Analyss of Tme Seres- An Inroducon o Inellgen Daa Analyss, M Berhold and D Hand, eds, pp 167-194, New York: Sprnger, 1999 [18] L, Zadeh, Fuzzy Ses, Informaon and Conrol, Vol 8, pp 338-353, 1965 I Aydn (M 006) was orn n Elazg, Turkey, n 1981 He receved he BS and MS degree n compuer engneerng from Unversy of Fra, Elazg, Turkey, n 001 and 006, respecvely He s currenly workng oward PhD degree n Deparmen of Elecrcal-Elecronc Engneerng, Fra Unversy, Elazg, Turkey From 001 o 006, he was wh he Unversy of Fra as a lecurer He s workng as a lecurer n Erzncan Unversy Hs research neress are sof compung, faul dagnoss, sgnal processng and daa mnng M Karakose was orn n Elazg, Turkey, 1976 He receved he BS and MS degree n elecrcal elecronc engneerng and compuer engneerng deparmens from Fra Unversy, Elazg, Turkey n 1998 and 001, respecvely He receved PhD degree n elecrcal-elecronc engneerng from Unversy of Fra, Elazg, Turkey, 005 He s currenly an Asssan professor wh compuer engneerng deparmen, fra unversy, Elazg, Turkey Hs man research neress are n fuzzy conrol and dgal conrol of varale-speed ac drves E Akn was orn n Erzncan, Turkey, 1963 He receved he BS and MS degrees n elecrcal engneerng from Fra Unversy, Elazg, Turkey n 1984 and 1987 respecvely, and he PhD degree n he area of ac drves from Fra Unversy, Elazg, Turkey n 1994 He was wh he Deparmen of Elecrcal Engneerng, Fra Unversy, frs as Asssan professor and hen as a Assocae profersor of elecrcal machnes He s currenly a Full Professor of compuer engneerng wh unversy of fra, Elazg, Turkey Hs man research neress are n power elecroncs, dgal conrol of varale-speed ac drves, fuzzy conrol and sof compung echnques 98