Long Term Power Load Combination Forecasting Based on Chaos-Fractal Theory in Beijing

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1 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS Long Ter Power Load Cobnaon Forecasng Based on Chaos-Fracal Theory n Bejng Janguo Zhou,We Lu,*,Qang Song School of Econocs and Manageen orh Chna Elecrc Power Unversy Baodng,07003, Chna.Sae Grd Jnng Power Supply Copany Jnng 700, Chna Absrac Long er power load has a bg pac on he developen of ndusry of power. The forecasng odels of lnear syses even a sngle forecasng odel of he nonlnear syses can no forecas he long er power load grealy. In he sudy, he cobned forecasng odel of nonlnear syses ncludng chaos and fracal was esablshed o prove he accuracy of he forecas. Frs, he characerscs of chaos and fracal of daa were analyzed. Second, he forecasng odels based on chaos and fracal were used o forecas he daa. Fnally, usng he cobned forecasng odel predced he long er power load and copared he resuls of cobned forecasng odel wh he resuls of he sngle forecasng odel. The resuls show ha he cobned forecasng odel based on chaos-fracal heory has beer effec on he forecas of long er power load. Keywords - Chaos; Fracal; Cobned forecasng Model; Power load forecasng I. ITRODUCTIO Forecas of power load whch can provde a relable bass for he consrucon of power plan n soe where s an poran par of he plannng of power syse. Therefore, he power load forecasng s very poran o he healhy developen of he power ndusry even o he developen of he naonal econoy. Trend exrapolaon, regresson odel and grey syse have been wdely used n he long er load forecas. However, hese ehods can no effecvely deal wh he phenoenon of rando and coplex. Because he power syse s affeced by any facors and uual nfluence of he facors he nonlnear heory are nroduced o analyze he long er power load. Chaos heory plays an poran role n nonlnear heory. He Yang, Zou Bo, L Wenq used chaos and he local odel o forecas he power load of a sngle day[]. Zhang Yongqang used he ehod of he chaoc local forecasng and larges Lyapunov exponen o forecas he shor er power load []. Shen Ja used chaoc neural nework o forecas he power load of 4 hours[3]. However, here are any defecs lke he local convergence and he convergence speed n he applcaon of he chaoc neural nework. Fracal heory as he perfec descrbe of he chaoc srucure s also appled o he forecas of he power load. L Xang, Guan Yong, Guan Xuezhong, Tong Yu all used he ehod of fracal collage and fracal nerpolaon o calculae he erave syse of he daly power load and forecas he shor er power load [4-6]. Because here are any shorcongs of he sngle forecasng ehod he cobned forecasng odel can prove he accuracy of forecas. Therefore, he cobned forecasng odel of chaos and fracal s used o forecas he power load n Bejng. A he sae e, he prevous sudes of chaos and fracal are all suck n shor er load forecasng, we wll ake an eprcal analyss o he long er power load syse abou chaos-fracal characerscs and hen forecas. II. THEORETICAL BASIS. Chaos Theory Chaos s a seengly rando phenoenon n a deernsc syse. Chaos has a sensve dependence on nal condons; n he phase space, he chaoc aracor has a self slar srucure whch show a fracal srucure; chaos s nernal randoness, he dsorder coes fro he nernal syse raher han ousde dsurbance; he rajecory of chaoc syse s always confned o a ceran regon; here s a Fegenbao unversal consan n he syse; ergodc propery akes he chaoc syse wh dfferen reacon o dfferen nal condons o convergence o a sascally slar aracor of phase space; he sae of he syse wll suddenly change; he srucure of local s slar o whole. The chaoc syse s anly due o he nsably of he nonlnear syse and he sensvy o he nal condons. The analyss of chaoc characerscs anly uses he axu Lyapunov exponen and fracal denson.. Fracal Theory Chaos and fracal are closely relaed and he orbs of he chaoc oon or he srange aracors are fracal. Moon of chaoc syse s hghly dsordered and chaoc and he naure s refleced n he nfne coplexy of fracal. Fracal s an approprae language o descrbe he phenoenon of chaos. The fracal denson s a quanave paraeer o sudy he chaoc phenoenon. Fracal was proposed by he French aheacan Mandelbro n 964 n order o represen he coplex graphcs and coplex process o nroduce o he feld of DOI 0.503/IJSSST.a ISS: x onlne, prn

2 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS aural Scence. The fracal whch s produced by eraon s rregular, approxae or sascal self-slar..3 Cobnaon Forecasng The ehod of cobned-forecasng weghs and cobnes he forecasng resuls of he sngle odel n order o ge a hgher precson of he predcve value. The cobned forecasng proves he accuracy of forecas by he eans of nforaon negraon o dsperse he uncerany of he sngle predcon odel [7]. Cobnaon forecasng can be dvded no sac cobnaon forecasng and dynac cobnaon forecasng. The wegh of he sac cobned forecasng odel reans he sae, and he wegh of he dynac forecasng odel change wh he saple [8]. III. FORECASTIG MODEL BASED O THE THEORY OF CHAOS-FRACTAL The esablshen of he odel s dvded no four pars ncludng he processng of raw daa, denfcaon of he characerscs of chaos-fracal, he esablshen of he sngle forecasng odels based on chaos heory and fracal heory, he esablshen of he cobned forecasng odel. The four pars for a reasonable forecasng odel. 3. The Preprocessng of Orgnal Daa Frs of all, he orgnal daa are processed by he frs order dfference afer akng a log n order o reduce he nose of he orgnal daa and prove he accuracy of he load forecasng. Calculaed as Eq.: lx log x log x () 3. Recognon of he Characerscs of Chaos-Fracal Chaos s produced because of he nsably of he nonlnear syse and he sensve o nal condons. The accurae quanave ehod s used o calculae he esaed value of he sngular aracor o judge he characerscs of chaos. The sngular aracor s a phenoenon ha s caused by nsably of he orbal and shrnk of phase space of he dsspave syse. Therefore, he axal Lyapunov exponen s used o descrbe he dvergng rae of he adjacen orb. The denson of he aracor s represened by he fracal denson. 3.. Phase Space Reconsrucon The calculaon of he axal Lyapunov exponen and fracal denson s based on he echnque of he phase space reconsrucon. Phase space s he geoerc space of he deerned sae. The elecrcy consupon of he whole socey s one densonal e seres, we ge he coordnae of he delay by esang he delayed paraeer and hen esae he ebeddng denson o reconsruc he phase space. The e seres of a ceran sae n a chaoc syse s {x }(=,,,), where s he nuber of saples. Accordng o he esaed paraeers, he delay т and ebeddng denson reconsruc phase space R oban he dynac characerscs of he orgnal syse. The pon se n he reconsruced phase space s: y x, x, x, x () The esaon of reasonable paraeers s very poran o reconsruc he phase space. As for he selecon of paraeers, he C_C algorh s easy o operae and he workng of calculaon s less. The e seres s dvded no dsjon sub sequences. Defne he S(,r,) of each sub sequence s: S, r, CS, r, Cs,, r, (3) s Order, S r, C s r, C, r,,,3,. (4) s s If each saple daa n he e seres s ndependen and dencally dsrbued, for he deerned and, When, o all r, all S ( R, ) s dencal o 0. However, n fac he daa we have chosen s led and nevable correlaon. The creron for deernng he nerval of local opal e s S ( r, ) =0 or S (, r) wh nu devaon for all radus of r. Selec he value of he axu and nu of radus r, defned devaon s: S ax{ S( rj, )} n{ S( rj, )} (5) Then he value of local opal e T s S ( r, ) =0 or nu ΔS(). The delay т s he frs local opal e. Calculae varables: M 4 S( ) S( rj, ) (6) *4 j M S( ) S( ) (7) S cor ( ) S( ) S( ) (8) Where s he nuber of r j= σ/,=,,3,4. Fnd he nu value of varable Scor (), oban he e wndow of he frs axu of e seres {x }. s obaned accordng o he followng Eq.9: w ( ) (9) We ge he esaon т of e delay and paraeers of ebeddng denson. 3.. Lyapunov Exponen The sensvy of he nal condon s expressed by he separaon speed of he neghborng wo pons n he chaoc syse. The Lyapunov exponen s he esae of he dvergng rae. Is defnon s: ( ) ( ) f ( x0) f ( x0 ) ( x0) l l log (0) 0 The dvergng rae of exponenal of adjacen nal rajecores n phase space s deerned by calculang he Lyapunov exponen, so as o quanfy he degree of chaos. Usng Wolf algorh o calculae he Lyapunov exponen: In he reconsruced phase space he nal pon Y( 0) s obaned, seng up he dsance fro he neares pony 0 (T 0) s L 0, wh he connuous oveen of wo pons, unl e T, he dsance beyond a ceran value ε>0, L 0 Y( )-Y0( ) >ε, rean Y( ) and hen n he vcny of Y ( ) o fnd anoher pon Y ( ), brng Y( )-Y ( ) <ε and DOI 0.503/IJSSST.a ISS: x onlne, prn

3 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS ake he angle beween he wo as sall as possble, cycle he above process, unl Y () runs o he end of he e seres. A hs e, he oal eraons of he whole process of oon s M, he axal Lyapunov exponen s: M ' L ' ln M ' 0 0 L () Lyapunov exponen descrbes he sae of wo nal close pons afer a nuber of eraons, hey can be posve, negave or zero. When he exponen s less han zero, he dsance beween wo adjacen pons keeps approachng by he rae of exponenal quany, he oon s sably, and he syse s no sensve o he nal condon. When he exponen s equal o zero, here s a sable boundary. When he exponen s greaer han zero, he rajecory of he adjacen pons s n a sae of rapd separang. The rajecory s local nsably and fors he chaoc aracor. Therefore, he axal exponen s greaer han zero s he bass for he denfcaon of chaos. In a uldensonal syse here s a Lyapunov exponen n each drecon. All he Lyapunov exponens for he se of Lyapunov exponen. Each of hese Lyapunov exponens descrbes he convergng sae of he rajecory n a ceran drecon n he chaoc syse. One of he necessary condons of chaos s he axu Lyapunov exponen greaer han zero. A he sae e, he Lyapunov exponen can be used o esae he forecasng duraon of he syse as Eq.: () 3..3 Fracal Denson By calculang he fracal denson we analyze anoher poran characersc of he chaoc syse. Tha s he se of all soluons of he rajecory n phase space has fracal characerscs. The fracal denson s calculaed by usng he G_P algorh whch s sple and easy. In he reconsruced phase space calculae correlaon negral: C( r ) ( r X X ) (3) j, j ; j Aong he θ(x) s he un funcon of Heavsde, when x>0,θ(x)=, oherwse θ(x)=0. When r 0, here s a relaonshp beween C(r) and r: D l C( r ) r (4) Aong he D s he fracal denson, ake a log of he above equaon: l og( C( r ) ) Dl og( r ) cons an (5) Lnear regresson of he forula, he esaed value of fracal denson D s he slope of logc(r) o logr. 3.3 The Esablshen of he Cobnaon Forecasng Model of Chaos-Fracal 3.3. eural ework Forecasng Model Based on Chaos Theory The forecas of chaoc e seres based on neural nework s by usng he ably of he nonlnear approxaon of neural nework n he phase space reconsrucon o fnd he slar evoluon law. The ransfer funcon of each hdden layer of neuronal of he nework consues a base funcon of he fng plane[9]. Generally use Gaussan funcon, whch was expressed as Eq.: x c R( x) exp( ),,,,. (6) Where: x s n-densonal enered vecor; c s he cener of -h bass funcon;σ s he plannng facor of he -h base funcon; s he nuber of hdden nodes. x c s he nor of he vecor x-c, usually represens he dsance beween x and c ; here s a unque axu of R (x) a c, wh he ncreasng of x c, Rx decay o zero rapdly. For a gven npu,only a sall poron near he cener of x s acvaed. Se npu layer enered as X=(x, x,,x j,, x n ), he acual oupu s Y=(y, y,, y k,, y p ).The npu layer acheves a lnear appng fro X R (x), he oupu layer acheves a nonlnear appng fro R (X) y k, k-h neuronal nework oupu n he oupu layer s Eq3: y w R( x),k,,,p. (7) k k Where: n s he npu layer nodes; s he hdden nodes; p s he oupu layer nodes; w k s he connecon weghs of he -h neuron of hdden layer and he k-h neuron of oupu layer; R (x) s he acon funcon of -h neuron of he hdden layer Fracal Inerpolaon Forecasng Model Based on Fracal Theory Gven a daa se{(x,y ):=0,,,...)}, he followng consrucs a IFS, s aracor G s he age of a connuous funcon f : [x 0,x ] R of nerpolaon daa. Consder IFS{R;w n,n=,,...}, Aong he W s a sulaon ransforaon wh he followng for. x a 0 e n x n w (8) n y c d f n n y n And x x x x 0 n n w n wn (9) y 0 y n y y n Where b n =0 s o ake sure ha he funcon of ner cell does no overlap. Specfcally wren as: ax e x, n 0 n n ax e x, n n n (0) cx dy f y, n 0 n 0 n n cx dy f y. n n n n There are fve paraeers n he four equaons. So here s one free paraeer. In he fac he ransforaons of arx n he defnon s elongaon ransforaon. The lne segen whch s parallel o he Y axs s apped o he oher lne segen of he Y axs and he rao of he lengh of he wo segens s dn. dn s also known as he vercal scalng facor of he ransforaon of he W.Obvously DOI 0.503/IJSSST.a ISS: x onlne, prn

4 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS we can choose dn as he free paraeer. Order dn <(oherwse IFS does no converge), solve equaon group, and order L=x -x 0, a L x x, n n n () L x x, forecasng ncludng he ean absolue error, he ean percenage absolue error, he roo ean square errors, he roo ean percenage square errors. Then we wll ake a coparave analyss of he dynac cobned forecasng odel wh he forecasng resuls of wo separae forecasng odels. The ean absolue error s he ean of he absolue value of he dfference beween forecasng resul and he acual value, as Eq.8: n MAE ( y y ) () xx 0 en n n c L y y d y y0, n n n n f L x y xy d 0 x y x y 0 0. n n n n Cobnaon Forecasng Model we choose four ndcaors o evaluae he effec of n The ean percenage absolue error s he ean absolue value of he rao of he dfference beween he forecasng resul and he acual value and he acual value, as Eq.0: n n ( y y ) MAPE (3) y The roo ean square errors are he ean square value of he dfference beween forecasng resul and he acual value, as Eq.9: n RMSE ( y y ) (4) n The roo ean percenage square errors s he exracon of a roo of he rao of he square of he dfference beween he forecasng resul and he acual value and he square of he acual value, as Eq.: n ( y y ) RMPSE (5) n ( y ) Aong he n s he nuber of he forecasng perod, y s he forecasng resul of y. Accordng o he prncple of he error nzaon of cobnaon forecasng he wegh funcons of he cobned forecasng odel are bul on he bass of usng he forecasng odel of chaos and fracal. The average forecasng error produced by he ndvdual forecasng odel s : MEA MAPE RMSE RMPSE 4 (6) Then, and correspond o he average forecasng error of he forecasng odel of chaos and fracal. The su of he average error funcon s denoed as SUM : SUM (7) Then he wegh funcons are bul accordng o he prncple ha he error of cobnaon forecasng s nzed. W SUM SUM SUM (8) (9) SUM W SUM SUM The purpose s o ake he sngle odel of he axu error o occupy he salles proporon n he cobned forecasng odel. Furherore, he seng of wegh funcon can guaranee ha he wegh coeffcens of he cobned forecasng odel are drven by he daa and avod he subjecve deernaon of he coeffcen of he forecasng odel[0]. Fnally, accordng o he seleced saple se and he above wegh funcons he weghed average of separae odels s calculaed and hen he predcve value s go based on dynac cobnaon forecasng odel. IV. LOG TERM POWER LOAD FORECASTIG BASED O CHAOS-FRACTAL THEORY I BEIJIG We selec he elecrcy consupon of Bejng fro 979 o 05 fro Bejng Elecrc Power Corporaon as he orgnal daa. In order o reduce he nose of he orgnal daa and prove he accuracy of predcon, use he forula of. () o process he daa, as shown n Table I. Afer he prereaen of he daa, usng he ehod of. calculae he axal Lyapunov exponen and he fracal denson of he syse. 4. Eprcal Analyss of The Characerscs of Chaos- Fracal The ehod of nuercal analyss s used o deonsrae he chaos-fracal characerscs of he daa of he long er power load. The paraeers of he phase space reconsrucon are obaned by he C_C algorh. The phase space s reconsruced accordng o he paraeers and hen he axal Lyapunov exponen and fracal denson are obaned by usng he Wolf algorh and he G_P algorh. The MATLAB sofware s used o esae he paraeers, reconsruc he phase space and oban he relevan values. DOI 0.503/IJSSST.a ISS: x onlne, prn

JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS TABLE I DATA AFTER PRETREATMET YEAR LOGX-LOGX- YEAR LOGX-LOGX- YEAR LOGX-LOGX- YEAR LOGX-LOGX- 980-0.038 990-0.034 000-0.

5 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS TABLE I DATA AFTER PRETREATMET YEAR LOGX-LOGX- YEAR LOGX-LOGX- YEAR LOGX-LOGX- YEAR LOGX-LOGX TABLE II PARAMETERS OF PHASE SPACE RECOSTRUCTIO т w т=3 and =5 are go hrough he C_C algorh. The axal Lyapunov exponen of he oal elecrcy consupon n Bejng fro 979 o 05 s The axal Lyapunov exponen s greaer han zero.i ndcaes ha he rajecory of he adjacen pons s quckly separaed. The orb s local nsably and he syse s sensve o nal condons, whch s sasfed he necessary condon of chaoc characerscs. Accordng o he Lyapunov exponen can be esaed ha he predced perod of syse s.5. A he sae e he calculang forula of G_P algorh s ran. The fracal denson of oal elecrcy consupon n Bejng fro 979 o 05 s , as shown n Table Fgure. Graph of fracal The axal Lyapunov exponen s posve and he fracal denson s non neger, whch proves ha he syse of long er power load has characerscs of chaos and fracal. Then he odels of he chaoc neural nework and he fracal nerpolaon can be used o forecas. 4. Long Ter Power Load Forecasng Based on Chaos Theory DOI 0.503/IJSSST.a ISS: x onlne, prn

6 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS Before he predcon, he daa have o be noralzed. The daa fro 979 o 996 are seleced as ranng daa, and he daa fro 997 o 05 are seleced as es daa. The dae s preprocessed by he phase space reconsrucon and he power load s forecased by he nellgen algorh of neural nework. Then we choose four ndcaors o evaluae he effec of forecasng, such as he ean absolue error, he ean percenage absolue error, he roo ean square errors and he roo ean percenage square errors. Error evaluaon ndcaors are shown n Table 3. TABLE III. PREDICTIO RESULTS Error of chaoc forecas MAE MAPE RMSE RMPSE As can be seen fro he above able, he ean absolue error and he ean percenage absolue error of he chaoc forecasng odel are relavely sall. The forer s less han 5/000, and he laer s only / The roo ean square errors and he roo ean percenage square errors are relavely large, and he error alos reaches 50%. So, chaos forecasng odel has boh advanages and dsadvanages. The bes resuls can no be obaned only by he chaos forecasng odel. 4.3 Long Ter Power Load Forecasng Based on Fracal Inerpolaon The orgnal daa s ploed accordng o he elecrc consupon n Bejng fro 979 o 05, as shown n Fg.. Before consrucng he fracal nerpolaon odel, he pon se of he fracal nerpolaon needs o be seleced frsly. Bejng power grd wll be dvded no 3 sub ranges fro 979 o 05 and he lengh of each nerval s. The longudnal copresson rao s se o be 0.03, and he eraon nuber s 4. The Malab progras are wren o consruc a deernsc erave funcon syse wh affne ransforaon based on he exsng nerpolaon pons and he longudnal copresson rao. The fracal nerpolaon curve s shown n Fg.3. Fgure.. Graph of orgnal daa Fgure 3. Graph of Fracal Inerpolaon Coparng he orgnal daa graph wh he graph ploed by fracal nerpolaon, we can see ha here are suble dfferences beween he wo aps. The error beween he acual value and he fed value s shown n Table IV. DOI 0.503/IJSSST.a ISS: x onlne, prn

7 JAGUO ZHOU e al: LOG TERM POWER LOAD COMBIATIO FORECASTIG BASED O CHAOS TABLE IV. HE OR OF FRACTAL ITERPOLATIO MAE MAPE RMSE RMPSE The error of fracal nerpolaon As can be seen fro he above able he ean percenage absolue error s /0000. The roo ean percenage square errors s larger bu s only 6%. Whle he ean absolue error s less han %, he roo ean square errors are less han 7%. The resul shows ha he odel of he fracal nerpolaon can predc he fuure value of he power load accuraely. However, he ndvdual ndcaor of error s sll larger han ha of he chaoc forecasng odel. 4.3 Cobnaon Forecasng for Long Ter Power Load In order o avod he defecs and naccuracy of he sngle forecasng odel, he cobned forecasng odel s pu no use o calculae he error on he bass of he above wo forecasng odels. Then, hs secon akes a coparave analyss wh he sngle forecasng odel. TABLE V THE OR COMPARISO OF SIGLE MODEL AD COMBIED MODEL MAE MAPE RMSE RMPSE Chaos Fracal Cobnaon The error of wo sngle forecasng odels s relavely sall and boh of he are less han % n he frs wo evaluaon ndexes. The error of he chaoc forecasng odel s saller and only reaches / In he las wo evaluaon ndcaors, he error of he chaoc forecasng odel s sgnfcanly larger han ha of he fracal odel, and he advanages of fracal forecasng odel are shown. However, he error of he cobned forecasng odel s conrolled whn a sall range n all he evaluaon ndexes. Usng he cobned odel, he advanages of he wo sngle forecasng odels can be cobned and he dsadvanages can be reduced. In he cobned forecasng odel he forecasng odel wh larger error accouns for a saller proporon and he saller one accouns for a larger proporon by seng he dynac wegh, so as o prove he accuracy and sably of forecasng. V. COCLUSIO Because of he randoness and nsably of long er power load, hs paper selecs he ypcal nonlnear analyss ehods such as chaos and fracal for cobned forecasng o prove he accuracy of forecasng. We ake an eprcal analyss of he long er power load by usng phase space reconsrucon echnque, C-C algorh and G-P algorh and found ha he e seres has characerscs of chaos and fracal. Then, he chaos predcon odel and he fracal nerpolaon ehod are used o predc he daa. On he bass of daa predcon by he neural nework forecasng odel based on Chaos heory and forecasng odel of fracal nerpolaon, hs paper akes he dynac cobnaon forecasng. I s found ha he predcon error s sgnfcanly reduced afer cobned forecasng and he effec of cobned forecasng s beer han ha of any sngle predcon odel. REFERECE [] He Yang, Zou Bo, L Wen-q, Wen Fushuan, We Ja Lu. Shorer load forecasng based on local odel of chaos heory. orh Chna Elecrc Power Unversy Journal (ATURAL SCIECE EDITIO), vol.40,o.04,pp.43-50,03. [] Zhang Yong-qang. Sudy on shor er power load forecasng based on chaos heory. ShenYang Lgong Unversy, 03 [3] Shen Ja. Applcaon of chaos algorh n shor er power load forecasng. Agrculural Unversy of Hebe, 007. [4] L Xang, Guan Yong, Qao Yan-fen. The power load endurance analyss and forecasng based on he fracal heory. Power Syse Technology, vol.30,o.6,pp.84-88,006. [5] Xue Wan-le, Yu J-la. Fracal exrapolaon algorh n power load forecasng. Power Syse Technology, vol.30,o.3,pp.49-54,006. [6] Xao Yao. Sudy on shor er power load forecasng based on fracal heory. Cenral Souh Unversy, 007. [7] Wang Sen, Xue Yong-duan. The opal edu and long er load varable wegh cobnaon forecasng based on golden secon ehod. Elecrcal Measureen and Insruenaon, vol.53,o.03,pp.85-9,06. [8] Wang Sa-shuang, Yong Hu Hou, Dng Y-xuan. Cobnaon forecasng ehod n he edu and long er load forecasng research and s applcaon. Scence and Technology and Enerprse, vol.5,o.04,pp.0-0,06. [9] Chen Hao, Huang Le, Y arbor, Tao Ya-long. Based on K-eans cluserng and BP neural nework odel of he cobned odel of power load forecasng. Power and Energy, vol.37,o.0,pp.56-60,06. [0] Yang, Xe Ch. The cobnaon of he nonlnear dynac characerscs of exchange rae forecasng. Hunan People's Press, 008,5-53. DOI 0.503/IJSSST.a ISS: x onlne, prn

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015

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