4h Inrnaional Confrnc on Elcrical & Elcronics Enginring and Compur Scinc (ICEEECS 216 Powr communicaion nwork raffic prdicion basd on wo dimnsional prdicion algorihms Li Xiao Xu Yang Min Zhu Lipng Zhu ( Sa Grid Mishan Elcric Powr Supply Company, sichuan 621, China; Kyword nwork flow horizonal prdicion vrical prdicion wo dimnsional flow prdicion Absrac. Thr is obvious priodic daa flow curvs of h powr ingrad srvic nwork basd on h full us of hisorical daa his papr maks full us of h hisorical daa, h horizonal and vrical dimnsions ar xracd from hisorical daa. In his papr, a wo dimnsional flow forcasing mhod is proposd by sudying h xising nwork raffic prdicion modl. In his mhod, a singl xponnial smoohing algorihm is usd o calcula h horizonal and vrical prdicions. i combins h advanags of h wo dimnsional prdicion modls, and can g br prdicion accuracy han h xising prdicion algorihms a h urning poin. Inroducion Wih h rapid dvlopmn of h nwork informaion and h nwork srvic in h lcric powr communicaion nwork, nwork raffic bhavior is incrasingly complx, and nwork businss nds (imag, vido confrnc srvic, c. ar incrasing. In h fac of h divrsiy of businss and h diffrnc bwn h informaion managmn and h opraion of powr nwork, h dmand of inllign lcric powr communicaion nwork is consanly improvd, which brings nw challngs o h nwork managmn and opimizaion of h communicaion ransmission nwork. Thrfor, forcas h chang rnd of nwork daa flow, raionally alloca h limid cybr sourc, and do opimizaion nwork xpansion plan ar of gra concrn o solv h nwork congsion and provid usrs br srvic qualiy. This papr inroducs h radiional raffic prdicion mhods, and his papr proposs a wo dimnsional prdicion mhod for nwork raffic classificaion basd on a comprhnsiv analysis of h characrisics of nwork raffic. This mhod can solv h problm of on sp dlay in h prdicion of priodic raffic flow[1]. Rsarch on Traffic Forcasing Modl of Powr Communicaion Nwork A prsn commonly usd nwork flow modl including Poisson procss Markov modl havy-aild ON/OFF modl discr wavl modl and so on.poisson procss modl is firs proposd basd on h characrisics of lphon srvic flow,i is good simulaing h arly modling nwork raffic,howvr, poisson modl alrady can' saisfy h acual s o obain h flow characrisic of modrn communicaion nwork.markov modl is basd on poisson procss modl of nwork raffic wih quuing prformanc and i is asy o dal wih im sris, bu h complxiy of h modl rsoluion is largr, a h sam im i can only for shor-rm forcasing nwork raffic.on/off modl can wll xplain h slf-similar nwork raffic phnomnon, bu oo sric assumpions of h modl for ach daa sourc, bcaus i mus b indpndn idnically disribud, and wih a consan oupu ra by using h modl of nwork raffic and will produc larg rror.arim and FARIMA is suiabl for procssing saionary sris, a h sam im hy can also handl h nonsaionary squnc ha ar sasonal, cyclical and ndncy. In his aricl, hrough h comprhnsiv analysis of h characrisic of nwork raffic, i is basd on a comprhnsiv powr nwork daa flow curv xiss obvious priodiciy, accoring o his phnomnon, w propos a wo-dimnsional flow prdicion mhod, using h singl xponnial smoohing algorihm o a ransvrs and longiudinal prdicion calculad prcision indx, a rasonabl combinaion of h wo dimnsion prdicion modl, h advanags of his Copyrigh 216, h Auhors. Publishd by Alanis Prss. This is an opn accss aricl undr h CC BY-NC licns (hp://craivcommons.org/licnss/by-nc/4./. 974
mhod can g highr han h xising prdicion algorihm in h urning poin of h prdicion prcision[2-3]. Traffic prdicion of lcric powr communicaion nwork basd on wo - dimnsional forcasing algorihm Nwork raffic analysis Th nwork raffic of h ingrad srvic nwork of h smar grid has obvious daily priodiciy. Thr ar som urning poins in h flow curv, such as crs, rough and local pak. Ths urning poins ar roughly h sam vry day. A h sam im hr is a daily flow of h uniqu rnd of h day, a som im i is clarly diffrn from hisorical daa. Th wo-dimnsional prdicion algorihm proposd in his papr can br capur h rnd of daa raffic on h sam day. Th vrical prdicion can wll rflc h posiion of h urning poin in h ingrad srvic nwork. Considring hs wo characrisics, Th problm of prdicion dlay xiss a h urning poin of h prvious algorihm is solvd and h prdicion accuracy of h rnd scion is guarand. ΔT Δ Tim(Δ :5 :1 :15 :5 :1 :15 Jan Jan 3rd 2nd Figur.2.1. Horizonal dimnsion As shown in Fig 2.1, h flow daa a diffrn ims of h sam priod in h sam da ar horizonal dimnsion, such as h ransvrs flow daa wih sampling inrval, is h sampling inrval lngh, T is h day Cycl lngh. S(,d is h sampld valu a h No. sampling im on day d, whr m is h sum days of h hisorical daa, so ha for h horizonal daa squnc, said as h lngh of h horizonal raining daa squnc, hr ar 2-1 2-2 T 2-3 Lx n ( n m Th daa flow a h sam im on diffrn das is h vrical dimnsion. Jan 1s { } y y(,i i 1, 2,, Ly L b longiudinal im sris, whr Ly is h lngh of h longiudinal squnc, hr is y { S (, d d 1, 2,, Ly ; Ly m } 2-4 Nwork prdicion modl Horizonal prdicion Sinc h horizonal dimnsion has obvious daily priodiciy, h random flucuaion componn is lss, and i is suiabl for using h nonlinar prdicion algorihm. Wavl nural nwork algorihm wih wavl basis funcion insad of h prvious S-yp funcion as h hiddn layr nod ransfr funcion, combind wih muli-rsoluion wavl analysis and nural nwork slf-larning abiliy, his papr slcs wavl nural nwork algorihm as h horizonal lin prdicion algorihm, Th Morl mohr wavl funcion is chosn as h wavl nural nwork implici layr nuron quaion, 2-5 is h xprssion, h funcion has highr im domain and frquncy domain rsoluion[4-5]. 2 2-5 ϕ ( cos (1.75 /2 Th laral prdicion is o rain h wavl nural nwork by h ransvrs raining squnc x { xi i 1, 2,, Lx}. Firs, h daa is procssd and h raining squnc is mappd o h 975
inrval [-1,1] by h formula (2-6. xi ( vmax vmin * ( xi xmin / ( xmax xmin + vmin ( i 1, 2,, m 2-6 v 1 vmin 1 xmax max ( xi xmin min ( xi Thn, h numbr of nods in ach Whr max layr of wavl nural nwork is drmind and h numbr of nods in h inpu layr is N, h numbr of nods in h hiddn layr is H and h numbr of nods in h oupu layr is M, H is xprssd as: 2-7 H < N + M + a, a [,1] Th wighs of h wavl nural nwork and h cofficins of h wavl basis funcion ar consanly modifid according o h prdicion rror unil h raining numbr rachs h prs numbr of raining ims or h prdicion rror rachs h prs rror valu. Using h raind modl o prdic, for h currn im, givn wavl nural nwork inpu layr daa, 1,, M +1 } x' { xi i o obain h prdicd oupu +1. Vrical prdicion Vrical dimnsion random flucuaion componn is larg, long-rm rnd is singl, suiabl for using simpl linar prdicion algorihm.in his papr, h ARIMA algorihm is slcd as h longiudinal prdicion algorihm. Th prdicd valu of h ARIMA algorihm is slf-lancy variabl and random variabls linar combinaions.and i suiabl for non-saionary squncs,h algorihm is applid o non-saionary squncs mad d-ordr diffrnc o obaind and hn prdicd h saionary squnc.th mahmaical xprssion of h modl is: y ϕ1 y 1 + ϕ 2 y 2 +... + ϕ p y p + u q1u 1 q 2u 2... q qu q 2-8 ( ( Among hm ui i, 1,..., p is random im, ϕi i 1,2,...q is auorgrssiv cofficin, qi (i 1,2,...q is moving avrag cofficin, yi is yi squnc afr d-ordr diffrnc. yi squnc abl o g afr yi squnc mad d cumulaiv. Th longiudinal prdicion firs ss whhr h longiudinal daa squnc is a saionary im sris. If i is no o carry on h d-ordr diffrnc o g h smooh squnc again.thn mak sur ARIMI(p,d,q modl ordr p and q.in his papr, h common AIC cririon is usd o drmin h modl ordr.slc AIC(p,q smalls s of p, q is h ordr of h modl,h formula is: AIC ( p, q N ln (σ ε2 + 2 ( p + q + 1 2-9 Whr N is h lngh of h squnc, h rsidual of h modl. Finally, h unknown cofficins ar simad, and paramrs of ach squnc ar simad o drmin h auorgrssiv cofficins and h moving avrag cofficins. Th prdicd modl is usd o prdic h im sris. A h im and, h longiudinal squnc is inpu o h modl, and is diffrnc is obaind d ims, and h prdicd valu is calculad[6]. Two - dimnsional prdicion algorihm As shown in Figur 2-2, h horizonal and vrical dimnsions of hisorical daa ar acquird, and h ARIMA and wavl nural nwork algorihms ar raind wih h horizonal and vrical dimnsion daa rspcivly. Thn, h raffic daa a im is rad and h horizonal prdicion Algorihm and longiudinal prdicor ar usd o calcula h prdicion valus of h horizonal and vrical dimnsions a im + T rspcivly. Th final prdicion oupu is obaind by summaion of wighs w, and finally h wigh w is updad by h singl xponnial smoohing algorihm rurn. 976
+T Gs h hisorical daa for h vrical dimnsion Training ARIMA modl Gs h hisorical daa for h horizonal dimnsion Rad h ralim daa a im Training Wavl Nural Nwork Modl Calcula h vrical prdicd raffic a im + T w And oupus h prdicd valu a h im + T a h nd Calcula h laral prdicion raffic a im + T Up da wi gh w 1-w Figur 2-2 Two-dimnsional prdicion modl Th mahmaical xprssion of h singl xponnial smoohing algorihm is: α (1 α S α X + (1 α S 1 i i 2-1 Xi X is h valu of h im sris a im, is h prdicd valu of h im sris a im Whr + 1, and is h wigh cofficin. For larg flucuaing im sris, h valu is largr o incras h ffc of h mos rcn daa on h prdicd valu. For h rlaivly sabl im sris, h valu is smallr o rduc h influnc of h mos rcn daa on h prdicion rsuls. Dfin h prdicion rrors of h horizonal and vrical prdicion a h im, rspcivly x, y,h final prdicion rror is x ' v 2-11 x y ' v y 2-12 p p v 2-13 ' In formula v is h ru valu of h nwork raffic a h momn, x is h laral prdicion y' prdics h valu of h horizonal dimnsion a im, is h longiudinal prdicion prdics h {w ' w ' [,1] } is usd 2-1 prdicd valu a h momn in h longiudinal dimnsion, p h wigh cofficin of h prdicd im. is h final prdicd oupu.th xprssion is: p w ' x ' + (1 w ' y ' 2-14 To nsur ha h prformanc prdicion rror p of h wo-dimnsional prdicion algorihm mus m h following xprssion: p min ( x, y 2-15 Undr h prmis of h known v,find opimal valu of w mad p min, h xprssion as follow: p w x ' + (1 w y ' v 2-16 w x + (1 w y p ± ( w x + (1 w y, w [,1] w w1, and mad min,and saisfy h formula (2-15.whn x and y diffrn numbr, p min is,a his im: Obviously,whn x and y sam numbr, 977
y w y x x y 2-17 x y {wi i 1,2,...} o compl h prdicion w' +1 from h squnc, h complion of w Using h dynamic wigh upda: w ' +1 α (1 α i i 2-18 wi In h formula, h minimum α MSE valu is slcd as h cofficin. Simulaion and prformanc comparison In ordr o valida our proposd prdicion analysis mhod,w collcd from a crain lcric powr company cor rour raffic daa of 218 days,including daa sampling inrval for 5 min/ims,a oal of 288 raffic daa poins a day.slcion in his papr,h simulaion analysis of h coninuous flow daa of 22 days and 21 days will b dividd ino 22 days raffic daa of h hisorical daa and s daa,1 day ransvrs daa raining daa sampling inrval for 5 min,lngh of im for four days.longiudinal raining daa using h hisorical daa of 21 days,according o h im is dividd ino 288 groups, and h sam im diffrn da for a group,ach group ladr dgrs for h 21s. whn 14 o 17 scion laral prdicion urning poin in h curv in a rlaivly ral and simad valus lag phnomnon,and h longiudinal prdicion in his scion is rlaivly accura,figur 3-2 shows in his inrval wighs of lss han.5.a 17 o 19 inrval,whn h longiudinal prdicion accuracy is dcrasd obviously,and laral prdicion is capurd vry wll on h day of h rnd,combind wih figur 3 is shown in figur 3-2-1 and h simulaion rsuls confirmd h wighs of h dynamic upda sragy wll complmnary advanags of wo dimnsions. horizonal prdicion 2-5 - -3-2 -1 1 vrical prdicion 2 3 5 - -3-2 -1 1 wo dimnsion prdicion 2 3 5 - -3-2 -1 2 3 5 2-5 2-5 1 Figur 3-1 Prdicion rror disribuion Figur 3-1 for h ransvrs,longiudinal prdicion and wo-dimnsional prdicion rror disribuion,i can b sn ha h wo-dimnsional prdicion of small rror rang forcas prcision is high,whn h horizonal and vrical dimnsions of prdicd valu is grar han or lss han ru valu, h wigh w valus mak small prdicion rror of h dimnsions of 1.A on hour in horizonal and vrical prdicion w valu can mak a gnral prdicion rror is lss han any a dimnsion and approach o zro. 978
18 horizonal prdicion vrical prdicion wo dimnsion prdicion 16 1 12 1 8 6 2 Man Squard Error Squar Dviaion Figur 3-2 Prdic MSE and varianc comparison char Figur 3-2 MSE and varianc comparison show ha his papr proposd a wo-dimnsional prdicion algorihm in prdicion ffc is br han wo dimnsions sparaly prdic,a h sam im, bcaus his aricl upda wighs using singl xponnial smoohing algorihm, rror flucuaion is lss han a singl dimnsion.comprhnsiv h abov analysis may safly draw h conclusion, his papr proposd a wo-dimnsional prdicion algorihm by combining h advanag of wo dimnsions, ffcivly solvd h problm of h urning poin in h dlay, a h sam im improv h prdicion accuracy of h algorihm. Conclusion Basd on h sudy of h xising raffic prdicion modl of powr communicaion nwork, his papr proposs a nw mhod of powr communicaion nwork raffic prdicion basd on wo dimnsional prdicion algorihms. By making full us of hisorical daa, h hisorical daa can b xracd from h wo dimnsions of horizonal and vrical. Th laral dimnsion rflcs h rising and falling rnd of h forcas day, and nsurs h prdicion accuracy of h wo dimnsional prdicion algorihms a h non- urning poin. Th vrical dimnsion rflcs h posiion of h urning poin of h day, and h daily priodiciy of h flow is usd o improv h prdicion accuracy of h wo dimnsional prdicion algorihms a h urning poin. Two dimnsional flow prdicion mhod calcula h accuracy of laral prdicion and vrical prdicion by using singl xponnial smoohing algorihm. Th wo dimnsional flow prdicion mhod combins h advanags of h wo dimnsional prdicion modl, and improvs h prdicion accuracy of h urning poin whil nsurs h prdicion accuracy of h non- urning poin. Rfrnc [1] A. Kshavarz-Haddad and R. H. Ridi, Bounds on h bnfi of nwork coding for wirlss mulicas and unicas, IEEE Transacions on MobilCompuing, vol. 13, pp. 12-115, 214. [2] T.-h. Kim, H. Choi, and H.-S. Park, Cnraliy-basd nwork coding nod slcion mchanism for improving nwork hroughpu, in16h Inrnaional Confrnc on Advancd Communicaion Tchnology (ICACT, 214, pp. 864-867. [3] X. Fang, S. Misra, G. Xu, D. Yang, Smar grid h nw and improvdpowr grid, in IEEE Communicaions Survys and Tuorials, vol.14,pp.944-98, Dcmbr 212. [4] V. C. Gungor, D. Sahin, T. Kocak, S. Ergu, C. Bucclla, C. Ccai, al, Smar grid chnologis: communicaion chnologis and sandards, IEEE ransacions on Indusrial informaics, vol.7, pp.529-539, Spmbr211. [5] J. Wang, A procss lvl nwork raffic prdicion algorihm basd on ARIMA modl in smar subsaion, in IEEE Inrnaional Confrnc on Signal Procssing, Communicaion and 979
Compuing (ICSPCC, pp.1-5, Augus 213. [6] W. Jin, X. Yong jun, Prdicion of smar subsaions nwork raffic basd on improvd paricl swarm wavl nural nworks, IEEE Inrnaional Symposium on, pp.1-7, May 213. 98