Computer Life (CPL) ISSN: Research on IOWHA Operator Based on Vector Angle Cosine

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1 Copuer Lfe (CPL) ISS: Delverg Qualy Scece o he World Research o IOWHA Operaor Based o Vecor Agle Cose Megg Xao a, Cheg L b Shagha Uversy of Egeerg Scece, Shagha 0160, Cha a x @163.co, b lcheg@sues.edu.c Absrac: Based o he bass of he IOWHA operaor cocep ad he predco aalyss ehod of varous derved fors, a cobed predco aalyss ehod based o he vecor agle cose s proposed. Frs, he predco aalyss odel of sgle e s cosruced, ad he aual passeger volue of Cha cvl avao rasporao s carred ou by he ulple regresso aalyss odel ad he e seres ARIMA odel. O he bass of sgle e, a ew cobed forecasg aalyss odel based o IOWHA operaor s se up, ad he exac aheacal prograg ehod s gve o deere he wegh ad he o aalyze ad predc. The aalyss of he predced daa proves ha he cobao forecasg ehod ca effecvely prove he predco accuracy ad reduce he rsk of predco. Keywords: cvl avao passeger raffc volue, cobao forecas, IOWHA Operaor, accuracy aalyss, vecor agle cose. 1. COMBIATIO FORECASTIG MODEL OF IOWHA OPERATOR BASED O VECTOR COSIE u a u a u a s wo-desoal arrays, ake If,,,,,, 1, 1,,,,, g u a u a u a 1 w a w 1 udex() called he duced ordered weghed haroc ea operaor geeraed by he fuco u1, u,, u, ha s, he IOWHA operaor, ad he subscrp of he large uber of 1 u s called he duced value of w ( w, w,, w ) s a weghed vecor relaed o g w, whch sasfes a. I s g as, u dex ()s u1, u,, u order fro large o sall, ad w 1, w 0, 1,,,. Aog he, he IOWHA operaor s a orderly weghed haroc average of he uber of a1, a,, a he correspodg order of he duced value u1, u,, u, whch s ordered fro large o sall. The wegh coeffce of he sze ad poso of he uber a. If you reeberx, 1,,, w s relaed o he poso of he duced value, bu s depede for he acual value sequece, x for he frs predcve ehod he predced value (or fg value) of he oe, 1,,,, 1,,,, l 1, l,, l, he 1 3

2 Volue 6 Issue 018 weghg coeffce of sgle forecasg cobao forecasg. Sasfed 1 l 1, l 0, 1,,,. Ad ake x x x x 1, whe 1 x x aj 1,,,, 1,,, x x 0, whe 1 x predco ehod a. Obvously a 0,1 ducee value of he predced value j he predco accuracy of he, we regard he predco precso x, so ha he predco accuracy of he a j as he sgle predco ehod a he e ad s correspodg predco value he saple erval a x a x a x. Order: cosue he wo-desoal array,,,,,, xˆ x g a1, x1, a, x,, a, x. 1 adex( ) xˆ s called he cobed predco value of he IOWHA operaor geeraed by he predco accuracy sequece a1, a,, a, where a dex ( )s he Le X 1 X,,, x1 x x 1,,, x 1 x x ˆ 1 1,,,, X,,, xˆ ˆ 1 x xˆ x x 's large predco accuracy subscrp. 1 1 x x x xˆ 1 1 s called he 1 1 x xˆ represe he logarhc vecor of he acual value of he predced objec, represes he predced logarhc vecor of he, 1,,, predco ehod, ad represes he cobed predco logarhc vecor. Se up s sgle predco ehod, he predced value logarhc vecor X ad he agle cose of he logarhc vecor X of he acual value of he predced objec, ad he s he IOWHA operaor cobed wh he logarhc vecor ˆX of he IOWHA operaor ad he agle cose of he logarhc vecor X of he acual value. 33

3 Volue 6 Issue 018 Make Ej,, j 1,,,, he x x 1 adex adex j arx j E E s he cobed predco forao arx based o he IOWHA operaor of vecor cose, ad 1 1 l l l l l E L EL ˆ Therefore, j j j 1 x x 1 j x x 1 j1 adex adex adex j he IOWHA operaor cobao predco odel based o he vecor agle cose ca be expressed as follows: ax l, l,, l 1 l 1 s. 1 l 0, 1,,, l x xadex 1 L EL 1 x Ths odel s a olear prograg odel ha ca be solved usg he correspodg aheacal ools (MATLAB or LIGO).. BASED O IOWHA OPERATOR COMBIATIO FORECAST MODEL PREDICTS CIVIL AVIATIO PASSEGER TRAFFIC.1 Sgle regresso aalyss ad predco Regresso aalyss ad forecasg s a predco ehod ha predcs he fuure perforace of he forecased objec by aalyzg he red of pheoea ha are relaed o he forecased objec, sarg fro he relaoshp bewee varous ecooc pheoea. Whe we geerally use he regresso aalyss odel o ake predcos, s ecessary o clearly ad accuraely aalyze he exsece of he relaoshp bewee he wo varables, ad he selec he a facors ha affec he resuls as he correspodg depede varables are also very ecessary. The a facors ha eed o be cosdered he regresso odel for ar passeger raffc forecas clude regular flgh roue leage, uber of boud ourss, gross aoal coe, gross doesc produc, ad ralway passeger raffc. Regresso predco ca geerally oba good forecasg accuracy ad predco resuls uder he codo of a large aou of daa ad s rchess. A he sae e, ca also aalyze he pac facors ha have a large dead for raspor volue. Through he colleco of daa (he daa s based o he 016 Cha Sascal Yearbook), a ulple regresso odel was cosruced o frs se he cvl avao passeger volue as a varable y, regular flgh le leage as depede varable x 1, he uber of boud ourss s se x, GI s se o x 3, GDP s se o x 4, Ralway passeger volue s se o x 5. 34

4 years x1 Volue 6 Issue 018 Table 1 Daa for x x3 x4 x5 y Regular flgh roue leage (10,000 kloeers) uber of boud ourss (10,000) aoal coe (100 llo yua) Gross doesc produc (100 llo yua) Ralway passeger raffc (10,000 people) Cvl avao passeger raffc (e housad people) I order o ehace he fg effec of he orgal daa, he grey syse heory ca be used o perfor a cuulave accuulao of he orgal daa o geerae a operaor, ad he o pass hrough a accuulaed varable operaor afer a sgle accuulao x, x, x, x, x, ad depede varable Esablsh a ulvarae lear regresso aalyss odel ad use he copuer o oba he releva regresso coeffces of he equaos o oba he ulple regresso equaos: y 8.74x 0.38x 0.006x 0.033x y 35

5 Volue 6 Issue 018. Idvdual Te Seres Aalyss The ARIMA odel s called he auoregressve ovg average odel, whch ARIMA(p, d, q) s called dffereal auoregressve ovg average odel, AR s auoregressve, p s auoregressve; MA s ovg average, q s ovg average uber of ers d s he uber of es he e seres has bee ade o be sable. ARIMA(p, d, q) s called a auoregressve ovg average odel. There are hree basc ypes: auoregressve (AR) odel, ovg average (MA) odel, ad auoregressve ovg average (ARMA) odel. AR(p) odel: porder auoregressve odel ha sasfes he followg equao: y y y y e p p MA(q) odel: Geerally relaed o he q-order ovg average odel, he followg equao s sasfed: y e e e e q q The ARMA(p,q) odel cobes AR(p) ad MA(q) ad he derves a geeral auoregressve ovg average equao ARMA(p,q): y y y y e e e e p p q q Table shows he sascs of he ARIMA odel cosruced ad esed. As you ca see fro he able, he las opo s ARIMA ( 1,,. 11) The odel s o ake he logarh ad he he dfferece frs for he daa ad perfor a soohg process. The dfferece s 1 ad he level s sable. R The square s R For 0.998, he oralzed BIC s , dcag a good f. Table Model Sascs Model sascs odel Passeger raffc - odel_1 Model ype ARIMA(1,1,1) Sooh R-squared R squared Sadardzed BIC sascal daa DF 16 Sgfca Oulers 0.3 Based o Vecor Agle Cose IOWHAOperaor cobao forecas Accordg o he resuls obaed by he sgle predco, he wo-desoal array fored by he predco accuracy a he -h e ad s correspodg predco value he saple erval a, y, a, y, 1,,,19, he he IOWHA cobed predco value s calculaed as follows: 1 l1 l xˆ

6 Volue 6 Issue l1 l xˆ l1 l xˆ l1 l xˆ l1 l xˆ We use Malab's opzao oolbox o perfor a soluo o cosraed olear prograg by frs creag a fu. arge-ype fuco fle, he cosrucg a o-learzed fle ha cosras olearcodo., ad he eerg he correspodg he opool oolbox. Paraeers, ca be solved based o vecor agle cose cobao forecasg odel s as follows: l 1 1, l 0. IOWHA. The soluo of he operaor I order o reflec he adequacy ad effecveess of he cobao predco odel based o vecor agle cose proposed hs paper, accordg o he geeral evaluao ad aalyss crera of he predco effec, he followg dcaors are usually seleced as evaluao paraeers. SSE, MSE, MAE, MAPE wh MSPE As evaluao paraeers, he calculao resuls are show Table 3. Table 3 Regresso predco, e seres predco ad IOWHACobao forecasg effec coparso Forecas effec evaluao dex Regresso predco Sgle forecas Te seres forecas Cobao forecas SSE MSE MAE MAPE MSPE By coparso, s o dffcul o fd ha he evaluao dex paraeers of he cobed predco resuls based o he vecor agle cose are lower ha hose of he dvdual predco paraeers, whch dcaes ha he cobao predco has beer predco resuls ad he accuracy of he predco ore acurrae. I shows ha s effecve ad reasoable o adop a cobao forecasg ehod for cvl avao passeger raffc. The eprcal resuls show ha he average absolue perceage error bewee he predced value ad he acual value obaed by he regresso predco aalyss odel s.3%. For he e seres ehod, he average absolue perceage error bewee he predced value ad he acual value predced by he ARIMA odel s 3.0%, ad he regresso predco odel s already opzed afer usg he grey syse heory o accuulae he orgal daa oce o geerae he operaor. The odel, ad usg he opzed cobao odel provded by hs paper wll show a hgher 37

7 Volue 6 Issue 018 predco accuracy wh a accuracy of.1%. I cofrs ha he cobed forecasg odel afer opzao s effecve ad reasoable, ad ca be played Reduce he role of forecasg rsk. REFERECES [1] Lu Hoge, Lu Japg.The forecas of ourss source of Lusha red ours araco based o grey odel [J].Ecooc Geography,010,30(6):1050. [] JEOG HEO-YEOG,KIMSEOG-CHU.Forcasg of eraoal ar raspor dead of souh rego o cosder behavor of access[j].korea Socey of Cvl Egeeers,004,4: [3] Ba Yag, L Wehog. Forecas of Ieraoal Ar Fregh Volue Cha [J]. Sascs ad Decso, 006(3): [4] Che Huayou, Lu Chul, Sheg Zhaoju. IOWHA Operaors ad Ther Applcao Cobao Forecasg [J]. Chese Joural of Maagee Scece, 004, (05): [5] L Sog, L Yu, Wag Lu. Iproved IOWHA operaor cobao predco odel [J]. Copuer Egeerg ad Applcaos, 015, (03): [6] Gaxua Ga, Duau Jgshu, Gao Jaguo, Zhao Lufeg. Accde Te Seres Predco of Avao Equpe Based o ARIMA Model[J]. Cha Safey Scece Joural, 01, (03): [7] Ma Jayu, Ha Zhaozhou. Research o coplex seasoal e seres odel[j]. Sascs ad Decso, 017,(06):