Journal of Chemical and Pharmaceutical Research, 2014, 6(7): Research Article

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1 Avalable ole Joural of Chemcal ad Pharmaceutcal Research, 04, 6(7):4-47 Research Artcle ISSN : CODEN(USA) : JCPRC5 Predcto of CNG automoble owershp by usg the combed model Ku Huag, You Lv*, Cheg Huag, Yja Wag, Ygq Nu ad Wetg Yag School of Petroleum Egeerg, Southwest Petroleum Uversty, Chegdu, Cha ABSTRACT I order to accurately predct the owershp of CNG automoble, Grey System Theory G odel ad Elastc Coeffcet ethod were vestgated to ad compared terms of ther predcto errors.. A ew Combed odel was establshed based o the Weght Factor, whch s calculated by usg Suboptmal Combato ethod ad the Lear Combato odel. Compared to the Sgle odel, the predcto accuracy of the ew Combed odel s greatly mproved whe t was appled to predct the CNG automoble owershp S provce ad the errors acheved are o more tha 0% tha before Thus the study demostrated that the ew Combed odel was effectve ad practcal ts applcato o the ratoal layout of the gas statos. Key words: grey theory; elastc coeffcet method; combed model; CNG automoble INTRODUCTION I recet years, wth the crease of the vehcle populato Cha, a large amout of automoble exhaust has bee dschargg whch leads to the serous atmosphere polluto. The developmet of compressed atural gas (CNG) automoble s the mportat way to solve the problem. Compressed atural gas automoble has advatages of safety ad evrometal fredless. After years of developmet, the techologes of CNG automoble ad gas stato have become creasgly mature, but the theory of the layout of the CNG statos s stll the explorato, t brgs adverse effect to the developmet of CNG automoble dustry our ato. Takg Schua provce as a example, durg the Eleveth Fve-Year perod, the umber of CNG stato oly creased by 57 whch s far less tha that of CNG automobles []. The shortage of gas stato ot oly poses a obstacle to the CNG vehcles refuelg, but also has a ufavorable mpact o the developmet of CNG automoble dustry. We should focus o the study of the reasoable layout of gas stato so as to effectvely promote the use of atural gas resource, the predcto of CNG automoble populato s a prerequste for the plag of CNG statos. Accordg to that predcto, the more precse projecto of the eeds of gas stato ca be made to keep the balace betwee developmets of both gas stato ad CNG automoble ad avod overbuldg ad defcet buldg as well. EXPERIENTAL SECTION The combed model There are may predcto methods, some of them are used commoly may felds, cludg: grey theory G (, ) model, regresso aalyss, elastcty coeffcet method ad etc. Amog those theores, the grey theory model whch requres a small sample sze, has bee used wdely data forecast, such as predcto of cdece, electrcty demad forecastg ad traffc volume forecast. But the predcto accuracy s acceptable oly whe the sample data coform to the dex uder the codto of creasg ad decreasg, t s dfferet from the actual stuato of the growth of the atural gas car owershp, Secodly ecoomc developmet s a mportat factor for the developmet of CNG car owershp, the grey theory model ca't establsh drect cotact betwee CNG automoble owershp ad the speed of ecoomc developmet. Elastc coeffcet method ca dcate the relatoshp betwee the ecoomy 4

2 You Lv et al J. Chem. Pharm. Res., 04, 6(7):4-47 ad predcto result. Although elastc coeffcet method has bee appled may felds, t ca't reflect the mpact of other factors ad the predcto accuracy s ot hgh. Combed model ca tegrate the advatages of sgle models, t mproves the predcto precso. We predcted the CNG automoble owershp through adoptg ler combato model to establsh ew model o the bass of those two methods. The grey system G (, ) model The "Grey" the grey forecastg method meas complete formato. grey predcto method s establshed based o the ucertaty of formato, the establshmet of the grey predcto model does ot requre lots of sample data, so the applcato rage s very wde []. The G (, ) model s used usually, Here s how t s costructed: X Assumg a tme seres have observatos: X = X (), X (), L, X ( ) { } We ca get a ew seres through accumulato: = k () X ( k) X ( k) X () t= () () () = { X ( ), X ( ), L, X ( }) The correspodg dfferetal equato of grey G model s: () dx () + α X = µ dt () () (3) (4) α developg gray scale; µ The edogeous cotrol gray scale αˆ s estmated parameter vector, we ca got t by the least square method: T T [ ] ( ) T, B B B y ˆ α = α µ = y y = s a colum vector, [ X (), X (3), L, X ( ) ] T - B = - - () () [ X () + X ()] () () [ X () + X (3)] () () [ X ( ) + X ( ) ] Solve the dfferetal equato, got the G(,) predct model: µ µ α k X ˆ () (0 ( k + ) = X ) () + α e α ( k = 0,,, L, -) Restored the model to get: () () x ( k + ) = x ( k + ) x ( k) x ( k + ) s the predct result of CNG automoble owershp. (5) (6) (7) (8) Elastc coeffcet method CNG automoble owershp ad ecoomc developmet have close relatos, Wth the developmet of ecoomy, the CNG automoble owershp s creasg. ecoomc developmet s characterzed by GDP. Elastc coeffcet s the 43

3 You Lv et al J. Chem. Pharm. Res., 04, 6(7):4-47 key of elastc coeffcet method [3, 4], Elastc coeffcet s the rato of CNG automoble owershp rate ad GDP aual growth rate. Elastc coeffcet e ca be calculated by the formula below: e β = α (9) β s the aual growth rate of CNG automoble, α s the aual growth rate of GDP, usually we get the Average value as sample data. To predct model s: ( ) t = t 0 + e α 0 s the predct result of CNG automoble owershp, 0 s the CNG automoble owershp base year, e s t Elastc coeffcet, α s predcted aual growth rate of GDP, t s the predcted year, 0 s base year. The ew combed model Bates ad Grager combato forecast theory put forward for the frst tme the 960s [5-7], a combed model ca mprove the predcto accuracy, t has bee wdely studed ad appled. Accordg to the fucto relatoshp betwee combato predcto ad sgle predcto, t ca be dvded to lear combato model ad the olear combato model, the lear combato model s more sutable for the applcato. Lear combato descrbed as: m = = f ( t) w f ( t) f(t) As the combato model predcto, the scope of w s 0 to,ad the sum s. f ( t) () s the frst I forecast model t tme, w s the weght of the model, Got the weght factor The key of combed method s determg the weght, there are two methods to determe the weght :optmal combato method ad the suboptmal combato method, the calculatg process of optmal combato method s relatvely complex, the suboptmal combato method s smple, ad the predcto accuracy of the two methods are almost same[8], the suboptmal combato method s more coveet. The optmal combato weghts calculato formula s: = ( xt µ ) m = = = () (3) w = m (4) s the stadard devato of the error of model, s the sum of the stadard devato of the error of models, w s the weght of model. 44

4 You Lv et al J. Chem. Pharm. Res., 04, 6(7):4-47 RESULTS AND DISCUSSION Examples of applcato Predct the CNG automoble owershp S provce by The grey system model, the elastc coeffcet model ad the ew combato model.select the CNG automoble owershp the S provce from 003 to 007 as samples. The CNG automoble owershp ad ecoomc developmets the S provce from 003 to 007 such as table : Table S provce CNG car owershp ad ecoomc developmet tme GDP(0 8 Yua) GDP growth CNG automoble Growth rate of CNG (Aual %) populato(0 4 ) automoble (aual %) average Grey system method Frst, We used sample from table to make the orgal tme seres () traslated t to a ew tme seres { 4.7,0.6,5.85, 4.43,37.4} B = y = We got ˆ [ 5.55,5.95,8.58,.98] T α = [ 0.335,.338] T ˆ () 0.335k ( ).74e { 4.7,5.55,5.95,8.58,.98 } X =, X = establshed matrx B ad y : by ATLAB ad establshed the model: X k + = ( k = 0,,, L, ) X k X k X k () () = ( + ) = ( + ) ( ) s the predcted result of CNG automoble owershp by grey system method Accordg to the model, we got the predcted result of S provce CNG automoble owershp from 008 to 0 by grey system method as show table : Table The predcted results of the grey system model tme The predct result(0 4 ) Actual value(0 4 ) error -3.8% 7.5% 46.39% 49.6% As table, the frst year the result s very accurate, the error s wth 5%, but the secod year, t s close to 0%, wth the passage of tme, error s bgger ad bgger, the grey system model s ot sutable for medum ad log term predcto of CNG automoble. Elastc coeffcet method Got the elastc coeffcet from the sample the table: 7.83% e = β.4 α = 3.0% = 45

5 You Lv et al J. Chem. Pharm. Res., 04, 6(7):4-47 β s average aual growth rate of CNG automoble owershp of the sample,α s average aual growth rate of GDP of the sample. We got the elastc coeffcet e Set 007 as base year, accordg to data released form the govermet of S provce 007, the growth rate of expected GDP s 9%, establshed the ew combed model: 007 =.98 (.96) t (t=008, 009 ) s the predct result of CNG automoble owershp by elastc coeffcet method To research the relatoshp betwee the growth rate of expected GDP ad the accuracy of the predcted result, we * establshed aother model by usg a more accurate the growth rate of expected GDP, the value s 3%: * 007 =.98 (.78) t (t=008, 009 ) The predcted result of S provce CNG automoble owershp from 008 to 0 by elastc coeffcet method as show table 3: Table 3 The predcted results of elastc coeffcet method model tme The predct result whe the growth rate of expected GDP s 9%(0 4 ) The predct result whe the growth rate of expected GDP s 3%(0 4 ) Actual value(0 4 ) Error (GDP9%) -3.03% -0.39%.6% 6.37% Error (GDP3%) -6.8%.96% 7.58% 0.35% We could see that the error of elastc coeffcet method s smaller tha the error of the grey system method log-tme predcto from table 3.usually the error of elastc coeffcet method s less tha 5%,f we ca mprove the accuracy of the growth rate of expected GDP, the error wll less tha 0%. the error of elastc coeffcet method become bgger as the predcted tme become loger The predcted result of combed model Got the weght factor by suboptmal combed forecastg method Stadard devato of grey system model =.94 Stadard devato of elastc coeffcet method =3.49 The weghtg factor of grey system model: The weghtg factor of elastc coeffcet method: w 0.38 m w = = 0.6 m = = New combed model: 3 = s the predct result of grey theory model; s predct result of elastc coeffcet method. 3 s the predct result of ew combed model. The predct result of S provce CNG automoble owershp from 008 to 0by ew combed model as show Table 4 (the growth rate of expected GDP s 9%): Table 4 The predcto results of combed model tme The predct result(04) Actual value(04) error -9.49% 0.4% 9.80% 8.69% 46

6 You Lv et al J. Chem. Pharm. Res., 04, 6(7):4-47 CONCLUSION ()Although grey system model ca be used coveetly, t does ot apply to the predcto of CNG automoble owershp, especally for medum ad log-term predcto. The loger tme we predcted, the more errors we wll get. It just has certa accuracy whe t s used short-term forecast such as - years. ()Elastc coeffcet method ca accurately reflect the relatoshp betwee the ecoomy developmet ad CNG automoble owershp, f ecoomy developmet tred ca be predcted accurately, t wll mprove the predcto accuracy greatly, especally short-term predcto. (3)Based o the predcted results of combed model, we kow the ew combed model ca sythesze the advatages of the sgle model, mprove the predcto accuracy, Ad the ew combed model does ot eed a qute bg sample sze, so that the ew model ca be used smply ad easly. (4)We should cotrol the predcto tme a small rage as far as possble the accuracy s bad log predcto tme, ad we suggest that t s advsable to predct tme wth fve years. Ackowledgmet Ths research s supported by PetroCha Schua arketg Compay. Ad specal ackowledgemet should be gve to the Project-Research o Plag of CNG automoble from Southwest Petroleum Uversty. REFERENCES []ZX Lao., Tech&market.,03,0(05), []WS Ta.,Comm Std.,007,04(6),5-7. [3]JP Xue;LI Zhag., Shax Archt.,03,05(39),99-0. [4]XS Lu;R la.,j XZTU.,009,5(05), [5]Y Wag, J XU(Nat Sc).,998,37(l),6-0. [6]JC Y;ZB Lu.,Nat Gas Id.,004,4(), [7]JC Y;Z Yua;K Ce.,Ol gas storage ad trasp.,004,4,7-0 [8]GQ Xog;HL Lu.,Stats ad Decso.,007,03(05),-. 47

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,