Optimization and Application of initial Value of Non-equidistant New Information GM(1,1) Model

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1 IJCSI Inernionl Journl of Copuer Science Issues, Vol., Issue, No, Mrch 3 ISSN Prin: ISSN Online: Opiizion nd Applicion of iniil Vlue of Non-equidisn New Inforion GM, Model Youin LUO College of Mechnicl Engineering, Hunn Universiy of Ars nd Science, Chngde, 45, P.R.Chin Asrc Aiing he prole of deerining iniil vlue of nonequidisn new inforion GM, odel, reserching odeling echnis of non-equidisn new inforion GM, odel which ing he newes coponen of originl d s he iniil vlue of response funcion of grey differenil equion, he cuse of he prole ws found ou, new ehod for iniiing vlue of non-equidisn new inforion GM, odel ws proposed o iniize he qudric su of is fiing error nd he opiu forul of iniiing vlue ws deruded. he new non-equidisn new inforion GM, odel wih he proposed forul of iniiing vlues hs he chrcerisic of high precision s well s high dpiliy. Eples vlide he prciciliy nd reliiliy of he proposed odel. Keywords: Iniilizion, cground vlue, GM,,New inforion principle, Non- equidisn, Opiizion, Grey syse.. Inroducion Grey odel s n iporn pr in he grey syse heory hs een successfully used in ny fields. Aong he odels, GM, hs een grely concerned nd een widely used ecuse of he reserch chrcerisics such s he sll sple nd he poor inforion, s well s he dvnges which is siple nd prcicl [-6]. he ccurcy prole in odeling hs een he reserch focus in he grey syse heory field. Sequence spcing ws regrded s uliplier o eslish he non-equidisnce GM, odel which supposed h here is he liner relionship eween d difference nd ie difference [], u he resul fro his odel cn' e ensured o e consisen wih he reliy. Funcion rnsforion ehod ws doped o reduce he sndrd deviion coefficien o e he originl sequence s new d sequence nd esie he odel preers, nd hen GM, ws se up [3], u here is he copliced clculion. In order o iprove he ccurcy of he fiing nd he predic, he es clculion forul for cground vlue ws deduced using non-hoogeneous eponen funcion o fi one-ie ccuuled genering sequence nd non-equidisn GM, odel ws eslished [4]. cwrd ccuulion generion ws pu forwrd nd GOM, sed on cwrd ccuulion ws eslished [5]. GRM, sed on reciprocl generion ws uil fer proposing reciprocl generion [6]. GRM, ws iproved o eslish he iproved grey odel CGRM, sed on reciprocl generion wih eer odeling ccurcy [7]. u ecuse he firs coponen of he sequence is oo s iniil condiion of grey differenil equion in his odel, i is indeque for uilizing new inforion ccording o new inforion prioriy principle in he grey syse where here is ore cogniive funcion in new inforion hn in old one. Equidisn new inforion GM, odel regrded he nh coponen of he sequence s iniil condiion of grey differenil equion ws eslished [8,9], u he prole of deerining iniil vlue is negleced in he course of odeling. Mulivrile equidisn new inforion MGM, n odel ws uil, where he nh coponen of he sequence is regrded s iniil condiion of grey differenil equion nd he iniil vlue nd he coefficien of he cground vlue re opiized [, ]. Hoogeneous eponen funcion fiing one-ie ccuuled genering sequence ws used o eslish GM, wih he nh coponen of regrded s iniil condiion nd he opiizion iniil vlue [], u he clculion is ore copliced. In his pper, he ides iproving iniil vlue of equidisn GM, odel in [3] ws sored. Aiing he prole of deerining iniil vlue of non-equidisn new inforion GM, odel, he pper reserched odeling echnis of non-equidisn new inforion GM, odel nd found ou he cuse of his prole. On he view of iniizing he qudric su of fiing error of he odel, new ehod o oin he iniil vlue ˆ ws proposed nd he copuion forul oining he iniil vlue ˆ ws derived. A nonequidisn new inforion GM, odel wih high precision s well s high dpiliy ws eslished. Eples vlide he prciciliy nd reliiliy of he proposed odel. Copyrigh c 3 Inernionl Journl of Copuer Science Issues. All Righs Reserved.

2 IJCSI Inernionl Journl of Copuer Science Issues, Vol., Issue, No, Mrch 3 ISSN Prin: ISSN Online: Modeling of Non-equidisn New Inforion GM, Model Definiion : Supposed he sequence X [, L, ], if i i i cons where i, L,, X is clled s non-equidisn sequence. Definiion : Supposed he sequence X [,,, ], if L n nd where, L,, X is one-ie ccuuled generion of non-equidisn sequence X, nd i is denoed y -AG. Supposed he originl d sequence X [, L, ], where j j,, L is he oservion vlue j, is he d nuer, nd he sequence [,, L, ] is non-equidisn, h is, he spcing j is no consn. j Ae + C. Supposed h runs hrough, ], [, ] nd, ], i [ cn e oined s: ln [ + +, 3,4, L, A, 4 e e C Ae As he resul for of he lino differenil equion is: Ae + C, i is derived o oin s: ' ' Ae, nd hen + C. Supposed h z ', when, 3 is he cground vlue of In order o eslish he odel, firsly he originl d is ccuuled one ie o genere new sequence s: z + C 5 X [,, L, ] where, j j,, L, ees he condiions in he Definiion, h is, j j j j, L, Accouning o one-ie ccuuled generion, nonequidisn GM, odel is eslished s firs-order d grey differenil equion s: + ζ,where d ζ is he cground vlue. Is lino differenil equion is s: d d + As he resul for of he lino differenil equion is eponenil, cn e fied y he equion s When ', he lino differenil equion is discredied o ge he following for s: + z he ri is epressed s follows. L 3 4 z 3 z 4 L z 6 L Supposed 3 z 3 Y 4 z 4,, Φ L L L z Where, Φ is preer vecor o e idenified, nd re he consn o e idenified. he os les-squres esiion of Φ is: Copyrigh c 3 Inernionl Journl of Copuer Science Issues. All Righs Reserved.

3 IJCSI Inernionl Journl of Copuer Science Issues, Vol., Issue, No, Mrch 3 ISSN Prin: ISSN Online: Φ ˆ Y 7 According o he new inforion prioriy principle of he grey syse, fer ing full use of new inforion nd ing n iniil vlue of grey differenil equion is:, he ie response equion ˆ o, Eq.8 will e rnsfored ino Eq.. Considering he slles error of he overll d, he error squre su of he odel cn oin he iniu y using he les squre ehod h deerine he iniil condiions ˆ when he error of he les fiing d poins is no equl o zero. ˆ + e,, L, 8 ˆ + ˆ e,, L, ˆ In Eq.8, when. Afer resoring he fiing vlue of he originl d is: li Δ e e,3, L, ˆ he solue error of he fiing d: q 9 ˆ he relive error of he fiing d%: e ˆ * i he en of he relive error of he fiing d colun: f e i In non-equidisn GM, odel, he iniil vlue of he differenil equion is en s ˆ. he slles error of he iniil poin is zero, nd he odel preer ˆ [, ] nd he odel fiing vlue hve [3]. nohing wih he iniil vlue In non-equidisn new inforion odel, he iniil vlue is oo s ˆ. Afer odeling nd clculing, i is ˆ [, ] found h he odel preer nd he odel fiing vlue hve reled o he iniil vlue, u he error of he les poin is he slles. According o he selecion rules for he odel esiion equion fro he erology econoeric, his ehod is no he es [3]. If iproving iniil vlue While Eq.9 is rnsfored ino he following equion: li ˆ e e,3, L, ˆ Δ Supposed e e c, ˆ c ˆ ˆ cn lso e epressed s ˆ c ˆ, Δ li e e where c.considering he effec of copuer nuericl ccurcy i is generlly en s *,.., so he fiing vlue of he originl d is oined: ˆ ˆ c ˆ 3 If is nown, soe d such s he siulion vlue, he prediced vlue nd he error in non-equidisn new inforion GM, odel cn e oin y Eq.3, nd hen he odel is esed [,4,5]. 3. Opiizion of he Iniil Condiions in Non-equidisn New Inforion heore : In he sense of error squre su in nonequidisn new inforion GM, odel, he opil iniil condiion of his odel is: Copyrigh c 3 Inernionl Journl of Copuer Science Issues. All Righs Reserved.

4 IJCSI Inernionl Journl of Copuer Science Issues, Vol., Issue, No, Mrch 3 ISSN Prin: ISSN Online: where, c + c / c e c e ˆ 4,,3,, L, li e e, c Δ Proof: ecuse ˆ c ˆ,,3, L,, supposed s indices he error squre su of he odel, we cn oin he following equion: S [ ˆ ] [ c ˆ. ] Assued ds, we cn oin he iniu dˆ ˆ poin. his proof is copleed. ˆ is oined in he cse of he slles error squre su of he odel, so i is clled s he opil iniil condiions. 4. Eple P. G. Foleiss reserched h here is he influence of he eperure on figue srengh under he long life syery cycle of ny erils. le shows he eperienl d of he chnge relion of i lloy figue srengh long wih eperure, which is sequence of non-equidisn spcing. he d in [,3] were odeled y using he ehod proposed in his pper nd we oined he following resul:.94344, , ˆ e ˆ le Chnge relion of i lloy figue srengh long wih eperure Mp / C σ / C σ he fiing vlue of he originl d: ˆ [56.34, , , 56.55, , , 47.6, , ] he solue error of he fiing d: q [.34, -3.83,.6644,.445, , -.339,.66,.9363, 3.565] he relive error of he fiing d%: e [.4435, ,.497,.77979, -.644, ,.5566,.353,.8694] he en of he relive error of he fiing d is.43583%. Afer he originl d were pre-processed y using 5 nd σ 4 X in [], he 5 5 iu relive error is 4.86% nd he en relive error is 3.9%. he odel ws eslished y using he funcion rnsforion ehod in [3] nd he en relive error is.6587%. Hoogeneous eponen funcion fiing one-ie ccuuled genering sequence ws used in [5] nd i is.9765%. hus, he eple vlides he dpiliy nd he scienific of he proposed odel. he coinion forecs odel [6] cn e uil wih he proposed odel insed of rdiionl GM, odel nd he odel preers cn lso e found he opiu ehod [7-8]. 4. Conclusions Grey syse heory ws used nd he odeling echnis of non-equidisn new inforion GM, odel which ing he newes coponen of originl d s he iniil vlue of response funcion of grey differenil equion ws reserched. A new ehod for iniiing vlue ˆ ws proposed o iniize he qudric su of is fiing error nd he opiu forul of iniiing vlue ws deruded. Non-equidisn new inforion GM, odel ws eslished nd he MALA progr of his odel ws wrien. Copyrigh c 3 Inernionl Journl of Copuer Science Issues. All Righs Reserved.

5 IJCSI Inernionl Journl of Copuer Science Issues, Vol., Issue, No, Mrch 3 ISSN Prin: ISSN Online: he odel proposed in his pper hs he chrcerisic of high precision s well s high dpiliy. Eple vlides he correcness nd vlidiy of he proposed odel. here is iporn prcicl nd heoreicl significnce nd his odel should e widely used. Acnowledgens his reserch is suppored y he grn of he h Five- Yer Pln for he consruc progr of he ey discipline Mechnicl Design nd heory in Hunn provincexjf[76] nd Hunn Provincil Nurl Science Foundion of ChinNo:3EGC. References [] S. F. Liu, Y. G. Dng nd Z. G. Fng: Grey Syse heory nd Is Applicion Ediion 3. eijing:science Press,4. [] Y.X. Luo nd J.R. Zhou, "Non-equidisnce G, Model nd is Applicion in Figue Eperienl D Processing nd on-line Conrol ", Journl of Mechnicl Srengh, Vol. 8, No.3, 996, pp [3] Y.X. Luo, X. Wu nd M. Li, "he Funcion-rnsfer Mehod of Preers Esiion of Grey GM, Model nd I's Applicion ", Journl of Mechnicl Srengh, Vol. 4, No.3,,pp [4] Y.M. Wng, Y.G. Dng nd Z.X. Wng, "he Opiizion of cground Vlue in Non- Equidisn GM, Model", Chinese Journl of Mngeen Science, Vol. 6, No.4, 8,pp [5] Z.M. Song nd J.L. Deng, " he Accuuled Genering Operion in Opposie Direcion nd Is Use in Grey Model GOM,", Syses Engineering, Vol. 9, No.,,pp [6].H. Yng nd Z.Q. Zhng, "he Grey odel Accuuled Genering Operion in reciprocl nuer nd is pplicion", Mheics in Prcice nd heory, Vol. 33, No.,3, pp. -5. [7] X.HE, W.F. LIU, "Iproveen of Grey CRM, Model nd is Applicion, Journl of Souhern Yngze Universiy: Nurl Science Ediion, Vol., No.3,,pp [8] Y.M. Wng, Y.G. Dng, Z.X. Wng, he Opiizion of cground Vlue in Non-Equidisn GM, Model, Chinese Journl of Mngeen Science, vol. 6, no. 4, pp.59-6, 8. [9] Y.G. Dng, S.F. Liu nd K.J. Chen, "he GM odels h n e en s iniil vlue", Kyernees, Vol. 33, No., 4,pp [] Y. X. Luo, W. Y. Xio, New Inforion Grey Mulivrile Opiizing Model NMGM,n,q,r for he Relionship of Cos nd Vriiliy, In Proceedings of 9 Inernionl Conference on Inelligen Copuion echnology nd Auoion ICICA 9, pp. -3, O coer-, 9. [] Y. X. Luo, Z. M. He, he new Non-equidisn Opiu GM, of Line-Drwing D Processing in Copuer Aided Design, In Proceedings of 9 4h Inernionl Conference on Copuer Science & Educion ICCSE9, pp , 9. [] Y.X. Luo nd X.Y. Che, " he Non-equidisn Opiu GM, wih Modified nh Coponen e en s Iniil Vlue nd is Applicion o Mel Cuing ", 9 Asi- Pcific Conference on Inforion Processing APCIP 9, 9, pp [3] Z.. WANG,X.PENG nd X. DAI, " Iproveen nd Applicion of Gry Forecsing Model sed on IniiVlue Modificion", Journl Of Chongqing Insiue of echnology Nurl Science Ediion, Vol., No., 7, pp [4] Y.X. Luo, L.. Zhng nd M. Li, Grey Syse heory nd Is Applicion o Mechnicl Engineering, ChngSh: Nionl Universiy of Defense echnology Press,. [5] Q.Y. Wng, Y.M. Cui, X.H. Zho e l., Unceriny heicl odel of forecs & decision-ing. eijing: Mellurgicl indusry Press,. [6] K. Zho,L. Gn, H. Wng, A.H.Ye, "Applicion of Coinion Forecs Model in he Mediu nd Long er Power Lod Forecs", IJCSI Inernionl Journl of Copuer Science Issues, Vol. 9, Issue 5, No 3,,pp.4-8. [7] M. A. Shohl, A. A. El-swy, M. Nofl nd S. F. El-Zoghdy, "Using Hyrid Pricle Swr Opiizion o solve Mchine ie Scheduling Prole wih Rndo Sring ie", IJCSI Inernionl Journl of Copuer Science Issues, Vol. 9, Issue 5, No 3,,pp [8] Hifz Afq nd Snjy Sini, "On he Soluions o he rveling Slesn Prole using Nure Inspired Copuing echniques", IJCSI Inernionl Journl of Copuer Science Issues, Vol. 8, Issue 4, No,,pp Youin LUO received he.s nd M.S. degrees in Mechnicl Design & Mnufcuring, Meril Engineering fro Chongqing Universiy, HUAZHONG Universiy of Science nd echnology, Chin, in 988, 3 respecively. Since 4, he hs een professor College of Mechnicl Engineering, Hunn Universiy of Ars nd Science, Chngde, P.R. Chin. His curren ineress re inforion science, grey syse, echnics, nd opiizing. Copyrigh c 3 Inernionl Journl of Copuer Science Issues. All Righs Reserved.

2k 1. . And when n is odd number, ) The conclusion is when n is even number, an. ( 1) ( 2 1) ( k 0,1,2 L )

2k 1. . And when n is odd number, ) The conclusion is when n is even number, an. ( 1) ( 2 1) ( k 0,1,2 L ) Scholrs Journl of Engineering d Technology SJET) Sch. J. Eng. Tech., ; A):8-6 Scholrs Acdemic d Scienific Publisher An Inernionl Publisher for Acdemic d Scienific Resources) www.sspublisher.com ISSN -X