Traffic Demand Forecasting for EGCS with Grey Theory Based Multi- Model Method

Transcription

1 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): Traffc Deand Forecastng for EGCS wth Grey Theory Based Mult- Model Method Zhenshan Yang, Yunl Zhang College of Engneerng, Boha Unversty Jnzhou, 3, Chna Center of Coputer & Network, Laonng Medcal Unversty Jnzhou,, Chna Abstract Elevator traffc deand forecastng s the essental prerequste for effectvely pleentng elevator group control syste (EGCS). Consderng that there exsts lots of abnoal nforaton n elevator traffc caused by subjectvty and occasonalty n huan behavour and that observng traffc nforaton contnuously s costly and dffcult, an proved grey forecastng based ethod usng ult-odel to forecast future elevator traffc deand of EGCS s proposed, the abnoal nforaton whch refers to outlers s processed, based on whch a soothng technque on orgnal traffc data s conducted to transfor the raw data nto an ncreasng sequence, to further reduce the randoness of the observed traffc data and to ake full use of regularty nforaton. The proposed ethod not only avod the theorrtcal error of grey odel per se, but also proved the forecastng accuracy, whch s sutable for short perod forecastng for elevator traffc deand. Sulaton experents show the valdty of the proposed ethod. Keywords: Elevator Traffc Deand Forecastng, Elevator Group Control Syste (EGCS), Grey Model (GM), Abnoral Inforaton, Mult-Model Forecastng, Soothng Processng.. Introducton The ncreasng perfecton of the functon of odern hghrse buldngs akes the elevator vertcal transportaton becoe ore and ore coplcated. Elevator traffc deand forecastng deals anly wth the traffc condtons, evaluatng the future traffc deand on realte observed traffc data. Elevator traffc deand forecastng s the essental prerequste for elevator traffc pattern recognton, selectng control strategy to effectvely pleentat EGCS []-[5]. Many studes have been done regardng the elevator traffc deand forecastng related probles based on, such as, neural network, exponental soothng, fuzzy logc theory and so on, and sgnfcant progress has been ade [6]-[9], but the proble to deal wth both the abnoral traffc data accordng to the specfed forecastng odel and the the lted nuber of saples and the ncoplete or nsuffcent nforaton, has not been taken serously. Therefore, the characterstcs of elevator traffc deand ake the applcatons of those ethods not be effectvely appled n soe practcal cases, and the satsfactory forecastng accuracy s hard to obtan. So, to develop effectve forecastng ethod s of the utost portance. In ths thess, an proved grey predcton based ethod usng ult-odel to forecast the future elevator traffc deand of EGCS s proposed based on the followng reasons.. Elevator Traffc Deand Possesses Obvous Grey Characterstcs For the elevator traffc syste wth EGCS, the passenger arrval process s a stochastc process [], and the theory of grey syste holds that any stochastc process s the grey varables changng n a certan apltude range for a certan perod of te []. The traffc flow of EGCS n the sae te perod of dfferent workng day ay fluctuate dfferently to soe extent, but stable n a long ter. Snce obtanng the observed traffc data s costly and dffcult as stated above, t s usually requre that the traffc deand be forecasted based on less saple data, whch provde opportuntes for eployng grey forecastng ethod.. The Essence of Grey Forecastng Grey theory focuses on uncertan syste wth lted nuber of saples and aount of nforaton, the valuable nforaton s extracted by generatng and developpng operaton on part of the known nforaton to realze the correct understandng and effectvely forecastng of the syste operatng regularty []. It can be sply stated that the developent regularty of objects whch contan ncoplete nforaton s forecasted based on the prncple of grey syste analyss. The core of Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

2 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): whch s Accuulatng Generaton Generators (AGO) whose a s to ncrease the sgnfcance of syste operatng regularty by reducng the randocty of the observed traffc saples, ts forecastng technque s to set up grey forcastng ode extendng fro the past to the future on the bass of the past known or present unknown nforaton eployng sall saples. The reander of ths thess s organzed as follows. In Secton, Probles descrpton and odellng s dscussed. In Secton 3, the applcaton of the proposed ethod to elevator traffc deand forecastng for EGCS s dscussed n detal. In Secton 4, sulaton experents and analyss are presented. And conclusons are drawn n Secton 5.. Probles Descrpton and Modellng. Descrpton of Elevator Traffc Flow The operaton of EGCS s essentally to transport a certan aount of passengers n the buldng fro ther orgnal floors to the ultate destnaton floors n a tely anner. Traffc flow whch ndcates the traffc status of EGCS s expressed by the nuber of passengers, the perod of passengers appearng, as well as the postons of passengers. It can be descrbed by several knds of data [3], but only part of the data whch reflect the traffc characterstcs nsde the buldng are used n traffc analyss, whch are the nuber of passengers enterng and leavng the an ternal n specfed te ntervals, the total nuber of passengers wthn the buldng and the nterfloor traffc condtons, etc. Accordng to the characterstcs of elevator traffc, the traffc flow s classfed nto four dfferent traffc patterns: uppeak traffc; downpeak traffc; rando nterfloor traffc and lunch te traffc [, 3]. The uppeak traffc pattern arses when all passengers are ovng up fro the an ternal floor, t occurs n consderable strength n the ornng when prospectve elevator passengers enter a buldng ntent on travellng to destnatons on the upper floors of the buldng. The downpeak traffc stuaton s observed when the donant or only traffc flow s n a downward drecton wth all, or the ajorty of, passengers leavng the elevator syste at the an ternal of the buldng. The rando nterfloor traffc s a characterzaton n whch passengers are ovng equally lkely between floors, t exsts for the ajorty of the workng day n offce buldngs. Lunch te traffc occurs n the ddle of the day and exhbts a donant traffc flow to and fro one or ore specfc floors, one of whch ay be the an ternal. Based on years of research, the 5 n. nterval for traffc flow data collecton has acheved general acceptance [3]-[5], on whch the traffc data n a day are obtaned at the an ternal every 5 n. nterval along te axs under the two an traffc patrterns: uppeak traffc condton and downpeak traffc condton, and the traffc flow te seres wll be consttuted, then the traffc deand forecastng odels are constructed to forecast the traffc deand at the specfed perod of te n the future on the observed hstorcal traffc data.. The Tradtonal Grey Model GM (, ) The key technology of grey theory s the grey odel whch takes the grey generaton functon as ts foundaton, and dfferental fttng as the core. The grey theory shows that all the rando varables are the gray varables and gray processes vary durng a certan perod of te wthn a certan range. Grey forecastng ethod nether eploes drectly the raw data to odel, nor fnds the statstcal laws and probablty dstrbuton of stochastc varables, but the generaton operaton on the raw sequence data s conducted to get new sequences wth strong regularty n order to dnsh the randoness and volatlty of the raw data. Modelng and forecastng s based on the new sequences [4]. Utlzng the grey forecastng ethod to forecast elevator traffc deand needs nether to deterne whether the passenger flow obeys a certan probablty dstrbuton, nor requre a large nuber of observed saples. ) Accuulatng Generaton Generator (AGO) The sequence atrx of the raw data s constructed as follows. Applyng AGO to = n n gves = n () Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

3 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): where = { x ( j) =,,, n, j =,, } = { x ( j) =,,, n, j =,, },, and x ( j) s the observed nuber of passengers who arrve at the an ternal and go to the upper floors or who coe fro the upper floors to the an ternal by elevators wthn the th t for the jth day and j k = x ( j) = x ( k), =,,, n, j =,,,. ) Modellng of Grey Mult- Model Method Ths odel s a te seres forecastng odel. The generated adjacent neghbor ean sequence Z of s defned as follows where Z = z j n (3) z ( j ) s the ean value of adjacent data,.e. z j αx j α x j = ( ) + ( ), =,, n, j =, 3,,, {,3,,,,, } Z = z j j = = n, usuallyα s set as.5 []. x ( j) approxately follows the exponental rule, n ters of x ( j ), the whtenzaton dfferental equatoncan s constructed as follows z () x () z (3) x (3) Β =, Y =, =,, n. n z ( ) x ( ) 4) Forecastng Results Accordng to Eq. (4), the soluton of forecasted value xˆ j of x ( j ) s gven as u u + = + a a a j xˆ ( j ) x e (7) =,,,, n, j =,,,, To obtan the forecasted value xˆ ( j ) of the prtve data x grey odel ( j ), the IAGO s used to establsh the followng a a j xˆ j+ = e x e u a (8) =,,, n, j =,,,, d dt u + a = (4) The above shows that each observaton perod t whch s set 5n corresponds to a forecastng odel, therfore the ethod proposed here s called ult-odel ethod. Dscretzng Eq. (4) yelds grey dfferental equaton as shown below = - a Z u (5) Then the sequence paraeters to be dentfed are a = [ a u] T, where a s developng coeffcent, u s grey nfluencng coeffcent. 3) Fnd Paraeters a and u Applyng the least squares ethod yeldss 5) Ltatons of the Tradtonal Grey Model n Practcal Engneerng Applcaton As stated earler, grey forecastng s sutable for the stuatons n whch the dffculty of ncoplete or nsuffcent nforaton s faced [6]. Snce t can well reflecte the past state and future varaton tendency, t has been wdely used especally n short-ter forecast. But lke other ethods, tradtonal grey forecastng ethod has ts ltatons [7]-[], soe of whch are suarzed as follows:. As the dscrete degree of data ncreases, vz. the gray level ncreases, the forecastng accuracy becoes worse. where [ a u] T T T a = = ( B B) B Y (6) n. The forecastng result wll be better, for a copletely exponental growth sequence, and t s dffcult to consder the stuatons where there exsts outlers n the sequence, especally when the saple data growth devates fro Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

4 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): exponental rule, the forecastng accuracy wll be gettng worse. 3. Because the knowledge and rule are dscovered on the raw sequence data takng no account or lackng of qualtatve consderatons and quanttatve analyss for the objectve factors whch ay pact the forecastng effect. Therefore, t s nferor n flexblty of applcaton. 4. The growth rate of the raw data sequence d d λ = = = a s a constant, but n dt dt general t s dffcult to eet such plct requreent. A slght change of a has lttle nfluence on forecastng accuracy, but a greater change of a wll lead to the deteroraton of forecastng accuracy. 5. Takng the prtve value x as the ntal condton of the forecastng odel casues that ˆ ( ) x s rrelevant to the ntal value of the raw data sequence. The nforaton about x s overlooked, n ths case, t s dffcult to guarantee the nu of the entre forecastng error. Because of the reasons stated avove, to prove tradtonal grey forcastng ethod to ncrease forecastng accuracy concernng the specfc engneerng applcatons s of great sgnfcance. 3. Elevator Traffc Deand Forecastng for EGCS 3. The Processng of the Raw Data Sequence The oveent of people around a buldng s very coplex, there s unpredctablty n huan behavour. Due to soe accdental or exceptonal crcustances caused by the huan occasonalty and subjectvty, great rando fluctuatons of passenger traffc flow ay occur durng soe specfc te perods, whch results n the outlers n the raw data sequence. Asde fro the outlers processng, soothng of the raw data sequence s needed for better forecastng results. ) Outlers Dscrnaton The outlers nether reflect nor represent the overall traffc characterstcs, and wll ake the forecastng accuracy serously deterorate. Such outlers ust be odfed to refne the traffc odels. for all { ( ),, ( ) } x j x x j + If x > γ x ( j ) + x ( j + ) or x ( j) < γ x ( j ) + x ( j + ) Then x ( j ) s called outlers, where =,,, n, j =, 3, γ, γ satsfes γ >, < γ <, the value of γ, γ are deterned by the specfc crcustance. ) Outlers Modfcaton The outlers should frstly be reoved, and the related data pont n wll be epty, then epty data postons n wll be updated wth the new data whch are generated by non-adjacent neghbor ean generaton ethod gven as follows. x ( j) =.5 x ( j ) +.5 x ( j + ) (9) k 3) Soothng Processng of the Raw Data Sequence If the randoness of the raw data sequence s soehow soothed, t wll be easer to odel and to forecast the expected perforance of the syste. Soothng processng s to transfor the raw data nto an ncreasng sequence, whch s ntended for futher soothng the randoness of the raw data sequence based on the above step ). for j x =.5 x j + x j + x j+ and for j =, ( ) ( ) ( ) x =.5 3 ( ) x + x ( ) x ( ) =.5 x ( ) + 3x ( ) The above processng not only ncreases the weghts of the current data, but avod the value fluctuatng excessvely, Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

5 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): and slowng the changng rate of the prtve sequence whch tends to grew quckly to ake the randoness of the new data sequence weaker than that of the raw data sequence. In ths way, the applcaton scope of the tradtonal grey odel s expanded. 4) Elevator Traffc Deand Forcastng Results Let the forcastng output of the accuulated sequence by the processed raw data sequence be { = ( + ) xˆ ( + ), =,,, n} ˆ ˆ, x where ˆ () xˆ +, x +, =,,, n, are respectvely the forcastng output of the accuulated sequenc of the (+)th day, (+)th day,. Eployng IAGO to ˆ yelds the elevator traffc deand forcastng results xˆ ( + ) = xˆ ( + ) x ( ) 5) Model Accuracy Testng (3) The odel accuracy s tested by error of resduals to check whether the the relatve error eets the gven requreents. Let the resdual sequence be {,,,,,, } E = e j = n j = (4) where e j = x j xˆ j Defne ε = e j x j % as the average j = relatve error of odel, and p = ε % s referred to as the accuracy of odel, whch s the generally accepted crtera for evaluatng the odel evaluaton grade whose values are set as shown n Table. Table : Crtera for evaluatng the odel Accuracy of odel p Model evaluaton grade p 9% excellent 8% p <9% good p <8% poor or unacceptable ˆ 4. Sulaton Experents and Analyss The sulaton data are fro an offce block wth a dnng-hall n the frst floor, the legal workng te of the people n the block s fro 7 : n the ornng to 9: n the evenng fro Mon. to Fr. The te nterval for observng traffc s t =5n, observatons were ade durng 5 days fro Mon. to Fr. between 7: and 9:, 44 data were collected n a day. The observed data fro Mon. to Thur. for the raw data sequence, and the Fr. s observed data are taken as the coparson saple..e. usng the raw data sequence fro Mon. to Thur. to forecast the Fr. s elevator traffc deand. Here γ, γ are set as,.5 n up traffc and.4,.6 for down traffc, respectvely. The accuraces of the odels of the proposed ethod are shown n Table ndcatng that both under up- and down traffc all the odels eet the requreent of gry forcastng [], where there are 3 odels are wth excellent level and wth good level for up traffc, and 34 wth excellent level, and wth good level for down traffc. Traffc patterns Up traffc Down traffc Table : Model accuracy Model Nuber Model accuracy of odels evaluaton [.8,.9) Good [.9, ) 3 Excellent [.8,.9) Good [.9, ) 34 Excellent The sulaton results are shown n Fgure ~ Fgure 6, where Fgure and Fgure, show the elevator traffc deand forecastng results of Fr., applyng the raw data sequence fro Mon. to Thur., copared wth the obsvered data sequence on Fr. under up and down traffc patterns expectvely. In order to copare the proposed ethod n ths thess wth the tradtonal ethod, two types of error whch are the ean square relatve error (MSRE) and the ean relatve error (MRE) are suggested. The forcastng err curves shown n Fgure 3 and Fgure 4 deonstrate that the proposed ethod perfors better results than the tradtonal gry forcastng ethod under both up and down traffc n ters of forecastng errs as shown n Fgure 5, Fgure 6, whose MSRE and MRE are gven by Table. The results n Table suggest that both MSRE and MRE of the proposed ethod are uch less than that of the tradtonal ethod, the reason for whch s that there are soe outlers n the raw data sequence created by huan subjectvty and occasonalty, whch ake the raw data sequence serously devate fro the exponental growth rule resultng greater errors. After soothng the randoness, the raw data becoe soother, consequently, the forecastng accuracy s proved. Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

6 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): Nuber of passengers Observ ed v alue f or up traf f c Sulated v alue f or up traf f c 7: 9: : 3: 5: 7: 9: Observng te peropd/5n Fg.. Sulated result for up traffc on frday by proved ethod Forecastng error/person : 9: : 3: 5: 7: 9: Observng te perod/5n Fg.5. Forecastng error for up traffc by tradtonal ethod Nuber of passengers Observed value for down traffc Sulated value for down traffc -7 7: 9: : 3: 5: 7: 9: Observng te peropd/5n Fg.. Sulated result for down traffc on frday by proposed ethod Predcton error/person : 9: : 3: 5: 7: 9: Observng te perod/5n Fg.6. Forecastng error for down traffc by tradtonal ethod 5. Conclusons Predcton error/person -4 7: 9: : 3: 5: 7: 9: Observng te perod/5n Fg.3. Forecastng error for up traffc by proved ethod : 9: : 3: 4: 7: 9: Observng te perod/5n Fg.4. Forecastng error for down traffc by proved ethod Forecastng error/person 4 - In reguard to the strong grey characterstcs of elevator traffc deand, a grey thoery based ult- odel ethod to forecast the elevator traffc deand for EGCS s proposed n ths thess. Takng full advantage of the grey forecastng, the ethod s suted to the EGCS wth lted nuber of saples and the ncoplete nforaton, on the other hand, for futher soothng the randoness of the raw data sequence and weakenng the nfluence of abnoral nforaton caused by huan subjectvty and occasonalty, the raw data sequence s processed by coparng real te traffc data wth the hstorcal ones to odfy the outlers to refne the traffc odels, whch effectvely decrease the odel error of the gry forcastng to reduce the pact of randoness on accuracy of odelng shch that the forecastng errs can be controled wthn the acceptable range for engneerng probles, and consequently, akng up for the defcency of the grey forecastng ethod n theory. The sulaton experent ndcates that the proposed ethod perfors better results than the tradtonal gry forcastng ethod n forecastng auucracy, qute proxatng to practcal stuaton. The proposed ethod needs lted nuber of saples, especaly, t s sutable for short-ter predcton of elevator traffc deand, provdng the essental prerequste for effectvely pleentatng the EGCS. Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.

7 IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): ISSN (Onlne): Acknowledgents Ths research was partally funded by the Natonal Scence Foundaton of Chna (698746) and the Doctoral Scentfc Research Startng Foundaton of Boha unversty ( BSQD-5) References [] G. C. Barney, Elevator Traffc Handbook, London, Spon Press, 3. [] Zhenshan Yang, Cheng Shao, and Guzh L, Mult- Objectve Optzaton for EGCS Usng Iproved PSO Algorth, n the Aercan Control Conference (ACC 7), 7, Vol., pp [3] Zhenshan Yang, and Zunl Zhang, A Sulaton Based Verfcaton Method for Elevator Traffc Plannng, n the IEEE Internatonal Conference on Coputer Applcaton and Syste Modelng (ICCASM ),, pp [4] [4] Anna Shang, Elevator Traffc Flow Predcton Methods, Hunan Agrcultural Machnery (n Chnese), Vol. 37, No. 3,, pp [5] Yunl Zhang, and Zhenshan Yang, Fuzzy logc controller for elevator traffc schedulng, Lft Report, No., 9, pp. 64, [6] [6] Lxa J, aogang Fu, The Applcaton of LS-SVM to the Predcton of The Elevator Transportaton Flow, Journal of Shangha Danj Unversty, Vol. 9. No. 3, 6, pp [7] Shuguo L, Le Zhang, and Yang Ba, Elevator Syste Applyng Volue Estatng Method Based on The Data Mergence, Chna Elevator, Vol.. No. 3, 6, pp [8] Hayan Tang, Delang Yu, Bao Dng, et al., Te Seres Predcton of Elevator Traffc Flow Based on SVR, Control Engneerng of Chna, Vol. 8, No. 5,, pp 73-76,79. [9] Zhenshan Yang, Traffc Regularty Evaluaton for Elevator Vertcal Traffc Syste, Advanced Materals Research, Vol ,, pp [] Sfeng Lu and Y Ln, Grey Systes, Theory and Applcatons. Berln Hedelberg, Gerany: Sprnger- Verlag Press,. [] aoxuan Zhang, The Essental of GM(, ) Model, Journal of Grey Syste, Vol.. No., 7, pp [] FR Johnston, JE Boylan, and EA Shale, An Eanaton of the Sze of Orders Fro Custoers, Ther Charactersaton and The Iplcatons for Inventory Control of Slow Movng Ites, Journal of the Operatonal Research Socety, Vol. 54, No. 8, 3, pp [3] G. C. Barney, S M. Dos Santos, Elevator traffc analyss: Desgn and control. London:Peter Peregrnus Ltd, 985. [4] Meng, Lu, Kees Wevers, Grey syste theory and applcatons: A way forward, Journal of Grey Syste, Vol.. No., 7, pp [5] CIBSE Gude D: Transportaton Systes n Buldngs, Norwch Norfork: Page Bros, 5. [6] Erdal Kayacan, Bars Ulutas, and Okyay Kaynak, Grey syste theory-based odels n te seres predcton, Expert Systes wth Applcatons, Vol. 37, No.,, pp [7] D. Zhang, S. Zhang, and K. Sh, Theoretcal Defect of Grey Predcton Forula and Its Iproveen, Systes Engneerng -Theory & Practce, Vol., No. 8,, pp, 4-4. [8] n Zhang, Gang We, Mn Zhou, and Yjuan Yang, Applcaton of grey theory n forecastng Cty annual electrcty consupton, Journal of Shangha Unversty of Electrc Power, Vol. 8, No.,, pp. 9-. [9] png Wang, Grey Predcton wth Rollng Mechans for Electrcty Deand Forecastng of Shangha, n the IEEE Internatonal Conference on Grey Systes and Intellgent Servces, 7, pp [] Huazhu Shu, Suarze on the Forecast odels of road traffc accdent based on grey theory, Road Traffc & Safety, Vol. 9, No. 6, 9, pp Zhenshan Yang receved the B.S. degree n ndustral electrcal autoaton fro Shenyang Janzhu Unversty, n 987. He receved the Ph.D. degree n control theory & control engneerng fro Dalan Unversty of Technology, n 8. He s a cottee eber of Chna Electrotechnology Socety (CES), the Deputy Secretary-General of the Afflated Socety of CES of Laonng Provnce and the edtoral board eber of the Internatonal Journal of Urban Plannng and Desgn Research (UPDR). Currently, he s a professor at Boha Unversty. Hs research nterests nclude ntellgent buldng, elevator traffc analyss, desgn, and ntellgent Control. Yunl Zhang receved the B.S. degree n appled atheatcs fro Northeastern Unversty, n 987, and the aster's degree n coputer technology and applcaton fro Dalan Unversty of Technology. Currently, she s a Professor at Laonng Medcal Unversty, Jnzhou, Chna. Hs nterests are n data nng and ts applcaton n ntellgent control systes. Copyrght (c) 3 Internatonal Journal of Coputer Scence Issues. All Rghts Reserved.