ICTCT Extra Workshop, Bejng Proceedngs The Appcaton of BP Neura Network prncpa component anayss n Forecastng Road Traffc Accdent He Mng, GuoXucheng &LuGuangmng Transportaton Coege of Souast Unversty 07 room,yfu Budng, Souast Unversty 20096 Nanjng, Chna Phone: (0)38408366 Fax: 025-83795528 E-ma: hemng9302@63.com, seuguo@63.com, gm0926@sohu.com Abstract Accordng to compexty and comprehensbty of factors whch affect road traffc safety, we use method of prncpa component anayss to refne new factors whch are neary ndependent, n we forecast road traffc accdent accordng to prncpa component by BP neura network smuaton, anayse reatonshp between traffc accdent evauatng ndex and causes of traffc accdent, ncudng peope, vehces, road and envronment. At ast we apped method to a case, from smuated resut we can nfer that method of BP neura network smuaton prncpa component anayss s superor to mutnoma fttng and BP neura network smuaton n effcency and precson. Key words: road traffc accdent, forecastng, BP neura network, prncpa component anayss.introducton In pannng of road safety, traffc forecastng s one of most basc tasks n pannng process, and t s most mportant ssue. Understandng future traffc accdent Scentfcay and accuratey s of great sgnfcance for overa grasp of road safety n order to prefabrcate correspondng measures. Exstng traffc forecastng methods can be grouped nto three genera categores[]: Frst extrapoaton method, that s, y use past to predct future state of nformaton, such as tme seres; Second, causaty, that s, based on avaabe nformaton, to dentfy reatonshp between varabes to predct future state, such as regresson anayss; Thrd, judge anayss, Experts predct future state rey on past experence and abty of comprehensve anayss methods. Athough forecastng methods have r advantages, but due to compex nature of transport system and dversty of traffc accdents, most do not ft data exst very we, extrapoaton s not enough, and forecastng resuts may devate from actua resuts and so on. Such as tme seres predcton, t uses ongtudna data of number of traffc accdents n past to predct ts movements over tme. The process does not nvove any or reevant factors. Athough regresson anayss can forecast accordng to transverse and ongtudna data, but t estabshes regresson equaton usng just some hstorca data, regresson equaton often consders ony part of affectng factors. Therefore, mode s not accurate enough. Judge anayss s quatatve, t based on subjectve experence, so forecastng may not accurate. POSTER SESSION 305
ICTCT Extra Workshop, Bejng Proceedngs In recent years, rapd deveopment of computer and artfca ntegence technoogy provde traffc modeng and forecastng wth new methods. Artfca neura network s composed of neurons wth dfferent functons, t can be used to smuate, operate and reason compcated nonnear system through neura network nteracton. It has extensve adaptng abty, earnng abty, mappng abty, and can approach to any nonnear functon n ory. In mutvarabe nonnear system modeng, t has made remarkabe achevements. BP neura network structure s ntutve, and t s most wdey used neura network. Whe Usng BP neura network system to smuate, frst s to dentfy factors. Traffc s very compex, we often adapt quatatve anayss to fnd a accdent factors so as to avod major factor be mssed.however, when nput varabes are too many, t w obvousy add to compexty of network, reduce network performance, greaty ncrease cacuaton of operatng tme, and decrease precson. To sove probem of too many nput varabes, ths paper proposes use of BP neura network traffc forecastng mode combned wth prncpa component anayss decreases orgna nput varabes through prncpa component anayss, obtans neary ndependent new factors whch ncude nformaton of orgna nput varabes. Then t uses se new factors as nput varabes so as to smpy nput varabes. Fnay, paper uses actua traffc data for traffc forecastng. 2.Traffc forecastng mode based on BP Neura Network prncpa component anayss 2. The structure and prncpe of BP Neura Network BP Neura Network s a one-way transmsson to mut-forward network, and except for nput and output nodes, re are aso one or more ayers of hdden nodes, nodes of same ayer s out of coupe wth each or, nput sgna passes from nput ayer nodes to hdden nodes foowed by transfer functon, n spread to output nodes. The output of each node ony nfuenced next output nodes, as shown n fgure : Fgure structure of BP Neura Network BP Neura networks can be vewed as a hghy nonnear mappng from nput to output n m n m namey F R : R,f(x)->Y For pattern: nput x R output y R g ( x ) = y (=, 2, n) The neura network s approxmate to compex functon after a number of smpe nonnear functons, and t can obtan output usng nput at w. 306 POSTER SESSION
ICTCT Extra Workshop, Bejng Proceedngs.transfer functon often s 0 S functon g(x)= x + e 2.error functon The pth pattern error computng formua E p = ( t p O p 2 ) 2 t p, O p are expected output and network s computng output. Through correctng weghts of network w j, T j and threshod θ,to make error functon E descend foowng drecton of mnmum oca gradent [3],[5] BP network nodes ncude: nput nodes x j, hdden nodes of network between nput nodes and hdden nodes s 2 y, output nodes O. The weght w j, weght of network between T hdden nodes and output nodes s. When desred output of output nodes s t, cacuaton formua of BP mode s: 3. formua of output O of output nodes: nput of nput nodes: x output of hdden nodes: output of output nodes connectng weght s j w j nodes threshod 4. output ayer s correctng formua: desred output of output nodes: t w x θ j j 3 j O = f Tj y θ 4 y =f O a patterns error: one pattern s error: e k = P e k k= E= p s number of patterns n s number of output nodes. error formua: correctng weght: δ = k s number of number of teratons. correcton of threshod 5. correcton formua of hdden node: error formua correcton formua of weght correcton of threshod n = <ε 5 ( k ) ( k ) t + O 6 t O * O * O 7 T ( k+ ) ( k ) = T + ηδ y ( k+ ) ( k ) θ = θ + η' δ ' δ ' = y ( y ) δ T 0 w ( k + ) j = w ( k ) j +η' δ ' x ( k+ ) ( k ) θ = θ + η' δ ' j 8 9 2 POSTER SESSION 307
ICTCT Extra Workshop, Bejng 2.2 Traffc accdent forecastng mode Proceedngs 2.2. The major nfuencng factors of accdents Traffc accdents happen because of co-ordnaton of varous factors such as cars, roads, cmate and envronment. In consderaton of many factors that mpact on traffc, we seected popuaton, drvers, popuaton of arge vehces, popuaton of sma cars, meage of artera road, meage of mnor artera roads, ran and snow as seven factors. 2.2.2 Traffc accdent forecastng mode 2.2.2. Prncpa component anayss Prncpa component anayss s use of dmenson reducton by constructng approprate near combnaton of orgna ndex, to produce a seres of uncorreated comprehensve ndexes, and to seect some of se ndexes, whch ncude as much nformaton as od ndexes, so as to use se new ndexes to refect ndvdua. Because method reduces dmenson by emnatng correaton between ndexes, t has been brngng n concern n recent years and becomng a unque mut-evauaton of technca ndexes. Based on anayss of man nfuencng factors of accdent, paper seects seven factors of accdent are x, x2, x3, x4, x5, x6, x7, adopts prncpa component anayss frst, and anayses se seven factors, as foows: Step Normazaton of factors Because every ndex has dfferent concept of magntude, before anayzng prncpa component, we need to normaze data, makng vaues range from 0 to. The method s as foows: ' x x = 3 max( x ) Step 2: Usng standardzed data to cacuate correaton matrx n R = ( r j ) 7 7 ( rj = n = x ' x ' j,,j=,2 7) 4 Step 3: Cacuate egenvaue and egenvector of correaton matrx R to get prncpa component Make R λ I = 0 cacuate 7 egenvaue such as λ (=,2 7), y are varances of prncpa components, rank m from sma to arge: λ λ2... λ7 0,so expresson of prncpa component s Y = X X X... X 5 ' = + 2 2 + + =,2, 7. 7 7 Step 4 Seect m prncpa components to make sure varance contrbuton rates a = m = 7 λ / λ >0.995. = 308 POSTER SESSION
ICTCT Extra Workshop, Bejng Proceedngs Through step to 4,we can cacuate r prncpa components are Y, Y2,... Ym m<7,and Y (=,2,,m) s near combnatons wth x ' (=,2,,7) and make Y, Y2,... Ym as nput of BP Neura Network to get forecastng resuts by study of BP network agorthm. 2.2.2.2 BP Neura Network smuaton usng prncpa components as nput factors The ory has been proved that three-ter Network system s a better mode for nonnear modeng, every contnuous functon can be reazed through one three-ayer neura network. In neura network forecastng mode, we use a three-ter network. That s, one nput ayer, one hdden ayer, one output ayer. Because network s abty to express s ncreasng wth number of nput ayer and output ayer ncreasng, and aso convergence rate s ncreasng, so mode s heoretca workabe. In condton of consderng factors of traffc accdent, paper uses m prncpa components as nput ayer, nput ayer has 7 neurons, hdden ayer has 0 neurons, output ayer has neurons. The output ayer s object varabe, namey number of traffc accdents. Iteraton process of BP neura network s as foows:. Gve nta vaue for weght coeffcent w j of a ayers. 2.Get a nodes output accordng to 3 4. 3.Get error e k accordng to 6,f t meets 5,or go to step 4. ' 4.Get errors( δ, δ ) of prncpa components and hdden ayers accordng to formua (7) and (0), n correct weghts accordng to 8 and,n go to step 2. (2-4 s teratve process). 3. Exampe Take a cty as an exampe, descrbe method of paper, data can be seen from tabe : year popuaton ten thousand drvers (ten thousand Tabe The traffc accdent data of a cty number of arge vehce number of sma vehce meage of artera road (km meage of mnor artera road km ran or snow d The number of traffc accdent 997 87.9 306867 6520 40935 4549 49 0 5804 998 89.5 358603 970 44605 4950 28 2 5962 999 90.2 437264 2320 5395 5662 544 4 6273 2000 9.2 62729 32960 799 796 98 8 67725 200 92.8 85636 4490 90305 855 2735 24 68930 2002 93.9 96200 49460 9304 9539 3008 28 69802 2003 96.3 37364 57620 06006 3388 3934 32 73 2004 98.6 28030 63880 228 5424 4335 34 7352 2005 0.8 43064 69970 4030 732 4739 37 76308 2006 04.9 564299 75280 42527 8980 567 42 79532 POSTER SESSION 309
ICTCT Extra Workshop, Bejng Proceedngs 3. Data processng The factors of accdents ncude popuaton, drvers, popuaton of arge vehces, popuaton of sma cars, meage of artera road, meage of mnor artera roads, ran and snow, namey x, x2, x3, x4, x5, x6, x7, change of accdents wth years s as fgure 2. Fgure 2 change of accdents wth years Fgure 3 change of accdents wth years after normazaton Because dfference between factors s too arge, we normaze m accordng to data of 2006, as can been seen from fgure 3 and tabe 2. year popuaton ten thousand Tabe 2 The traffc accdent data after normazaton drvers (ten thousand number of arge vehce number of sma vehce meage of artera road (km meage of mnor artera road km ran or snow d The number of traffc accdent 997 0.8379 0.962 0.294 0.2872 0.2397 0.2224 0.245 0.7298 998 0.8532 0.2292 0.2546 0.330 0.2608 0.2479 0.2880 0.7496 999 0.8599 0.2795 0.3083 0.3785 0.2983 0.2988 0.3386 0.7885 2000 0.8694 0.400 0.4378 0.4995 0.379 0.3834 0.4270 0.855 200 0.8847 0.5444 0.5870 0.6336 0.4487 0.5293 0.5684 0.8667 2002 0.895 0.650 0.6570 0.6532 0.5026 0.5822 0.6674 0.8777 2003 0.980 0.727 0.7654 0.7438 0.7054 0.764 0.7599 0.8966 2004 0.9399 0.883 0.8486 0.8499 0.827 0.8390 0.843 0.9244 2005 0.9704 0.943 0.9295 0.9844 0.926 0.972 0.8804 0.9595 2006.0000.0000.0000.0000.0000.0000.0000.0000 30 POSTER SESSION
ICTCT Extra Workshop, Bejng Proceedngs 3.2 Prncpa component anayss Do prncpa component anayss, get 3 prncpa components n condton of varance contrbuton rates s over 0.995, as can been seen from tabe 3: Tabe 3 The new components factors factor factor 2 factor 3 x 0.074705 0.05684-0.06927 x2 0.50227-0.478 0.38855 x3 0.2269-0.26258 0.25926 x4 0.4032-0.4789-0.787 x5 0.69495 0.70893-0.034 x6 0.756-0.04852 0.2459 x7 0.2087-0.692 0.33379 contrbuton rate 99.07% 0.63% 0.27% 3.3 BP Neura Network combnng wth prncpa component anayss Take factor as nput and traffc accdent afer normazaton as output, we set up threeayer neura network mode, nput ayer has 7 neurons, hdden ayer has 0 neurons, output ayer has neurons. The process of smuaton can been seen as fgure 3,n order to make precson s hgh enough(<0e-4), resut s 0.9995,namey number of traffc accdent s 79495.If put prncpa component of years from 997 to 2005, resut s [0.7298 0.7496 0.7885 0.855 0.8667 0.8777 0.8966 0.9244 0.9595].( comparson between smuaton resut and actua data can been seen from fgure 4) Fgure 3 resut of BP Neura NetworkFgure 4 comparson between combnng wth prncpa component anayss smuaton resut and actua data 3.4 The comparson of resuts Compare resut of BP Neura Network combnng wth prncpa component anayss, resut of BP Neura Network and resut of nonnear regresson by puttng factor as ndependent varabe,we fnd resut of BP Neura Network combnng wth prncpa component anayss s better than one of BP Neura Network and nonnear regresson. POSTER SESSION 3
ICTCT Extra Workshop, Bejng Proceedngs Tabe 4 comparson of resuts year 997 998 999 2000 200 actua data 5804 5962 6273 67725 68930 nonnear regresson BP Neura Network BP Neura Network combnng wth prncpa component anayss 58042 59593 62775 6760 6927 57708 5999 62965 67332 68835 58042 5967 627 6772 68930 year 2002 2003 2004 2005 2006 Actua data 69802 73 7352 76308 79532 nonnear regresson BP Neura Network BP Neura Network combnng wth prncpa component anayss 6959 7428 73464 7639 8045 70044 789 73663 76239 79389 69805 7308 7359 763 79495 The resut ndcates that BP Neura Network combnng wth prncpa component anayss s better than BP Neura Network n effcency and precson [4][6]. BP Neura Network combnng wth prncpa component anayss s very practcabe. 4.Summary We can concude from paper: The mert of mode:.the mode of BP Neura Network combnng wth prncpa component anayss s feasbe, resut s better than BP Neura Network and regresson. 2.The mode can consder a factors affectng traffc accdents, through prncpa component anayss, we get ess new factor as nput, t s better than BP Neura Network n effcency and precson. But se are aso some shortages:.the ory about stabty of BP Neura Network s fautness, we can ony try to cacuate hdden ayers and nodes, and method s mted n use. 2.The mode s same wth forecastng traffc accdents n stabe condton, not consderng change of exteror condtons, such as change of transport pocy and so on,ths s aso an mportant factor of traffc accdent. In a word, The mode of BP Neura Network combnng wth prncpa component anayss s feasbe,consderng compexty and randomcty of urban transportaton, appy range coud be deveoped except accdent forecastng, and mode needs to studed and mproved. 32 POSTER SESSION
ICTCT Extra Workshop, Bejng Reference Proceedngs Wang We.Research on Sustanabe Deveopment Pannng Theory of Urban Transportaton [J].Journa of souast unversty,200,3:(:6) Awtan, Modeng of Matera Behavor Data n a Functona Forms Utabe for Neura Network Representaton[J].Computtona Materas Scence,999,5:493502 Martn E W,Defferyes D W,Hoffer J A eta. Managng nformaton technoogy. New York:MacMan,99 Su Jnmng ZhangLanhua LuBo. The Appy of Matab. BeJng: The Chna Eectronc Industry Pubshng House,2000.00-30 H.I.CHOI.F Abrcaton of Hgh Conductvty Copper Aoys by Rod Mng. Journa of Materas Scence Letters,997,6:600602 I.A.Basheer.Artfca, neura network: Fundamentas, Computng, Desgn, and Appcaton. Journa of Mcroboogca Methods,2000,43:33 POSTER SESSION 33