XIII International PhD Workshop OWD 2011, October 2011

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1 XIII Iteratioal PhD Workshop OWD 011, 5 October 011 A applicatio of cloud programmig, eolutioary optimizatio ad aalytic geometry for the eeds of ehicle crash aalysis Vasil Peche, Boris Tudjaro, Techical Uiersity of Sofia, Bulgaria Abstract The authors propose a framework of a complex itegrated cloud programmig based system for support of actiities of goermetal ad ogoermetal orgaizatios ad persos, which is related to maagemet of iformatio about traffic support, trasport meas, accidets ad etc. (for ex. oe task ca be: the stages from fillig of basic crash documets to fial expert coclusio for the accidet). Here it is show the applicatio of a deeloped part of the work, which combie the adatages (discussed i the paper) of cloud programmig, eolutioary optimizatio ad aalytical geometry for solig of mechaical tasks- i our case impact betwee two ehicles. The experimet is made by a deeloped by the authors module Web based Geetic Algorithms Calculator, which ca hae may purposes ad ery wide usage. For the aim of our work, which is crash aalysis, it has bee ecessary to write a special fitess fuctio by usig the aalytic geometry. The screes from the experimetal applicatio are represeted. The work assists the actiities i the field of ehicle crash accidets iestigatio with differet leels of ambiguities ad ca be used as a tool for fial expert coclusios ad checks. 1. Itroductio Vehicle crash accidets are eets, which lead after themseles material ad omaterial damages of the participats ad eiromet ad ery ofte take away life of huma. The process of ehicle crash iestigatio icludes may ad differet tasks ad actiities. They are performed i differet stages of foresic iestigatio. Eeryoe actiity has a differet duratio for its performace. The actiities that are icluded i ehicle iestigatio process usually cosist: - documetatio of accidet; - a expert iestigatio ad modelig of accidet; - preparig of the fial expert coclusio for the accidet. Very ofte the iformatio, that a expert is receied is isufficiet ad ambiguity. Also i accidet scees ay witesses are missig ofte too. I this coditios the task, that a expert must sole, ca be too difficult A Crash Aalysis Task with Differet Leels of Ambiguities Modelig ad aalyzig of ehicle crash accidets is a task which cosist i it may costats ad/or ariables. The easiest way to sole the tasks of crash aalysis ad to make expert coclusio, is whe all of these costats ad ariables are kow. The mai iformatio for the aalysis is related to the participats ad eirometal coditios, which are the base of calculatio process. Sometimes this iformatio is too poor or missig. The the solig of the task of crash aalysis will be difficult ad ambiguity. Fig.1. Leels of idefiiteess i iitial data O fig.1 a possible ariats about mai iformatio are show. Here (two) leels of idefiiteess: Leel of fully defiiteess ( Leel of defiite alues ) ad Leel of defiite alues with 4

2 limits are preset. Three differet combiatios of iitial data meaigs are possible: 1. All of basic iformatio, ecessary for crash aalysis is defied. Here, all of iitial data is strog defied with its alues (type, maufacturer ad model of participat s ehicles with their characteristics, crash place coordiates, driers ad eiromet coditios ad etc.).. The ecessary iformatio about crash accidet is partially defied ad a part of it is partially ambiguous. The ambiguous iformatio is preset with alues i a field with upper ad lower limits of alues (for example: type, maufacturer ad model of participat s ehicles with their characteristics is kow; ukow are: crash place coordiates, a part of drier ad eiromet coditios ad etc.). 3. The iitial data alue is totally ambiguous. I these coditios the idefiiteess i iitial data creates difficulties i accidet aalysis. Accordig to these three combiatios preseted aboe, expert work ca be: easy, difficult ad more difficult, regardig to iitial alues. All iformatio about crash accidet ca be preset i defiite fields betwee exact alues, which are chose or established from the expert ad/or are kow from witess descriptio documets. 1.. A Framework of the Proposed Itegrated Cloud Eiromet I the paper, we are represetig a ew additio to our research i the directio of the strategic goal called by us Cleer Ratioal Society -CRS [3]: through the usage of the cotemporary Iteret ad other techologies ad sciece to assure the correspodece betwee the society goals ad the iterests of humas ad huma groups, ad ratioality eerywhere. Our work, here, is related to the deelopmet of a ew cocrete module for crash accidet iestigatio. By the deelopmet of this module we try to implemet i practice our CRS approach. The framework of itegrated cloud programmig [4] based CRS [3] system with the ew additio is gie o fig... Cloud Programig ad Eolutioary Optimizatio.1. Cloud Computig (Programig) As it is described i [4] cloud computig has bee the most hyped terms i recet times, a prolific techology that is flourishig like aythig. Cloud computig allows: - cosumers ad busiesses to use applicatios without istallig at their eds; - access their persoal files just with iteret access; - it allows much more efficiet computig ad processig, about which the ed users hae to be least bothered. For the realizatio of the itegratio ad assure iteroperability betwee differet software ad deices we chose as mai laguage XML (extesible Markup Laguage)[7]. By usig of XML ad PHP[6] we deeloped a cloud applicatio - web based calculator of geetic algorithms. Its applicatio for solig task of ehicle crash aalysis is show below. Fig.. A framework of CRS with ehicle crash aalysis module... Geetic Algorithms Calculator O are represeted some fudametals of geetic algorithms [5]. These algorithms are used whe pursuig a specific result (objectie), whe the solutio requires a relatiely large time resource or i cases where the solutio is ot kow or has o solutio. Algorithm starts with a set of solutios (represeted by chromosomes with specific iformatio about gees) called iitial populatio. Accordig to their iability are chose solutios to form the ext populatio (offsprig). To more appropriate decisios (decisios are compared i terms of pursued result/goal) are gie better chaces for reproductio. New populatio is expected to be better tha the old. This is repeated util some coditio (for example: a 5

3 umber of geeratios or a sufficietly good solutio) is satisfied. We deeloped experimetal cloud applicatio, which assures remote creatio of models of geetic algorithms ad receiig of the results for ery wide field of cases. By usig this applicatio user ca create ad edit the iitial iformatio about his cocrete task ery easy ad ca receie the calculatio results as web page ad/or as MS Excel file. For modelig of geetic algorithms a XML descriptio is proposed ad a XML trasport file (which trasports the user iformatio to the serer) is used (see the structure of the file o fig.4.). More detailed iformatio ca be see i poit 4., where are show experimetal results 3. Geetic Algorithms Calculatios ad Impact betwee two Vehicles Impact betwee two Vehicles - Task. I our case (show o the fig.3) the task is as follows: A. Gie- the fial dispositios of the ehicles (after the impact) by their coordiates P1x, P1y ad Px, Py. B. Requested to fid- the way o which the collisio occurred (how it was doe): the right place of the collisio ad the elocities of the ehicles before the impact (their alues ad directios). For solig the task we propose to use the described aboe calculator of geetic algorithms. The fitess fuctio summarized the alues of the distaces betwee the gie fial dispositios of ehicles (P1 ad P) ad calculated, fial dispositios (T8 ad T9) marked o the fig.3 as D1 ad D. Fitess calculatio (D1+D) hae to be with miimal alue. O eery oe step of the geetic algorithm we hae to calculate the fitess fuctio about eery oe chromosome (combiatio of the gees ad their alues). So, it is importat to fid the alues of D1=? ad D=?. As it is clear from the priciple of Coseratio of mometum: for a system of iteractig objects, the total mometum remais costat, proided o exteral resultat force acts o the system [1, ]: total iitial mometum is equialet to total fial mometum. For two-object collisio, mometum coseratio is easily stated mathematically by the equatio: m u + m u = m + m (1) where: - m1 is mass of ehicle 1; - m is mass of ehicle ; Fig.3. Impact betwee ehicles elocities ad trasitios (displacemets). 6

4 - u 1is the elocity of ehicle 1 prior to the collisio; - u is the elocity of ehicle prior to the collisio; - 1 is the elocity of ehicle 1 after the collisio; - is the elocity of ehicle after the collisio. If exteral forces are igored, the sum of the mometa of two ehicles prior to a collisio is the same as the sum of the mometa of the ehicles after the collisio. Note that mometum is a ector. I our case as omial (perpedicular) directio is chose the ector subtractio u 1 u (the directio of the coergece of the ehicles) ad tagetial directio is perpedicular to. Vectors ca be projected o the ad, ad followig equatios are obtaied from (1): m1 u1 mu = m11 + m + () m + + (3) 1u1 mu = m11 m So, we hae 4 ukows 1,, 1, ad we eed to add two equatios more. New two equatios ca be added to the system by the usage of the experimetally defied coefficiets k ad λ [1, ]: 1 = k (4) u1 u 1 = 1 λ 1 (5) u1 u Ad ow, we ca calculate 1 ( 1, β 1, e 1 x, e 1 y ) ad (, β, e x, e y ), if we hae the iitial data about the accidet: m 1, m, u 1( u 1, α 1, eu 1 x, eu 1 y ), u ( u, α, eu x, eu y ) ad T1 (place of the accidet: T1x ad T1y). I our case iitial data are automatically geerated for eery oe populatio of the geetic algorithm. 1 ad ca be easily receied from their projectios (6-9). If we kow the breakig acceleratios a 1 ad a it is o problem to calculate the fial positios of the ehicles. By usig meas of the aalytic geometry (ectors, strait lies, itersectio equatios ad drawig up projectios ad agles) ad aboe equatios we defie the places of the poits from T(Tx,Ty) to T9(T9x,T9y) ad calculate the distaces D1 ad D. So, the deried fitess fuctio is: f m, u, m, u, T1) = D1 + f + ( 1 1 D = ( P1x T8x) ( Px T 9x) + ( P1y T8y) + ( P y T 9 y) where: T8x = T1x cos( β ) a ; 1 x 1 1 / 1 y1 si( β1) / T8y = T1y a ; x cos( β ) / T 9x = T1x a ; y si( β ) / T 9y = T1y a ; T 6y T1y β 1 = a ta( ) ; T 6x T1x (10) (11) 1, 1, ad are calculated from the system (-5): m = u1 ( 1+ k) ( u1 u ) (6) m + m 1 1 m1 = u + ( 1+ k) ( u1 u ) (7) m + m 1 1 = u1 (8) = u (9) Fig.4. Structure of XML model for geetic algorithm calculator. 7

5 T 7y T1y β = a ta( ) ; T 7x T1x e... x ad e... y are uit ectors o X ad Y axes. Below it is show the implemetatio of aboe calculatios for the eeds of modelig ad aalyzig crash accidets by the calculator of geetic algorithms. 3.. Parameters, Chromosome (Gees) ad Fitess Fuctio of the Geetic Algorithm. As it was already writte, the geetic algorithm calculator is workig by sedig to the serer a XML model, which structure is represeted o fig.4. The structure of the XML model cotais mai parts: A. Part of parameters - closed betwee tags INITIAL : ame of the calculatio, type, fitess fuctio, size of populatio, umber of geeratios, data about crossoer, mutatio ad stayed alie idiiduals, ad type of requested report from the calculatios. B. Part of chromosome betwee tags UNITS, which cotais gees (closed betwee Fig.5. Workig screes from the experimet. 8

6 tags UNIT ) : check - mark for editig the gee iformatio, ame of the gee, type, lower ad upper limits, accuracy of calculatios ad alue of the gee, which is take for fitess fuctio calculatios. For the eeds of our task we defied a XML chromosome with followig 19 gees: -crashx- coordiate X of crash place (T1 o -crashy- coordiate Y of crash place (T1 o -X1p- coordiate X of fial ehicle 1 place (P1 o -Y1p- coordiate Y of fial ehicle 1 place (P1 o -m1- mass of ehicle 1; -u1- ehicle 1 elocity before the impact; -u1ex-uit ector of u1 o X; -u1ey-uit ector of u1 o Y; -alpha1- agle of u1 ( α1 o -a1- breakig acceleratio of ehicle 1; -Xp- coordiate X of fial ehicle place (P o -Yp- coordiate Y of fial ehicle place (P o -m- mass of ehicle ; -u- ehicle elocity before the impact; -uex-uit ector of u1 o X; -uey-uit ector of u1 o Y; -alpha- agle of u ( α o -a- breakig acceleratio of ehicle ; -k- coefficiet of restitutio, see (4). Here, we use the possibility, assured by the used calculator of geetic algorithms, to write a PHP program text iside the ode FITNESS istead of just simple fitess calculatio (our PHP fuctio cotais 88 rows). 4. Experimetal Results. O fig.5. are gie example workig screes from our experimet. O the left side is represeted the module for creatio ad editig of the model of geetic algorithm ad o the right side - two parts of geerated, after calculatios, report. As it ca be see from the figure the user ca create ad edit the model iformatio ery easy by usig the checkbox for poitig o differet fields (rows) ad buttos for to delete or isert iformatio. Other buttos, show o the figure allows saig, readig ad calculatig the geetic algorithms. It ca be see o the right side of the figure how the geetic algorithm is workig by comparig of the best Fitess alues of 1st ad 10000th geeratios. Uder eery Fitess alue there is show the iformatio about the cotets of gees, which alues correspod to the Fitess alue. 5. Coclusio. I our work we combie the adatages of cloud computig, dyamics, aalytical geometry ad eolutioary optimizatio for solig a task about ehicle crash aalysis. As a cloud tool it was used, deeloped by us, Web based calculator of geetic algorithms. Our work ca be implemeted i practice i the actiities o ehicle crash accidets iestigatio. It assures the oercomig of the egatie effects of the geographical ad temporal commuicatio fragmetatio ad ecoomizes time ad costs. Bibliography [1] Belikoloski Boris: Chose Chapters of Dyamics, Techical Uiersity of Sofia, Bulgaria, 004, pp. (i Bulgaria) [] Pisare Alexy et al: Course i Theoretical Mechaics Part, Dyamics, Techics, Sofia, Bulgaria, 1988, pp. (i Bulgaria) [3] Tudjaro Boris et al: A logistic system for discoerig of the best way for cooperatio through Iteret egieerig coordiatio ceter, Proceedigs of the XIX Iteratioal Coferece MHCL 09, FME, Belgrade, Serbia, 009, pp. (i Eglish) [4] Web page: -comput9ig-a-isight-kow-your-clouds/, accessed August 011 (i Eglish) [5] Web page: accessed February 011 (i Eglish) [6] Web page: accessed February 011 (i Eglish) [7] Web page: accessed February 011 (i Eglish) Authors: Assist.Prof. Eg. Vasil Peche Techical Uiersity of Sofia, Departmet of Desig Fudametals, Office 4519, 8, Klimet Ohridski Str., Sofia-1000, BULGARIA, Tel asil_peche@tu-sofia.bg Assoc.Prof. PhD Eg. Boris Tudjaro Techical Uiersity of Sofia, Departmet of Desig Fudametals, Office 4519, 8, Klimet Ohridski Str., Sofia-1000, BULGARIA, Tel bt@tu-sofia.bg 9