STUDY ON AIRCRAFT EVACUATION MODELING AND MODEL PARAMETERS BASED ON SOCIAL FORCE

Transcription

1 SUDY ON AIRCRAF EVACUAION MODELING AND MODEL PARAMEERS BASED ON SOCIAL FORCE Kun Chen*, Ybng Wu*, anchun Zou* *Laboratory of Cvl Arcraft Arworthness echnology, CAAC, Cvl Avaton Unversty of Chna, anjn 33, Chna Keywords: Arcraft emergency evacuaton; Partal evacuaton experment; Socal force model; Model parameter; Cabn confguraton; Abstract Emergency evacuaton s an mportant factor to ensure passengers safety after an arcraft accdent. In order to predct passengers emergency behavor n arcraft cabn, the smulaton model applcable to arcraft emergency evacuaton was establshed. In ths paper, the force balance phenomenon whch means the passenger keeps stll n a certan poston occurred when smulatng arcraft emergency evacuaton because of the lmtaton of orgnal socal force theory. A partal emergency evacuaton experment was made to modfy the psychologcal repulson between passengers and physcal boundary n the orgnal socal force model. he modfed model was appled to smulate the emergency evacuaton test conducted by the ransportaton Development Center of Canada. he smulaton data shows that force balance phenomenon s elmnated, and the modfed socal force model can effectvely predct the emergency evacuaton behavor of passengers n arcraft cabn. 1 General Introducton Arcraft cabn emergency evacuaton after the accdent s a key factor affectng cabn safety. Under current arworthness regulatons set by FAA, to assess the new arcraft evacuaton capablty, for an arplane carryng more than 44 passengers, the cabn confguraton wth the maxmum seatng capacty s requred to demonstrate that the passengers and crew can be evacuated from arcraft to the ground under smulated emergency condtons wthn 9 seconds by arcraft manufacturers [1]. Complance wth ths rule s demonstrated by carryng out a full-scale evacuaton demonstraton, commonly known as the 9 second certfcaton tral. he certfcaton tral spends too much tme and money, and partcpants are vulnerable to njury. herefore, computer smulaton has become an mportant method to study the characterstcs of passenger emergency evacuaton under the cabn confguraton [2]. he socal force model s a contnuous mcroscopc smulaton model of pedestran movement where every pedestran s treated as an ndvdual. It can explan the pedestran behavor drven by nternal and external factors n the dynamc surroundngs. Under the cabn envronment, the bottleneck phenomenon wll appear n the emergency evacuaton, whch can not be smulated by the cellular automata model and other models [3, 4]. he socal force model can express ths conflct between man and man or between man and obstructon n terms of force, and reflect more detals when the passenger walks. In ths paper, we found the force balance phenomenon when smulatng arcraft evacuaton process based on the orgnal socal force model. Here, force balance phenomenon means that the pedestran can not move and keep stll when gettng through bottlenecks. Socal force model was modfed to be appled to the pedestran evacuaton process under cabn confguraton. Sgnfcant mprovement ncludes the followng aspect: an nfluental factor s added nto the modfed model and an approprate range of the factor s gven. By takng account nto the factor, a seres 1

2 Kun Chen, Ybng Wu, anchun Zou of computer smulatons are conducted to evaluate the mpact on arcraft emergency evacuaton, and the result shows that the modfed socal force model have a good performance on predctng the emergency evacuaton behavor of passengers n arcraft cabn. 2 Analyss of socal force model for arcraft emergency evacuaton 2.1 Socal force model he socal force model descrbes a pedestran s movement wth ntenton to reach certan destnaton at a certan target tme under the acton of multple forces. In ths model, the change of velocty at tme t can be presented by Eq. (1). m ( ) e ( ) v ( ) v t t t dv = m + j + W dt τ j( ) W f f (1) Where, Each of N passengers of mass m lkes to move wth a certan desred speed v n a certan drecton e, and therefore tends to correspondngly adapt hs or her actual velocty v wth a certan characterstc tme τ. he second term n the rght hand of Eq. (1) represent the force between passengers and j. And the last term n the rght hand of Eq. (1) represent the force from the wall W. Self-drven force ( f ). As shown n Fg. 1, the frst term of Eq. (1) represents the motvaton to move forward. Pedestran wll keep certan desred speed wthout changng ther speed vectors dynamcally f there are no stmul of surroundng envronment. Interactve force from other pedestrans (fj). he second term of Eq. (1) represents the nteractons to other passengers. It s assumed that one conflctng pedestran wthn the subject pedestran s range wll generate a crcle force feld that results n repulsve effect to the subject pedestran, whch s called psychologcal force Fs. Besdes, when a large number of passengers gathered n the narrow space, such as the cabn, passengers wll nevtably come nto touch wth surroundng passengers durng the evacuaton leadng to physcal forces ncludng the normal extruson force Nj and the tangental frcton force j. he force s shown n Fg. 2. Repulsve force from the wall (fw). he force from the wall s smlar wth the nteractve force from other pedestrans and the wall may refer to unmovable obstacles such as cabn parttons, seats, etc. he correspondng nteracton force wth the wall s gven by Eq. (7) and s shown n Fg. 3. e () t Desred drecton Fg. 1. Self-drven force. dj j j N j dj Goal Fg. 2. Repulsve force between passenger and j. Fsw f w Nw v w Fg. 3. Force from the wall. ( ) e t v ( ) v t t f (2) () = m τ f = F + N + (3) j s j j ( ) Fs= A exp rj dj / B n (4) j ( d ) N = kg r n (5) j j j j 2

3 SUDY ON AIRCRAF EVACUAION MODELING AND MODEL PARAMEERS BASED ON SOCIAL FORCE f ( ) t =κg r d v t (6) j j j j j { A exp ( r d ) / B kg( r d )} = + n w w w w ( d )( ) κg r v t t w w w w sw w w (7) f = F + N + (8) In Eq. (7), A s the ntensty of the nteracton, and B s the range of the repulsve force. he functon g ( θ ) s zero f the passengers do not touch each other ( θ <, and θ = r - dw ), otherwse, t s equal to the argument θ. he detaled other parameters n the formula can be found n Ref. [5, 6]. 2.2 Problem of socal force model smulatng arcraft emergency evacuaton In the smulaton, accordng to the real cabn confguraton of 737-2, the pedestrans n Anylogc M, can have the state of evacuatng [7]. When pedestrans are evacuatng to the target locaton wth emergency scenaros, the range of average speed and dameter are (.96m/s, 1.25m/s) and (.363m,.469m), respectvely [8]. he key parameters of cabn are shown n able 1, and the partal cabn confguraton s represented n Fg. 4. able 1.he basc parameter selecton of cabn. Cabn confguraton Parameter value Asle wdth Bulkhead wdth Ptch wdth Ext wdth arcraft evacuaton smulaton they can not move through the bulkhead. It s because passengers n the arcraft cabn structure get force balance n a certan poston, that s, the repulsve force from wall toward pedestran and hs/her self-drven force acheve balance, makng the passenger keepng stll. Fg. 5 shows the exstng force of pedestran. f w1 f w2 Fg. 5. he force of passenger. For socal force model calbraton, a hybrd method contanng emprcal trajectory data and smulaton data of pedestran movement n largescale buldng or other scenaros has been used by Helbng[9]. However, the confguraton between large-scale buldng and arcraft cabn s obvously dfferent. he dfferences nclude: Emergency evacuaton route for passengers are relatvely fxed under the arcraft cabn confguraton, and they have less choce, causng the passengers to be gathered together to evacuate; he cabn has many obstacles such as seats, lavatory, dstrct celng and so on. Passengers n cabn would nevtably touch wth the seats when gettng through the asle, whch could not comply wth the phenomenon that pedestrans keep enough dstance from the wall based on the orgnal socal force model [5, 6]. f 3 Study on smulaton model of arcraft emergency evacuaton Fg. 4. Smulaton scene of cabn. he fact shows that the actual bulkhead wdth s enough for passengers to pass, but n the 3.1 Partal evacuaton experment In vew of the problem on the orgnal socal force model, the partal evacuaton experment 3

4 Kun Chen, Ybng Wu, anchun Zou was repeated twce ndependently to observe the passengers characterstcs n the cabn confguraton and obtan the evacuaton data. he partal expermental confguraton s shown n able 2 and Fg. 6. Cabn confguraton Parameter value able 2. he basc parameter value of experment cabn. Asle wdth Bulkhead wdth Ptch wdth Ext wdth Fg. 7. Evacuaton tme for each passenger n one of the experment Partal evacuaton experment Fg. 6. Snapshot of the experment process. he overall layout of the experment cabn s smlar wth the actual cabn, such as the asle wdth, ext wdth, bulkhead wdth and ptch wdth seen n able 2. It ensures that the ease of leavng the seat s lke that of actual cabn, and the cabn's narrow and sealng characterstcs wouldn't be changed. In ths experment, ffty-four 22-year-old unversty students consstng of 3 males and 24 females were randomly selected as partcpants, and the evacuaton process was recorded wth camera. he evacuaton tme for each passenger n one of the experment s shown n Fg. 7. he frst passenger evacuaton tme s 3.28 seconds, and the total evacuaton tme s seconds, whle the mean total evacuaton tme s seconds for the partal evacuaton experment. he range of average speed s (1.15m/s, 1.25m/s) for males and (1.5m/s, 1.15m/s) for females, and dameter s (.349m,.499m), respectvely. All the nformaton are nput nto the Anylogc M as the basc data, and Anylogc M smulaton process are shown n Fg. 8. Evacuaton data acquston (e.g. cabn sze, passenger speed, passenger dameter, etc.) Input to Anylogc M Select a specfc c value Computer smulaton Smulaton data and phenomena output c value data s suffcent? End YES NO Fg. 8. Anylogc M smulaton flow chart. 3.2 Modfed socal force model Record the relevant data and change the value of c Analyss of the modfed socal force model In the orgnal socal force model, the pedestran would try to keep a certan dstance from the wall to prevent the collson durng the walkng 4

5 SUDY ON AIRCRAF EVACUAION MODELING AND MODEL PARAMEERS BASED ON SOCIAL FORCE process, and ths s controlled by the psychologcal repulsve force between the pedestrans and wall. he psychologcal repulsve force formula s presented n Eq. (9). ( ) Fsw = Awexp rw dw / B w n w (9) In Eq. (8), Aw = 1 m/s 2, Bw =.2m, these values were got n the large-scale buldng [5]. Whle the cabn confguraton has a number of obstacles, ndvdual would not have enough dstance to avod obstacles durng evacuaton. It means that the range of repulsve force n cabn confguraton s less than the dstance requred by the socal force model n large-scale buldng. Accordng to the above analyss, consderng the nfluence of relatve dstance on the psychologcal repulsve force based on the orgnal socal force model, we try to modfy the socal force model by reducng the psychologcal repulsve force between pedestrans and wall. hus, relatve dstance nfluence coeffcent c s ntroduced to solve the problem of balance force. We modfy the psychologcal repulsve force of pedestran from the wall, whch can be expressed as: ( ) ( w) Fsw = Awexp rw dw / c* B n w (1) Where c denotes the nfluence between pedestran and wall. In order to clam the effect of c on psychologcal repulsve force, the partal evacuaton experment s modeled and smulated, and smulaton process s seen n Fg. 8. In ths smulaton, when c takes dfferent values, the average, mnmum and maxmum dstrbuton of total evacuaton tme (total) under 1 runs are shown n able 3. able 3. Smulated evacuaton tme under parameter c. c=.56 c=.5 c=.45 c=.42 c=.39 total /Mn (s) total /Mean (s) total /Max (s) SD c=.42, t=11.25s. Fg. 9. Smulaton process of passengers. It can be seen from able 3 that the total evacuaton tme decreases wth the decrease of psychologcal repulsve force due to the reducton of c value. When c.5, the force balance phenomenon n the evacuaton process are obvously elmnated, and the smulated evacuaton tme approxmated to the expermental evacuaton results. However, when c.45, three pedestrans are quckly pass the asle (black crcle n Fg. 9) at the same speed, whch does not match the characterstc that the cabn asle can only accommodate two persons to pass n the actual experment. Wth the c value s reducton, the phenomenon of three people at the same tme passng the man asle s more obvous, so the smaller c value s not approprate Results of the modfed model he smulaton results ndcate that each passenger s evacuaton tme from the seat to the ext s approxmately equal to the real tme when c s (.45,.5). When c =.45, as showed n Fg. 1, the force balance phenomenon dsappeared. Meanwhle, some phenomena arose n the smulaton process (e.g., arch effect and avodng collson) were n lne wth those n classcal artcles [8], whch proved that the modfed model s effectve to some degree. (1)t=3.85s (1)t=25.92s Fg. 1. Smulaton process of passengers. After performng 1 smulatons, the dstrbuton of evacuaton tme s showed n Fg. 5

6 Kun Chen, Ybng Wu, anchun Zou 11 and able 4, and the mean frst evacuaton tme frst s 5.2 seconds, whle the mean total evacuaton tme total s seconds. he mean evacuaton tme s (37.5s, 4.5s), and t s n good agreement wth the expermental results. In Fg. 12, the smulaton evacuaton tme curve agrees wth that of the two experments. he frst eghteen passengers smulaton evacuaton tme was slghtly bgger than the experment data. It s because that there s no one n front of the evacuees when the evacuaton begns, as a result the passenger speed n the real trals s bgger than n smulaton. est number Quanttatve verfcaton 4.1. Smulaton envronment and parameter settngs In ths study, accordng to the evacuaton trals carred out by the Canadan Department of ransportaton, all settngs n our smulaton based on the modfed socal force model, are the same as the trals documented [1]. Fg. 13 s the straght asle cabn confguraton. Passengers n the cabn are dfferent ndvduals nfluenced by gender, body sze and other factors. he passengers were parttoned nto two parts: the men proporton s 64%, whose expected speed s (1.5m/s, 1.35m/s); the proporton of women s 36%, and the average range of expected speed nsde the cabn s (.98 m/s, 1.26 m/s) [11]. he other parameters set n the smulaton model are shown n able total(s) Fg. 11. Evacuaton tme dstrbuton (1 smulatons). Evacuaton tme Smulaton 1 1 st test 2 nd test 5 Mean test data ( sec) Fg. 12. Comparson between the evacuaton experments and the smulaton. able 4. Smulated evacuaton tme. frst (s) total (s) total /Mn total /Mean total /Max SD Fg. 13. Cabn confguraton of the experment. able 5. he ntal settngs for the smulaton Attrbutes settngs otal number of passenger 51 Dameter (.363,.469) Sex dstrbuton Men: 33 Women: 18 (64%) (36%) Ext choce L1: 26 (51%) R1: 25 (49%) Speed dstrbuton n cabn [11] (m s -1 ) Men: (1.5,1.35) Women: (.98,1.26) Pre-evacuaton tme (s) Smulaton results analyss In our smulaton scene, as seen from Fg. 14 and Fg. 15, the results of evacuaton tme obtaned from the two exts agree wth those of the trals n the straght asle for compettve scene conducted by the Canadan Department of ransportaton. However, the evacuaton tme obtaned from RI ext was slghtly smaller than the data from trals. he real reason s that the LI s slghtly bgger than RI n cabn smulator n the 6

7 SUDY ON AIRCRAF EVACUAION MODELING AND MODEL PARAMEERS BASED ON SOCIAL FORCE real trals, whch may lead that passengers need to reduce ther movng speed to evacuate safely through RI ext. Results based on modfed socal force model are smlar to the smulaton data based on VacateAr model and the actual test [12], as shown n Fg. 16. he phenomena of avodng collson appeared n the evacuaton process, whch ndcates that the smulaton model can accurately reflect the actual evacuaton process, as shown n Fg. 17. he modfed socal force model n ths paper s effectve n smulatng the arcraft emergency evacuaton. Evacuaton tme (sec) day1_li day4_li day6_li day8_li smulaton_li Fg. 14. Evacuaton tme of lght, straght asle, compettve scenaro (ext through R1, based on 1 smulatons). Evacuaton tme(sec) day1_ri day4_ri day6_ri day8_ri smulaton_ri Fg. 15. Evacuaton tme of lght, straght asle, compettve scenaro (ext through L1, based on 1 smulatons). Evacuaton tme(sec) est_ri VacateAr_RI Smulaton_RI (1) Evacuaton tme (ext through R1, based on 1 smulatons). Evacuaton tme(sec) est_li VacateAr_LI 5 Smulaton_LI (2) Evacuaton tme (ext through L1, based on 1 smulatons). Fg. 16. Comparson of the smulaton results of the model and VacateAr. (1) t=6.36s. (2) t=21.82s. Fg. 17. Smulaton state at the dfferent tme. 5. Conclusons hs study makes two man contrbutons. Frstly, we fnd out force balance phenomenon when smulatng arcraft emergency evacuaton based on the orgnal socal force model. Secondly, we further develop the socal force model and more smulatons are conducted. he results show that the ntroducton of the relatve dstance nfluence coeffcent c can effectvely reduce the psychologcal repulson force n the cabn confguraton. And when the value of c s (.45,.5), each passenger s evacuaton tme from hs/her seat to the ext s n good agreement wth the results n the experment, whch can truly reflect the actual movement characterstcs of personnel n the arcraft cabn confguraton. herefore, the smulaton model of arcraft emergency evacuaton establshed n ths study s reasonable and effectve. 7

8 Kun Chen, Ybng Wu, anchun Zou References [1] Code of Federal Regulatons. Aeronautcs and Space. Part 25 Arworthness Standards: ransport Category Aeroplanes, Offce of the General Regster, Washngton, DC, USA, 28. [2] Martínezval R. Computer model for numercal smulaton of emergency evacuaton of transport aeroplanes, Aeronautcal Journal, Vol. 114, No. 1162, pp , 21. [3] You L, Hu J, Gu M, et al. he smulaton and analyss of small group effect n crowd evacuaton. Physcs Letters A, Vol. 38, No, 41, pp , 216. [4] Cao S, Song W, Lv W. Modelng pedestran evacuaton wth guders based on a mult-grd model. Physcs Letters A, Vol. 38, No. 4, pp , 216. [5] Helbng D, Molnár P. Socal force model for pedestran dynamcs. Physcal Revew E Statstcal Physcs Plasmas Fluds & Related Interdscplnary opcs, Vol. 51, No. 5, pp , [6] Helbng D, Farkas I, Vcsek. Smulatng dynamcal features of escape panc. Nature, Vol. 47, No. 683, pp , 2. [7] X. Song, Z. Zhang, G. Peng, G. Sh, Effect of authorty fgures for pedestran evacuaton at metro statons, Phys. A, Stat. Mech. Appl. 465 (217) Song X, Zhang Z, Peng G, et al. Effect of authorty fgures for pedestran evacuaton at metro statons. Physca A Statstcal Mechancs & Its Applcatons, Vol. 465, pp , 216. [8] Zhang Q, Q H, Zhao G, et al. Performance Smulaton of Evacuaton Procedures n Post-Crash Arcraft Fres. Journal of Arcraft, Vol. 51, No. 3, pp , 214. [9] Helbng D, Shukla P K. Specfcaton of the Socal Force Pedestran Model by Evolutonary Adjustment to Vdeo rackng Data. Advances n Complex Systems, Vol. 1, No. 2, pp , 27. [1] Mur H, Cobbett A. Arcraft evacuaton tests-an ntal assessment of the nfluence of varous asle confguratons and lghtng condtons under dfferent evacuaton scenaros. Canada, ransportaton Development Centre, [11] Hedo J M, Martnezval R. Assessment of Narrow- Body ransport Arplane Evacuaton by Numercal Smulaton. Journal of Arcraft, Vol. 48, No. 5, pp , 211. [12] Xue Z, Bloebaum, C. A partcle swarm optmzatonbased arcraft evacuaton smulaton model VacateAr. Proceedngs of 46th AIAA Aerospace Scences Meetng, Reno, Nevada, USA, January 28. Contact Author Emal Address Correspondence author: Ybng Wu E-mal address: wybcauc@126.com Copyrght Statement he authors confrm that they, and/or ther company or organzaton, hold copyrght on all of the orgnal materal ncluded n ths paper. he authors also confrm that they have obtaned permsson, from the copyrght holder of any thrd party materal ncluded n ths paper, to publsh t as part of ther paper. he authors confrm that they gve permsson, or have obtaned permsson from the copyrght holder of ths paper, for the publcaton and dstrbuton of ths paper as part of the ICAS proceedngs or as ndvdual off-prnts from the proceedngs. 8