COMPARISON OF TWO MODELS FOR HUMAN EVACUATING SIMULATION IN LARGE BUILDING SPACES Bn Zhao 1, 2, He Xao 1, Yue Wang 1, Yuebao Wang 1 1 Department of Buldng Scence and Technology, Tsnghua Unversty, Bejng 100084, Chna 2 Tsnghua-U Penn. Smulaton Center (T C Chan center) ABSTRACT Ths paper presents the smulated results of human evacuaton n a large space buldng. Two dfferent models, Cellular Automata (CA) model and socal force (SF) model are adopted. The smulated evacuaton tme and man characterstcs of human evacuaton are smulated and these results by the two models are compared. To check the practcablty of the models for actual complcated cases, the smulatng tme s also compared. The results denote that both the two models can smulate the arch and faster-s-slower effect for human evacuaton. It also could be found that the CA model s easly analyzed and possess fewer CPU tme, whle the SF model s much easer to be expanded to consder more complcated human behavor models. KEYWORDS Human behavor, Smulaton, Cellular Automata (CA) model, Socal force model ntroducton INTRODUCTION Durng the last decade, the nvestgaton of vehcle streams by means of experments and models has captured the nterest of many scholars. The statstcal physcs or flud-dynamcs method was used to reproduce the mechansms behnd many observed phenomena such as dfferent forms of congeston and jammng. Those dverse phenomena between fluds, granular meda, vehcles and pedestrans were owng to dstnct laws and drvng terms. In classcal drven many-partcle system, there are mcroscopc, molecular dynamc models, lattce gas automata or cellular automata model, gas models and fluddynamc models (Helbng 2001). Whle n selfdrven many-partcle system, the drvng force s not of external, but s assocated wth each sngle partcle, an nternal force, whch can represent the moton and mentalty characterstcs of human bengs. Approxmately, the human behavor n conflct stuatons s guded by socal felds or socal forces (Lewn 1951), an dea that has been put nto mathematcal terms by Helbng (1995). researchers study the pedestran flow wth the smlar methods n traffc flow feld. Very recently, Song et al. (2006) have studed dynamcal features of fre escape panc by applyng the mproved cellular automata model. They have shown the characterstc features of escape pancs: Archng and faster s slower of people occur at ext. In most of the tme, human behavor s relaxed and normal, dfferent from the escape pancs. So t s essental to research those features n large buldng space n order to nstruct the archtects to desgn buldngs more optmzed and reasonable, and avod casualty n emergency cases. In ths paper, we learn to study the human evacuaton features n a large-space buldng. We apply the pedestran mproved cellular automata model (CA) and socal force model (SF) to smulate the crowd flow n a large-space buldng. We calculate the evacuaton tme and compare the two models result. We also smulate the man characterstcs of human evacuaton, such as arch and faster s slower effect, and draw the compared conclusons of two pedestran models. MODELS Cellular automata (CA) model Cellular automata (CA) model s a specal manypartcle model n whch the topologcal structure s fxed. It s wdely appled n both natural scence and socal scence. In ths paper, a large-scale buldng based on genetc cellular automata s establshed. Cells are used to represent people n the buldng, who has the capablty of self-learnng and are affected by the neghborng ones. The topologcal structure of CA n ths paper s a two-dmensonal square lattce, whch the neghborng relatonshp can be consdered as the Von Neunann style (Fg. 1.). Whle the pedestran flow dynamcs s also closely connected wth the traffc stream. So many - 805 -
Fg.1. (Zhou et al. 1999) (a-c) shows the three styles of the neghborng relatonshp. The dark black lattce s the center cell and the gray ones are neghbors. The center cell can only have the nteracton wth ther neghbors. confguraton (3-b): θ = 0.1,V = v, for confguraton (3-c): θ = 0.5,V = v. The two-dmensonal smulated room s represented by the square of L L stes where L s the length of the room. The room was dvded nto average cells 2 wth the square of 0.5 0.5m whch represents an adult. The room has a sngle ext wth wdth W. We assume that people are randomly dstrbuted, ntallyt = 0, over the square space of the room. At the next tme t > 0, all people n the room move toward the ext. We defne the evacuated speed v as the desred velocty, whle the Δ t = 0. 5 v as the tme-step. Update the dstrbutng at every tme step and export the map. People decson ncludes two steps: frst, each person makes a preparatory choce of the neghborng cells by the dstance force law (Song et al.2006.), they chose the lattce among the neghbors and go nto t whch has the smallest dstance to the ext. Second, each person judges and modfes ther prmary decson. If there are no other people chose the same lattce, ths person can walk nto the cell n the next tme step. But f there are more than one person make the same choce, we should calculate ther frcton and repulson probablty, then chose the rght person enter the target based on our random functon. Fg.2. ndcates all possble confguratons of repulson. The black dots and shadows ndcate walker and wall. The repulson probablty of the walker correspondng to each confguraton s gven by the followng equaton (Song et al.2006.): 1 e r = 1 + e αv αv (1) Where α s the rgdty coeffcent whch generally reflects the possble njury between people and people or people and wall. For confguraton (2- a): α = 1, for confguraton (2-b): α = 2. Fg.3. ndcates all possble confguratons of frcton. The frcton probablty of the walker correspondng to each confguraton s gven by the followng equaton (Song et al.2006.): f = θ V (2) Where θ s the frcton coeffcent whch reflects frcton degree between people and people or people and wall. In addton, V s the relatve velocty. For confguraton (3-a): θ = 0.1,V = 2v, for Fg.2. (Song et al.2006.) ndcates two possble confguratons of repulson. Fg.(2-a) llustrates the nteracton between several people. Fg.(2-b) llustrates the nteracton between people and wall. Fg.3. (Song et al.2006.) ndcates three possble confguratons of frcton. Fg. (3-a) llustrates movng vs-à-vs. Fg. (3-b) llustrates the quescence and movement. Fg. (3-c) llustrates the people and wall. Socal force (SF) model CA model focus on the partcle character of people, but for relable smulatons of pedestran crowds we do not need to know the moton character of a certan person, we pay more attenton on the whole crowd, the flud character nstead. On the other sde, human behavor often seems to be chaotc, rregular, and unpredctable, one s own mentalty and the nteracton between partcle bodes make more effect than external envronment, so those can not be well smulated by CA model. Lewn(1951) suggests an approach for modelng human behavoral changes. Accordng to hs dea behavoral changes are guded by so-called socal feld or socal forces. In ths study, we use the SF model establshed by Helbng (2000). Accordng to hs dea, a mxture of soco-psychologcal and physcal forces nfluences the behavor n a crowd: The mass of pedestran s m, movng wth a certan desred velocty v 0, whch has a certan drecton and a certan characterstc tme τ. 0 e, - 806 -
The nteracton force f j and f W whch represent the velocty-dependent dstance to other pedestran j and walls W. So n mathematcal terms, the change of velocty n tme t s then gven by the equaton: dv m dt = m 0 0 v e ( t) v ( t) τ + fj + j Then Helbng brngs the concept psychologcal tendency, and puts f j, fw nto mathematcal terms based on the defnton of body force and sldng frcton force. The change of poston r (t) s gven by the equaton v ( t) = dr dt. So we can calculate the poston r (t) by the twce-defnte ntegral of acceleraton. RESULTS COMPARISON Both two models smulate the same evacuaton process n a sngle-ext, 15 m by 15 m room. The wdth of the door s1 m. There are 196 pedestrans n 2 the room. The cell of the room s 0.5 0.5m. W f W (3) 4 130.39 93.96 4.5 135.20 99.02 5 136.03 108.95 Although the evacuaton tme of two models s dfferent, the typcal stages of the process are smlar. Fg.4. and Fg.5.denotes the patterns formed by walkers gong to the ext at four dfferent stages. The desred velocty s1 m / s.at (a) the begnnng stage ( t = 0 ), all walkers are dstrbuted and get the basc nformaton of the room, lke the locaton of obstacles and door. At (b) the archng stage ( 0 < t < 25 ), archng of walkers occurs snce only a few walkers go, throughout the ext, outsde the hall and most walkers cannot go out from the ext. At (c) the mddle stage ( 25 < t < 100 ), the archng decays and most of pedestrans go out of the ext. At (d) the end stage ( t > 100 ), the remanng walkers go out of the ext wthout chokng. Evacuaton tme Table 1.denotes the evacuaton tme based on the dfferent desred velocty of two models. Both of models consder that the pedestran can evacuate smoothly wthn two and a half mnute n our case, but the evacuaton tme calculated by SF s obvously faster than CA. Especally the desred velocty s hgher. The result depends on the dfferent features of two models. In the CA model, we consder more about the nteracton between cells, whle n the SF model, we pay more attenton to the flud dynamc characterstc of the pedestran. Table 1. The evacuaton tme of two models based on dfferent desred velocty Desred Evacuaton Tme( s ) Velocty( m / s ) CA model SF model Fg.4. ndcates the four typcal stages of CA model: the begnnng stage, the archng stage, the mddle stage and the endng stage. 0.5 122.12 130.12 1 114.10 105.14 1.5 115.34 88.82 2 118.61 79.97 2.5 120.18 82.10 3 125.42 84.96 3.5 126.82 92.19-807 -
flow, and reduces the effcency of leavng. But the speed threshold of two models s dfferent. The turnng pont of CA model s 1 m / s n round numbers, half of SF s. Fg.7. compares the evacuaton tme of two models and llustrates faster-s-slower effect. The upper lne s CA model and the nether one s SF model. Fg.5.ndcates the four typcal stages of SF model: the begnnng stage, the archng stage, the mddle stage and the endng stage. Arch effect The result denotes that both the two models could predct the arch effect reproduced at the ext, as shown n Fg.6. Because all pedestrans move towards the ext, t becomes a bottleneck of pedestran flow. The archng phenomenon of both the models s evdent. Fg.6. ndcates the archng phenomenon of the two models. Faster s slower effect If the desred velocty s small, along wth ts ncrease, the evacuaton tme wll decrease. However, both two models gve a same smulaton result that tryng to move faster above a speed threshold leads to longer evacuaton tme. Fg.7 llustrates the fasters-slower phenomenon reproduced by CA and SF as a comparson. The evacuaton tme of two models shown here does not decrease monotonously wth the ncrease of desred velocty, but behave a parabola shape nstead. Hgher desred velocty ncreases the nteracton between people, blocks the pedestran Predctng tme We use a same personal computer to calculate all the cases, the CA model needs 5 seconds to fnsh the calculaton approxmately, compares 85 seconds of SF model. So the CA model consumes less CPUtme than SF. The man reason s that regulaton of SF model s more complex, t should calculate whole people n the room durng a tme-step, whle the CA model just consders the neghborng ones. RESULTS COMPARISON Dscusson The current CA and SF models can evaluate the major nteractons between pedestrans, such as frcton, repulson and the dstance force. They use the randomzaton of probablty or the flud dynamc features of pedestran to smulate evacuaton case n realty. However both the models have obvous defcences. One hand, the parameters of the model should be researched over agan. We should desgn a seres of experment to test the human evacuaton behavor so as to confrm the certan parameters. On the other hand, we are now mprovng the arthmetc and rules and callng for complementary data and addtonal vdeo materal on evacuaton to test our model, consder mult-ext, obstacles and threedmenson cases, and mplement more complex strateges and nteractons. Concluson In ths paper, we use the mproved CA model to smulate an evacuaton case n a large-space twodmensonal room and compare ts performance wth the SF model. Despte the dfferent types of rules, both of the models can smulate the arch and faster-s-slower effect. Consderng the smple rules, the CA model s easly analyzed and possessed - 808 -
fewer CPU tmes, whle the SF model s much easer to be expanded to consder more complcated human behavor models. ACKNOWLEDGEMENT Ths work s supported by the Student Research Tranng (SRT) project of Tsnghua Unversty (071S0030). REFERENCE Drk Helbng. 1995. Socal force model for pedestran dynamcs, PHYSICAL REVIEW E, Vol 51, pp4282-4286 Drk Helbng. 2000. Smulatng Dynamcal Features of Escape Panc, arxv: cond-mat/0009448 v1 Drk Helbng. 2001. Traffc and related self-drven many-partcle systems, REVIEWS OF MODERN PHYSICS, Vol 73, pp1067-1069 Lewn K. 1951. Feld Theory n Socal Scence (Harper, New York) Song WG. Yu YF. Wang BH. Fan WC. 2006 Evacuaton behavors at ext n CA model wth force essentals: A comparson wth socal force model, PHYSICA A, Vol 37, pp658-666 Zhou CH. Sun ZL. Xe YC. 1999. Research of Cellular Automata n Geography. Chna: Chnese ScentfcPress - 809 -