A Cellular Automata-Based Simulation Tool for Real Fire Accident Prevention

Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 3058241, 12 pages https://doi.org/10.1155/2018/3058241

Research Article A Cellular Automata-Based Simulation Tool for Real Fire Accident Prevention

Jacek M. Czerniak ,1 Hubert Zarzycki,2 Aukasz Apiecionek,1 WiesBaw Palczewski,3 and Piotr Kardasz3,4,5

1 Artifcial Intelligence and Robotics Laboratory (AIRlab), Casimir the Great University in Bydgoszcz, Ul.Chodkiewicza30,85-064Bydgoszcz,Poland 2University of Information Technology and Management Copernicus, Ul. Inowrocławska 56, 53-648 Wrocław, Poland 3College of Management Edukacja, Department of Computer Science and Quantitative Methods, Ul. Krakowska 56-62, 50-425 Wrocław, Poland 4Cluster of Research, Development and Innovation, Ul. Piłsudskiego 74, 50-020 Wrocław, Poland 5Foundation for Research, Development and Innovation, Ul. Legnicka 65, 54-206 Wrocław, Poland

Correspondence should be addressed to Jacek M. Czerniak; [email protected]

Received 17 May 2017; Accepted 15 November 2017; Published 14 February 2018

Academic Editor: Andrzej Swierniak

Copyright © 2018 Jacek M. Czerniak et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Many serious real-life problems could be simulated using cellular automata theory. Tere were a lot of fres in public places which kill many people. Proposed method, called Cellular Automata Evaluation (CAEva in short), is using cellular automata theory and could be used for checking buildings conditions for fre accident. Te tests performed on real accident showed that an appropriately confgured program allows obtaining a realistic simulation of human evacuation. Te authors analyze some real accidents and proved that CAEva method appears as a very promising solution, especially in the cases of building renovations or temporary unavailability of escape routes.

1. Introduction applied in many real-life felds, such as biology, physics, and mathematics and in various felds of IT, such as cryptography Cellular automata are used by some of the IT branches, or computer graphics [6, 7]. including the feld of artifcial intelligence. Tey consist of a network of cells, each of which is distinguished by some 1.1. Application of Cellular Automata. Cellular automata have specifcstateandasetofrules.Techangeofthecurrent been applied in practice, for example, in simulation of the stateofagivencellistheoutcomeoftheabove-mentioned street trafc, where specifcally defned cellular automaton properties and interrelations with the neighboring cells [1, controls the trafc [8–10]. Te vehicle fow is managed 2]. Te theory of cellular automata was frst introduced basically at the specifc segment of a given trafc inten- by an American scientist of Hungarian descent, John von sity [11]. Tis applies, for instance, to the trafc intensity Neumann. He demonstrated, among others, that even simple control on highways of the Ruhr in Germany. Te moni- machines show an ability to reproduce, which was until that toring centers designed exclusively for that purpose collect time regarded as a fundamental feature of living organisms [3, the data from selected sections of the highways [12–16]. 4]. For many years cellular automata had been subject to theo- Te information thus obtained is analyzed and used for retical studies only. With the development of computers and preparing short-time simulations of the trafc intensity by sofware, optimizing methods based on this approach have means of cellular automata. Te projects websites publish been more and more frequently studied and implemented the statistical information about the studies performed on in practice [5]. Due to their versatility, cellular automata are the behavior of drivers who were prewarned about possible 2 Mathematical Problems in Engineering

Figure 1: Types of grids: 1D, 2D, and 3D [source: [14]].

trafcproblems[17]thatmightoccuroverseveralfollowing (i) the size of the space which depends on the magnitude hours [6]. Another example of cellular automata application of the studied problem, the examples of which are is demographic simulations for a given region. Te aim of showninFigure1(grids1D,2D,and3D); such simulations is to generate a model showing the size (ii) the provision of regularity, which requires the grid to of the population at a given area in a form of a map of beflledentirelywithidenticalcells; the forecasted population density. Such simulations can be basedonthewell-known“GameofLife”[18].Byintroducing (iii) the number of neighbors (dependent on both above- some modifcation to the algorithm, it is possible to monitor mentioned factors). the behavior of the surrounding cells [7]. Other examples In this article, the authors present the possibility of simulating of cellular automata implementations include image process- real fre accident to prevent huge fre accidents. For this ing, generation of textures, simulation of waves, wind, and purpose authors used Cellular Automata Evaluation method, people evacuation process as well as a simulation program, CAEva in short. Tis paper has following organization. Sec- developed for the purpose of this study [19–23]. Te aim tion 2 presents the idea of forecasting the fre hazard, two real of the proposed algorithm is to generate the simulations of accidents’ description, and CAEva simulation method with patterns of human escape from the building on fre with a their boundary conditions and transfer function. Section 3 given number of exits and fre sources [24–27]. presents the experiment results when the mentioned two real fre accidents were simulated. Finally Section 4 consists of 1.2. Te Grid of Cellular Automata. Agridoradiscrete fnal conclusions. space, where cellular automata evolution takes place, consists of a set of identical cells [26, 30, 31]. Each of the cells 2. Forecasting the Fire Hazard is surrounded by the same number of neighbors and can assume the same number of states [32–35]. Tere are three 2.1. Fire Accidents in Public Places. Fires are one of the structural factors which signifcantly infuence the grid form most uncontrollable calamities, especially when they happen and, as a consequence, the behavior of the entire cellular indoors. Tus, regardless of the edifces function whether automaton [8, 17, 23, 32–35]: it is a residential, business, or any other kind of building, Mathematical Problems in Engineering 3

Table 1: Fire accidents in public places.

Name Year Fatalities Injuries Stage Stage Study Club fre 1929 22 50 Cocoanut Grove fre 1942 492 166 Karlslust dance hall fre 1947 80–88 150 Stardust fre 1981 48 214 Alcal 20 nightclub fre 1983 82 27 Ozone Disco Club fre 1996 162 95 Bar Gothenburg discothque fre 1998 63 213 Volendam New Years fre 2001 14 241 Canecmo Mineiro nightclub fre 2001 7 197 WC Utopa nightclub fre 2002 25 100 Te Station nightclub fre 2003 100 230 Wuwang Club fre 2008 43 88 Santika Club fre 2009 66 222 Lame Horse fre 2009 156 ≤160 Figure 2: Kiss nightclub scheme [28]. Kiss nightclub fre 2013 231 168

Street, near Park Square, in downtown Boston, Massachusetts its design must comply with fre regulations. Te width of [29, 37]. According to Prohibition, it was very popular in corridors, number of emergency exits, and the permissible the 1920s. Te building structure was single-storey, with a number of people staying inside at the same time have a basement beneath. Te basement consists of a bar, kitchen, grave impact on the safety of its users. Simple presence of the freezers, and storage areas. Te frst foor contained a large doorsonfoorplanisnotsufcient;theyhavetobeopen.In dining room area and ballroom with a bandstand, along with many cases the high number of casualties stemmed from the several bar areas separate from the ballroom. Te dining emergency exit doors being locked. In the past decades there room also had a retractable roof for use during warm weather have been a number of disastrous fres in public places like to allow a view of the moon and stars. Te main entrance restaurants and nightclubs. Table 1 presents some examples to the Cocoanut Grove was via a revolving door on the of such accidents and lists the numbers of victims. As you Piedmont Street side of the building. On Saturday, November can see from the data provided, there have been many fres 28, 1942, there was a very large fre accident. During that in entertainment clubs over the years, causing many injuries, evening, a busboy had been ordered to fx a light bulb located irrespective of whether they occurred decades ago (1942) or at the top of an artifcial palm tree in the corner of the in recent times (2013). basement bar. A moment later decorations started burning. As other furnishings ignited, a freball of fame and toxic 2.2. Te Case of Kiss Nightclub Fire Accident. Te event called gas raced across the room towards the stairs. Te revolving “Aglomerados” began on Saturday, 26 January 2013, at 23:00 doorbecamejammedduetothecrushofpanickedpatrons. UTC at the Kiss nightclub. In the club there were students Lots of people stuck in fre. It was later estimated that more of six universities and people from technical courses at the than1000personswereinsidetheGroveatthetimeof Federal University of Santa Maria [36]. In the early morning the fre. Te fnal death count established by Commissioner hours of the following day, confagration took place while Reilly was 490 dead and 166 injured, but the number of the students were holding a freshers’ ball and a panic broke injured people was a count of those treated at a hospital and out. Witnesses testifed that the cause of the fre was either later released while many people were injured but did not afareoffreworkslitbythemembersofamusicband seek hospitalization. Figure 3 presented the scheme of the playing during the party. Te fre caused the roof to collapse Cocoanut Grove. in several parts of the building, trapping many people inside. Firefghters found numbers of bodies in the club’s bathroom. 2.4. CAEva Simulation Method. CAEva simulation method At the moment of confagration there were about 2,000 is a program prepared for the purpose of rehearsing the people inside the club. Tis number doubles the buildings fre escape scenarios in buildings [7]. It helps to compare maximum capacity of 1,000. At least 231 people died and various simulation results and to draw suitable conclusions. hundreds more were injured in this disaster. Many fatalities Te program has been implemented in the C++Builder were apparently caused by smoke inhalation, while other environment, which is an object-oriented programming tool victims were trampled in the rush for the exits. Figure 2 in Windows environment and is available free of charge at the presents the scheme of the Kiss nightclub. AIRlab web site [38]. Te program allows drawing a board of any size, including the plan of a single-storey building, to 2.3. Te Cocoanut Grove Fire Accident. Te Cocoanut Grove locate people inside and to indicate the source of fre. Te was a restaurant built in 1927 and located at 17 Piedmont board consists of a grid of cells. Each cell can assume only 4 Mathematical Problems in Engineering

(v) the attempt of the motion of the cell in “person” state to the cell in “fre” state increases the number of burns of the initiating cell. A special case is an attempt of the motion from the corner of the board. A rebound in three initiating directions does not change the state of a cell, but it may change it change as a result of an attempt of the motion in the consecutive fve directions. It should be also noted that motion rules and conditions apply to the cells in the “person” state as well as in the “fre” state. Te felds to which the motion cannot be executed arethecellsinthe“wall”state.Reboundconditionsoccur Figure 3: Te Cocoanut Grove scheme [29]. at the edge of the cellular automata grid, which constitutes a barrier from which moving virtual objects rebound (in visual sense). Tose conditions are used to simulate encased Empty empirical spaces.

2.6. Transfer Function. Te evolution of cellular automata takes place in discrete time determining consecutive processing cycles. Each discrete moment � = 0, 1, 2, . . . , � is used for Person Person Fire updating the state of individual cells; thus each automaton is on ﬁre a dynamic object over time. In every iteration, the transfer function can process (calculate) all the cells in the grid one by one according to specifc rules. Each processed cell receives its new state based on the calculation of its current state and states of the neighboring cells. Transfer rules and the Wall state space, as well as the defned neighborhood, are inherent elements of the cellular automata evolution process. Once Figure 4: Diagram of cell states. executed, the program displays main screen ready to draw the building plan and to arrange individual elements inside. Once the board is drawn and all the components are arranged, the usercanstarttheconfgurationoffreandpeopleparameters one of the following states: fre, wall, person, person on fre, and setting of the group efect. Fire parameters are as follows: oranemptycell.Figure4presentsthediagramofstatesfora single cell in the fre simulation automaton. (i) fre goes out alone if the number of neighbors is less than 1, 2.5. Boundary Conditions. Te discrete space, where various (ii) fre goes out from overpopulation if the number of evolutions of cellular automata take place, includes a d- neighbors is more than 3, dimensional, theoretically infnite grid. As this kind of grid cannot be implemented into computer application, it is (iii) new fre is generated when the number of neighbors represented in a form of a limited table. Terefore, it is is at least 3, necessary to set boundary conditions at the grid borders, that (iv) fre is generated when the number of neighbors is less is, at the table limits. Te set of basic conditions is shown in than or equal to 4. Parameters concerning people are Figure 5. Tese conditions are analogous afer grid rotation of as follows: 90 degrees, so further arrangements were skipped as trivial. (v) probability that a person goes towards the exit in Te following rules were used for the simulation of the cell default state is 50, motion in the wall direction: (vi) number of burns resulting in death is 5, (i) straight motion: the state of the cell remains un- (vii) group efect is On/Of. changed, (ii) diagonal motion: the state of the cell changes into an Tere are points in the screen simulating people escaping empty one, since the angle of incidence equals the towards the exit and the propagating fre. All the events are angleofrebound,thestateofthecellinthemirror recorded in the table of statistics. Tey include the number image shall change into the state of the cell which of people remaining within the board, saved from and died initiated the motion, in the fre or by crushing [39, 40]. Tat data obtained enable drawing conclusions from the experiments [41, 42]. (iii) motion conditions: (iv) motion is possible if the target cell is in the empty 2.7. Implementation of OFN Notation to Fuzzy Observation state. Otherwise, the cell will not change its state, of Real Fire Accident. Te use of ordered fuzzy numbers in Mathematical Problems in Engineering 5

nn+ 1 nn+ 1 nn+ 1

Figure 5: Boundary conditions (rebound from the grid edges).

is possible to perform arithmetic operations described in NxＪＩＭＣＮＣＰ？ = [3, 4, 5, 5] x literature [47, 55]: 0 345 (i) addition: �+�=(�+�,�+ℎ)=� ��→[�(0) +�(0) ,�(1) +�(1) ,�(1) +ℎ(1) ,�(0) (1) +ℎ(0)], 5 ] �=��=(��,��) = [5, 5, 5, 6] (ii) scalar multiplication: y ,7,7,6 6 N ��→[��(0) , �� (1) , �� (1) , �� (0)], (2) = [7 yＪＩＭＣＮＣＰ？ N 7 (iii) subtraction: �−�=(�−�,�−ℎ)=� ？Ａ；ＮＣＰ？ yＨ

N ��→[�(0) −�(0) ,�(1) −�(1) ,�(1) −ℎ(1) ,�(0) (3) −ℎ(0)],

N = [5, 4, 3, 3] xＨ？Ａ；ＮＣＰ？ (iv) multiplication: �∗�=(�∗�,�∗ℎ)=� Figure 6: Example of move in simulation algorithm. ��→[�(0) ∗�(0) ,�(1) ∗�(1) ,�(1) ∗ℎ(1) ,�(0) (4) ∗ℎ(0)], cellular automation seems to be a natural step. Tere are (v) division: �/� = (�/�, �/ℎ) = � many notations of fuzzy numbers that are introduced by � (0) � (1) � (1) � (0) Zadeh [43], Klir [44], Dubois et al. [45], and Kłopotek et ��→[ , , , ]. al. [23, 46, 47], among others. Since we have in this case a � (0) � (1) ℎ (1) ℎ (0) (5) two-dimensional apparatus in which Moore’s neighborhood is additionally used, there are eight available moves from cells A given set of possible moves in Moore’s neighborhood from ��, � � �� . An example of this situation is shown in Figure 6. the cell �,� to cell (�,�)� is shown in Figure 9. Depending on Tere is a part of the neighborhood that is closer to the settings of the algorithm, the trafc determinant can be the exit, and the other part closer to the group of cells in the human state [20, 48]. Tus, there are two possible sets (i) going towards the nearest exit, of movements for this cell in question, depending on the (ii) getting the nearest gathering of people. determinant [27, 49, 50]. Since each of the sets is a four- element, then the notation of fuzzy numbers called ordered Te determinant will be related to the fuzzy number in the fuzzy numbers introduced by Kosinskí is suitable for its OFN notation [46]. description [51, 52]. Afer the death of the creator OFNs (��, ��) in some works are also called Kosinski’ś Fuzzy Numbers Defnition 1. Let be two pairs of fuzzy numbers. [23, 47, 48, 53, 54]. In this notation, the fuzzy number A in Directing will be positive for a subset of moves closer to the general has the shape of a trapezoid described by coordinates indicated determinant: [��(0),��(1),��(1), ��(0)] �� [� − 1, �, � + 1, � + 1] , , which is presented in Figure 8. positive Arrow in Figure 8 shows directing that refects the order (6) �� [�−1,�−1,�−1,�]. of the individual coordinates. On such fuzzy numbers, it positive 6 Mathematical Problems in Engineering

Table 2: Results of simulation with CAEva method for the Kiss nightclub.

Group efect No Yes Number of people Probabilityofpeopleheadingtowardstheexit 25,00% 50,00% 75,00% 25,00% 50,00% 75,00% Died 649 471 325 506 455 428 Trampled 127 196 208 323 250 196 Saved from fre 224 333 467 171 295 376

Table 3: A comparison of the CAEva method results with actual numbers for the Kiss nightclub.

Group efect No Yes Relative error [%] Probabilityofpeopleheadingtowardstheexit 25,00% 50,00% 75,00% 25,00% 50,00% 75,00% Died 239 68 5 91 18 17 Trampled 83 64 5 281 221 58 Saved from fre 58 26 2 79 54 11

A pair of coordinates that are more distant from the determi- (ii) distribution of a defned number of people inside the nant will be denoted by negative directing: building at specifed places, �� [�+1,�,�−1,�−1] , (iii) setting the fre parameters: negative (7) �� [�+1,�+1,�+1,�]. (a) the fre goes out alone if there are no neighbors, negative (b)thefregoesoutbecauseofoverpopulationif A subset of cells to which further motion can be determined there are more than 3 neighbors, is a pair of fuzzy numbers satisfying the following rules: (c) new fre is generated when there are at least 3 neighbors, but not more than 4, IF �� ∗�� is positive THEN �� = �� positive ��negative = �� ∗ positive ELSE negative IF positive (iv) setting of the parameters for people (live cells): �� is positive THEN �� = �� ELSE ��negative = �� . positive (a) number of burns resulting in death is by default negative set to 5, � � From this set of pairs described (� ,� ), which represents � � (v)locationofthefresourceontheboard, the four possible moves in the next evolution of the cellular automaton, one pair of coordinates is drawn. By default, the (vi) specifying the probability of people heading towards felds in which the trafc is impossible must be eliminated the exit (three options): 25%, 50%, and 75%, from the list. If no movement is possible in any of the four (vii) specifying whether people move towards the exit in cells, the cell state will not change. Tis symbolizes a situation groups (two options): with or without a group efect. in which a person remains motionless. Figure 10 presents Kiss nightclub schema before the simulation process was started. Te red squares represent fre 3. The Experiment with CAEva Method while the blue ones represent people. Figure 11 presents Kiss nightclub schema afer completing the simulation. Figure 12 Te authors launched a simulation of the Kiss nightclub presents Cocoanut Grove schema before the simulation pro- scenario in CAEva program. Tey placed people inside and cess was started. Te red squares represent fre while the blue set the fre. Te building is comprised of seven rooms and ones represent people. Figure 13 presents Cocoanut Grove there was only one exit. Te blue points mark people and schema afer completing the simulation. Te simulation was the red ones fre. Several tests were performed based on this made two hundred times for each condition; there were schemeandtheassumedconditionswereasfollows:theaim six conditions which give 1200 simulations for one fre of the test was to simulate a fre of the building, based on cer- accident. Table 2 presents the average results of the performed tain rules and relations. Setting of the following parameters, simulation. Taking into account the real data concerning the selection of versions, and inherent rules altogether make up number of fatalities in the Kiss nightclub fre, the outcome an environment which afect the mortality rate. Te variables which was closest to the actual death toll was achieved using were 75% probability of people going towards the exit and with (i) the layout of the building foors, including the num- groupefectof.Table3comparestheaverageresultswithreal ber and location of doors, numbers. Mathematical Problems in Engineering 7

Table 4: Results of simulation with CAEva method for the Cocoanut Grove nightclub.

Table 5: A comparison of the CAEva method results with actual numbers for the Cocoanut Grove nightclub.

Group efect No Yes Number of people Probability of people heading towards the exit 25,00% 50,00% 75,00% 25,00% 50,00% 75,00% Died 32 4 34 3 7 13 Trampled 23 18 25 94 51 18 Saved from fre 33 0 40 49 12 13

AsyoucanseeinTable2,theincreaseintheproba- blue indicates the location of people at the start of an event, a bility of people heading to the exit reduces the number of fre. peoplewhodieasaresultoffre.Tenumberofvictims decreases only when the group efect is on. Furthermore 4. Conclusions theoverallnumberofpeoplewhohavesurvivedafrealso increases as the probability of people moving towards the exit As one can see, performed simulations can help understand increases. how people behaved at the time of the fre, whether they AsshownintheTable3,thesmallestrelativeerror followed the crowd in search of an exit, whether they were was obtained in the absence of group efect and at the acting alone, or were they determined enough to fnd a way value of 75% of the people heading to the exit. Te biggest out. In one case, people showed a higher level of determi- errors were achieved with the group efect enabled and nation (75% probability of going towards the exit), while with the 25% probability of people going to the exit. Tis in the second case the level was lower (50%). Simulations couldmeanthatintheeventofthisfre,thegroupefect canbeusedasawarningduringsecuritylevelanalysis,but did not work, and people were looking for a way out by also as an element of a detailed analysis of the events that themselves. occurred. As you can see in Table 4, here also the increase in the Te comparison of the proposed method with actual probability of going to the exit of the premises has reduced case demonstrated that it is extremely difcult to create thenumberofpeoplewhodiedinthefre.Table5compares a simulation of fre escape scenario. Te most challenging the average results with real numbers. Te smallest error was element is the people behavior, which may become stochastic obtained for the disabled group efect, but with a value of andunpredictable.Teauthorsofthisstudymanagedto 50% of people heading to the exit. Tis may mean that, in the recreate the scenario of the escape of people from a build- eventofafreinthisclub,groupefectalsodidnotwork,but ing by means of cellular automata, the implementation of people did not hurry to leave the club, which caused a tragic which was the object of this paper. Using an appropriate efect. confguration of the program: determining the probability Te mortality rate depends on the place of the fre of a person heading towards the exit, the fre parameters outbreak. If the fre blocks any room, then the people staying and on/of setting of the group efect allow to drawing the there are not able to escape and to reach the exit even if following conclusions. When the group efect is applied in they move towards it with 100% probability. Te group efect theprogramthenumberofpeoplewhodieasaresult used in the program does not necessarily help in escape of of trampling is larger than in the case when this efect is people from the building. It can generate crowd, as people disabled. Te mortality rate rises when people are not able are looking for others to form groups and thus trampling to move in any direction, which is a result of individu- can occur. When a person does not have any direction when als gathering in groups that create areas of high density, he/she could move, he/she is trampled. In Figures 6–9, the where trampling ofen occurs. Te results which proved to place of fre and the fre spread are marked in red. In contrast, be closest to the actual numbers were achieved when the 8 Mathematical Problems in Engineering

1 1

0.8 0.8

0.6 0.6 y=(x)

0.4 y=(x) 0.4

0.2 0.2

0 0

32.5 3.5 4 4.5 5 5.5 4.5 565.5 6 .5 x x

[3 4 5 5] [5 5 5 6] (a) (b)

1 1

0.8 0.8

0.6 0.6 y=(x) 0.4 y=(x) 0.4

0.2 0.2

0 0

32.5 3.5 4 4.5 5 5.5 5.5 676.5 7 .5 x x

[5 4 3 3] [7 7 7 6] (c) (d)

Figure 7: Te OFN visualization of Nx-positive (a), Ny-positive (b), Nx-negative (c), and Ny-negative (d).

1 (x) A 

0 24 6810

fA(0) fA(1) gA(1) gA(0) Figure 8: Fuzzy number with the extension. Mathematical Problems in Engineering 9

0 xi

i−1,j−1 i, j − 1 i+1,j−1

yj i − 1, j i, j i + 1, j y

i−1,j+1 i, j + 1 i+1,j+1

Figure 9: Possible move.

Figure 10: Kiss nightclub schema with people and fre in CAEva Figure 11: CAEva program afer simulating fre in Kiss nightclub. program.

value of probability with which people escape was around buildings may have tragic consequences at each stage of 50–75%.Tehindrancesthatafectthedecisionmaking thebuildingoperation.Tepeoplewhoareresponsiblefor process during the evacuation include, among others, limited fre safety and structural safety inspections may apply such visibility due to the smoke, resulting from combustion of tools to justify their decisions that sometimes could seem to fammable materials, high temperature, and toxic gases. Te be too strict. To make the simulation even more realistic, result achieved in the CAEva method can provide valuable it is worth considering the option of automatic change of information for architects and building constructors. Te the parameter related to the probability of a person moving resultsobtainedfromtheprogramconfrmthethesisthat towards the exit during the simulation. Adding further insouciant or unlawful blocking of escape routes inside conditions in order to provide more accurate results is also 10 Mathematical Problems in Engineering

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