cellular automata-based systematic risk analysis

8/8/2019 Cellular Automata-Based Systematic Risk Analysis

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Risk Analysis, Vol. 28, No. 5, 2008 DOI: 10.1111/j.1539-6924.2008.01104.x

Cellular Automata-Based Systematic Risk Analysis

Approach for Emergency Response

Xuewei Ji,1,2 Wenguo Weng,1 and Weicheng Fan1

Emergency response is directly related to the allocation of emergency rescue resources. Effi-cient emergency response can reduce loss of life and property, limit damage from the primaryimpact, and minimize damage from derivative impacts. An appropriate risk analysis approach

in the event of accidents is one rational way to assist emergency response. In this article, acellular automata-based systematic approach for conducting risk analysis in emergency re-sponse is presented. Three general rules, i.e., diffusive effect, transporting effect, and dissipa-tive effect, are developed to implement cellular automata transition function. The approachtakes multiple social factors such as population density and population sensitivity into con-sideration and it also considers risk of domino accidents that are increasing due to increasingcongestion in industrial complexes of a city and increasing density of human population. Inaddition, two risk indices, i.e., individual risk and aggregated weighted risk, are proposed toassist decision making for emergency managers during emergency response. Individual riskcan be useful to plan evacuation strategies, while aggregated weighted risk can help emer-gency managers to allocate rescue resources rationally according to the degree of danger ineach vulnerable area and optimize emergency response programs.

KEY WORDS: Cellular automata; domino effect; emergency response; risk analysis; social factors

1. INTRODUCTION

Disasters occur frequently, taking the form offloods, hurricanes, earthquakes, fires, terrorism, andnuclear and hazardous material accidents.(13) Theseemergency situations can result in great loss of lifeand property. Public awareness of hazards, emer-gencies, and disasters has increased as the cost ofdisasters has increased dramatically. Rapid popula-tion and economy growth in the most hazardous geo-

graphical areas of the country have created increased

1 Center for Public Safety Research, Department of EngineeringPhysics, Tsinghua University, Beijing, P. R. China.

2 School of Aerospace, Tsinghua University, Beijing, P. R. China. Address correspondence to Xuewei Ji, Center for Public Safety

Research, 4F, Section 1, the West Main Building, Tsinghua Uni-versity, Beijing, P. R. China; 100084; tel: +86-10-62792402;[email protected].

exposure to disaster impacts. In an effort to minimizethe potential and subsequent impact of disasters onlife and property, emergency response has receivedmore and more attention.(4,5)

Emergency response is applying science, tech-nology, planning, and management to deal with ex-treme events that can injure or kill large numbers ofpeople, do extensive damage to property, and dis-rupt community life.(3) Emergency response is di-

rectly related to the supplies of manpower and ma-terial resources for preventing accidents in an urbanarea, as well as the quantum of monetary resourcesto be committed for the purpose. Efficient emer-gency response can reduce loss of life and property,limit damage from the primary impact, and minimizedamage from derivative impacts. An appropriate riskanalysis approach in the event of accidents is one ra-tional way to conduct efficient emergency response.Risk is defined as the likelihood that an event will

1247 0272-4332/08/0100-1247$22.00/1 C 2008 Society for Risk Analysis


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1248 Ji, Weng, and Fan

occur at a given location within a given time pe-riod and inflict casualties and damage.(6,7) For about10 years, many methodologies have been developedto undertake a quantitative risk assessment, e.g.,MCAA (maximum credible accident analysis),(8)

FTA (fault tree analysis) study,(9) or any other ex-ercise in loss prevention and safety implementationwhose essential inputs come from the probability andthe enormity of the likely accidents. However, it hasbeen found that a risk analysis approach to serveemergency response during accidents is still missingin literatures. The methodologies mentioned abovecannot be applied to emergency response.

First, as we know, emergency response is urgentand the emergency managers need to know the riskof an accident scene as soon as possible. Accuracyand rapidity are two crucial factors for risk analysisthat can determine success or failure of the emer-gency response. Accident modeling is the foundationof risk analysis, so simulating the accident spread-ing accurately and rapidly is very important. Em-pirical formulas(10,11) or partial difference equations(PDEs)(1214) are usually used to model accidents inrisk analysis in previous studies. However, an empir-ical formula method is simple but not very accurate,while the PDE method is accurate but computationtime consuming. One needs to develop an approachthat is both accurate and rapid.

Second, the common feature of some method-ologies described above is that the accident impact is

usually assumed to propagate outward from the ac-cidental epicenter in a radically symmetrical fashion.With this basic assumption, the impact areas of theseaccidents are denoted with circles. The areas corre-sponding to, say, 100%, 50%, and 25% probability ofdeath due to an accident are bounded by circles ofincreasing radii, with the accident site serving as thecenter of the circles. But in real situations, the condi-tions prevailing in the neighborhood of the accidentepicenter are rarely homogeneous. The area of im-pact of an accident shall have an irregular shape.

Third, recently, domino accidents are more com-

mon on account of increasing congestion in indus-trial complexes and increasing density of humanpopulation around such complexes.(15) However, thedomino effect is often neglected or is badly dealtwith due to lack of related scientific support duringemergency response. The explosion in Jilin chemicalplant of China in 2005 leading to a series of emer-gencies, which formed an emergency chain, is thebest example. Therefore, in this complex emergencyresponse decision-making process, a systematic risk

analysis approach incorporating the domino effect isvery necessary.

Furthermore, it is important for the emergencymanagers to realize that not only technical aspectsbut also political, psychological, and social processes

all play an important role in risk analysis duringemergency response.(4) Without doubt, some socialfactors such as population density and populationsensitivity can directly affect emergency response.During emergency response, a sparsely populatedarea with high individual risk may be not the area inmost need of rescue resources. In contrast, the areawith high individual risk and dense population is themost dangerous area and needs more attention. Theconstitution of the population is of great importancedue to the vulnerability variation of different popu-lation groups to the hazards, such as children, elderlypeople, and patients. Accordingly, incorporation ofsome social factors into risk analysis is necessary.

Based on the above considerations, a cellularautomata-based systematic approach is presented toassist emergency response. The approach can fore-cast the risk of a single accident as well as a chainof accidents (domino effect) and deal with hetero-geneous environmental conditions. It can also sys-tematically consider multiple factors such as popula-tion density and population sensitivity. To meet therequirements of accuracy and rapidity during emer-gency response, a cellular automata (CA) method isadopted. After analyzing the spreading mechanism

of various accidents, three common rules (diffusiveeffect, transporting effect, and dissipative effect) areproposed to define cellular automata transition func-tion. Besides, two risk indices are adopted, e.g., in-dividual risk and aggregated weighted risk, to assistdecision making for emergency managers. Individualrisk can be used as prewarning information to helpthe people who are likely to be affected to select theappropriate escape routes. Aggregated weighted riskcan help emergency managers to allocate rescue re-sources rationally according to the degree of dangerin each vulnerable area and optimize emergency re-

sponse programs.CA is a class of automata defined on the simula-tion space divided into discrete areas called cells,and was developed by John von Neumann andStanislaw Ulam in the United States.(16,17) Thoughthe purpose of developing CA was said to modela self-reproducing machine or to understand themechanism of a neural system, it is currently beingemployed in diverse fields such as architectural de-sign, ecology, epidemiology, environmental hazard


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Cellular Automata-Based Systematic Risk Analysis 1249

management, genetics, medical sciences, road trafficflow modeling, cryptography, image processing, ur-ban dynamics modeling, and others.

2. THEORETICAL BACKGROUND

A physical quantity called accident intensity isdefined here to express the common characteristicof various accidents, which describes the ability ofan accident to cause losses to life and property. Itexpresses different meanings in different accidents,such as blast waves and shrapnel in explosions, gasconcentration in toxic gas dispersion, and so on. Therisk assessment here is performed by evaluating in-dividual risk for each cell and aggregated weightedrisk for a cluster of cells where population densityand population sensitivity are taken into considera-tion. Population density reflects the population mag-nitude per unit area, and population sensitivity in-dicates the constitution of the general population.Individual risk (t+1IRij) is deemed to be a function ofaccident intensity (t+1AIij) and population sensitivity(PSij), while aggregated weighted risk (

t+1AWRij) de-pends on individual risk (t+1IRij), population density(PDij), and population sensitivity (PSij). They can beexpressed as follows:

t+1IRij= f

t+1AIij, PSij

(1)

t+1AWRij= f

t+1IRij, PDij, PSij

. (2)

2.1. Cell Accident Intensity State Analysis

In most accidents, such as fires and gas disper-sion, the phenomenon of accident intensity spread-ing in an isotropic medium can be expressed by thefollowing equation:

t=

x

x

x

+

y

y

y

+

z

z

z

x

(U) y

(V) z

(W)+ S , (3)

where /t is the rate of transfer per unit space, isintensity of spreading accident, is the diffusive co-efficient describing transmissivity or conductance ofthe medium, U, V, and W are the convective coeffi-cient describing the degree of convection, and S isthe source intensity of accident epicenter. The term

x

(x

x)+

y(y

y)+

z(z

z) expresses diffusive

effect and the term x

(U)+ y

(V)+ z

(W) ex-

presses transporting effect. The above equation maybe generalized as:

t=

i=x,y,z

i

2

i 2Ui

i

+ S , (4)

where i represents the coordinates in which the pro-

cesses are considered.Accident intensity spreading is dominated bytwo ingredients: inner factor and outer factor.The dynamics of propagation of the intensity is firstcontrolled by the diffusive effect, which is the innerfactor. This implies that intensity flux liberated fromthe accident epicenter travels outward to the adjoin-ing cells and once each of these incident cells becomesaturated with the intensity, they in turn begin to actas new intensity sources and the intensity flux beginsto diffuse from these cells into their respective neigh-borhoods. The intensity gradient, which expressesdifferent meanings in different accidents, is the driv-

ing force governing this outward propagation of theintensity flux. It means concentration gradient intoxic gas dispersion and temperature gradient in heatspreading and so on. According to common sense,accident spreading is also influenced by some outerfactors. For example, wind and terrain slope will af-fect the distribution of the toxic gas concentrationand temperature difference between the ambienceand the accident hazards will result in convection. Wesay that the intensity propagation is also governed bythe transporting effect. The dissipative effect is alsoan important outer factor, which perhaps changes the

way of the intensity spreading. While spreading, bar-riers such as building, river, trees, and sedimentationmay all weaken the accident intensity.

Based on above analysis, three common rulescan be extracted, i.e., diffusive effect, transporting ef-fect, and dissipative effect, which the accident inten-sity spreading obeys. Three generalized coefficientsare defined to illustrate the three rules:

(1) Diffusive coefficient (): the ability of inten-sity spreading from high intensity to low in-tensity. It is the intrinsic attribute of the ac-

cident intensity spreading.(2) Transporting coefficient (): the ability thatenvironment transports the intensity.

(3) Dissipative coefficient (): the ability thatouter factors weaken (strengthen) theintensity.

The three general coefficients are critical for sim-ulation results, and they may be functions of otherphysical quantities in some complex scenarios. They


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express different meanings in different accidents. Forexample, the diffusive coefficient expresses gas dif-fusive coefficient in toxic gas dispersion, while itmeans thermal energy diffusive coefficient in heatspreading.

Under two-dimensional situations, Mooreneighborhood, which comprises of eight immediateneighbors to each cell, is used. The amount ofthe accident intensity in a cell ij(t+1AIij) at timestep t + 1 would depend on the magnitude of theintensity present in the cell at the time t (tAIij),the magnitude of the intensity present in neigh-borhood cells at the time t + 1 (t+1AINeighbour),and attributes of the cell and its neighborhoodcells ( i j, i j, i j). The attributes of each cellinclude accident intensity state, natural factors, andhazardous factors. Natural factors refer to windvelocity, wind direction, barriers, and so on. Haz-ardous factor expresses whether there are potentialhazardous sources in the cell or not, which maycause derivative accidents. The transition functionto compute accident intensity is established asfollows:

t+1AIij= f

tAIij, t+1AINeighbor, ij, ij, ij

. (5)

(1) Diffusive effect rule.

Two types of neighbors depending upon theirorientation around the central cellthe adjacent

neighbors and nonadjacent neighborsare consid-ered.(18) Thus:

t+1AIij = tAIij+ ija

adjacent

t+1AIadjacent t+1AIij

+ijb

nonadjacent

t+1AInonadjacent t+1AIij

,

(6)

where a is the adjacent neighbors weight to the tar-get cell and b is the nonadjacent neighbors weight.The two coefficients obey the following relationships:

a > b, a + b = 1.(2) Transporting effect rule.

In this approach, the transporting effect is sup-posed to be only affected by the cell, the line betweenwhose center and the target cells is not orthogonalwith the transporting force direction. The distancebetween neighborhood cells and target cell is also animpact factor. Thus:

t+1AIij = tAIij+

neighbor

neighbor

t+1AIneighbor t+1AIij

= tAIij+

neighbor

r

Uij

rnneighbor

t+1AIneighbor t+1AIij

,

(7)

where rneighbor andrare respectively scalar and vec-

tor indicating the distance between neighborhoodcells and target cell, n is the distance impact factor,

and

Uij is a vector indicating the direction of accidentspreading.

(3) Dissipative effect rule.

We regard the dissipative effect as a barrier,which is considered to be a property of the cell. Theeffect of barriers is likely to be anisotropic, e.g., the

effect of a wall as a barrier to toxic dispersions de-pends on wind direction. The anisotropy of barriersis not discussed here, and an isotropic effect of bar-riers is assumed. That is to say, if there is a barrierin the cell ij, the accident intensity increases or de-creases certain amount of quantity linearly. The rulebased on the above assumption is expressed as:

t+1AIij=1 t+1ij

f

tAIij, t+1AINeighbor, ij, ij

,

(8)

where ij is positive if barriers weaken the intensity,and negative otherwise.

Incorporating above three rules, the cell transi-tion function can be set up:

t+1AIij= tAIij+

1 t+1ij

ija

adjacent

t+1AIadjacent t+1AIij

+ijb

nonadjacent

t+1AInonadjacent t+1AIij

+neighbor

r

Uij

rnneighbort+1AIneighbor t+1AIij

.

(9)

2.2. Domino Effect Analysis

To study the domino effect, the cells are sortedinto two categories, general cells (cellg) and haz-ardous cells (cellh). General cells are the cells thatdo not contain the potential hazardous source, andthe hazardous cells are the cells that contain the


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potential hazardous source and serve as potentialseed cells. The domino effect is performed throughtwo levels.(15)

At the first level, a screening of all the hazardouscells is done in order to identify hazardous cells and

general cells. Then, we need to determine whethercertain hazardous cell can cause accidents accord-ing to the accident intensity the cell has perceived.For this purpose, three methods have been proposedin the literatures: (1) vulnerability threshold mod-els (the physical effect on the secondary target ishigher than a threshold value for damage and thendomino effect happens);(1921) (2) propagation func-tions based on empirical decay relations for physicaleffects;(22) (3) propagation functions based on spe-cific probabilistic models.(23,24)

At the second level, a more detailed analysis isconducted to compute the intensity states of all cellsunder domino effect. After obtaining the intensitystates of all cells resulting from the primary accidentat a time t, we further judge which cell can be servedas the seed cell based on the method referred at thefirst level. In the next time step, simulation is per-formed based on the propagation occurring from allseeds. With time going by, we will analyze the tertiaryaccident, the quartus accident, and so on in the sameway. In the approach, the vulnerability thresholdmodel is used. The domino effect can be expressedas:

If tAIij >AIthresholdij , t+1AIij= accident epicenter

otherwise t+1AIij= f

tAIij, t+1AINeighbor, ij, Uij, ij

.

(10)

2.3. Individual Risk and Aggregated WeightedRisk Analysis

Accident intensity provides a basis for systematiccomparison of different exposure. However, in caseof emergency response, the emergency managers aremore concerned about human lives rather than ac-

cident intensity itself. Furthermore, accident inten-sity from different phenomena, e.g., thermal heatflux and toxic concentration is not directly compa-rable. On the other hand, the type of health dam-age that an exposure might cause provides a commonbasis that allows direct comparison.(25) In the pro-posed approach, we will only consider death proba-bility of an exposed individual. The probability canbe calculated from the physical effects and the es-timated time of exposure using probit models for

human vulnerability.(26,27) The probit function for fa-tal injuries can be expressed as:

t+1 Pij= (5m/)+ (1/) ln

t+1AInij t

, (11)

where t+1 Pij is the probit value, m is the mean valueof the intensity fatal to population, and is the stan-dard deviation, both of which are from experimentson animals or the historical data.

Based on the assumption that the strength of thehuman body to accident intensity is normally dis-tributed with mean value of 5 and standard deviationof 1,(25) the probability of loss of life in cell ij on re-ceiving certain accident intensity AIij is given by:

t+1IRij=12

t+1 Pij5

exp

u

2

2

du. (12)

The approach proposed here to treat a sensi-tive population is based on the assumption that themean value of intensity fatal to a sensitive populationis lower than the mean value of intensity fatal to anormal population, and also that the standard devia-tion of the distribution for a sensitive population islower than the standard deviation for a normal popu-lation. Suitable probit function can be generated forthe estimation of individual risk to a sensitive popu-lation through adjusting and m.(28)

The overall individual risk due to contempo-rary exposition to different types of physical ef-fects (e.g., a toxic release and a fire, and so on)

is also considered. It is calculated as a combina-tion of each related individual risk. The combinationcan be performed by different strategies. Individualrisk is actually probability value; thus probabilisticrules are required for the combination. Four methodshave been reported elsewhere.(29) In the approach,one can choose one or several methods to computethe overall individual risk referring to detailed dis-cussions by Cozzani et al. (2005).

Aggregated weighted risk (AWR) is cited to de-scribe the risk of a cluster of cells. It expresses therelationship between individual risk and the number

of people suffering from a specified level of harm ina given population from the realization of specifiedhazards.(30) The factor of population density variesspatially and temporally, that is to say, different cellshave different population density states at differenttimes. Aggregated weighted risk is calculated by mul-tiplying population density inside a certain area (A)with its IRij level in cell ij. The effect of protectiondue to buildings is not accounted for here, so the re-sults are conservative.


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t+1AWRA =

A

t+1IRij PDij(t+ 1)d A (13)

2.4. Algorithm of the Systematic Approach

An algorithm of the systematic approach hasbeen developed (Fig. 1), where simulation starts att= 0 and T is the maximum time, user defined. Thestudy area is divided into a two-dimension lattice ofcells, and the attributes (hazardous factors, naturalfactors, and social factors) of each cell are identi-fied. Seed cells that can cause the primary accidents

Fig. 1. Algorithm of the cellularautomata-based systematic risk analysisfor emergency response.

are selected and accident scenarios are developed.The algorithm evaluates the intensity state of eachcell in the matrix with respect to the neighborhoodcells, taking into account diffusive effect, transport-ing effect, and dissipative effect. After obtaining the

intensity state of each cell, we judge whether somecell contains a potential hazardous source; if yes,we judge whether the intensity of the cell exceedsthe threshold; if yes, we take the cell as a seed cell inthe next time step. Otherwise, we directly do the nextsimulation. During each simulation step, we will takepopulation density state and population sensitivity


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state into consideration. And then, we can get indi-vidual risk state in each cell and aggregated weightedrisk in a cluster of cells at time t+ 1.

The algorithm is run synchronously for every cellpresent in the lattice. The emerging scenario includ-

ing domino effect in the subsequent time step is au-tomated. The algorithm is run repeatedly in order togenerate the scenarios for all subsequent time steps.This is pursued until the number of time steps be-comes larger than the user-defined constant. Conse-quently, the algorithm is able to generate real-timeindividual risk and aggregated weighted risk at theend of every time step.

3. APPROACH APPLICATION: ANILLUSTRATIVE EXAMPLE

3.1. Hypothetical Accident Scenarios

To illustrate the application of the systematic ap-proach, we made simulations on a fictitious city basedon THU-CPSR city model, which was designed tosimulate a real city with the scale of 5,250 4,410 m.There are two commercial buildings, 10 residentialbuildings, two workshops, three LNG gas contain-ers, and a petrochemical industry in the city. There

Fig. 2. THU-CPSR city model.

are river and virescence areas to separate the indus-trial and residential areas. Therefore, the model canrepresent a complex city with a cluster of potentialhazardous sources and heavy population density. Thecity model is shown in Fig. 2.

The fictitious city is divided into uniform gridsof 35 35 m. As illustrated in the article, the pur-pose of the approach proposed here is for risk anal-ysis during emergency response. According to Abra-hamsson,(31) the process of risk analysis has a lot ofuncertainty and the more detailed spreading simula-tion might not play a greater role for the results ofrisk.(31) Therefore, the size of cell needs not be toosmall. Besides, in our city model, the attribute of eachcell is homogeneous when the size is 35 35 m. If thesize is larger, the attribute of some cells may not behomogeneous. This will bring great trouble for thecomputations and may affect the precision of the re-sults. Taking the above analysis into consideration,we think that the size (35 35 m) is appropriate inour example.

L, M, and N (see Fig. 2) are potential hazardoussources that may cause pool fires. The vulnerable ar-eas are A to J (see Fig. 2), which represent residentialareas with heavy population. A hypothetical scenario


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is used to illustrate the application of the approach.A gasoline leak in one of the gasholders formed a liq-uid pool at M and flashing of the liquid gasoline re-sults in a pool fire. If the thermal intensity at L and Nexceeds the threshold value (10 KW/m2 is used here),

derivative pool fires may happen.During a fire incident, the dominant form of en-

ergy that causes maximum damage is the thermalintensity, which propagates via conduction, convec-tion, and radiation. Therefore, accident intensity ex-presses thermal intensity in this situation. For poolfires, there is an initial unsteady phase in which theburning rate accelerates, a steady state where equi-librium is achieved, and finally a dying down phasein which the accident intensity dissipates to zero. Theamount of thermal intensity is influenced by factorssuch as pool diameter, flame lip effects, the amountof fuels, and so on. In most pool fires, it passesvery quickly from unsteady state to steady state.(32,33)

Therefore, only the steady state is considered here,and thermal intensity from pool fire is considered tobe constant, i.e., 100 KW/m2.

A constant heat value distribution in spacewould be expected from a pool fire having a constantthermal intensity, but the constant value cannot beachieved as soon as the fire reaches the stable state. Itneeds time for each cell to achieve the constant statein the steady state. This time is vital for emergencyresponse. If efficient emergency rescue is performedduring this time, the loss of life and property may be

reduced and a domino effect may also be avoided.In our approach application, the process will be dis-cussed.

3.2. Methods

When heat flux passes from the source to thereceptor, significant attenuation of intensity occurs.The atmospheric conditions are the main factor toaffect diffusivity. Therefore, the following expressionfor diffusive parameter has been proposed:(34)

ij=

2.02

(Pij

r)0.09, (14)

where:

Pij= 1013.255 (RHij) exp

14.4144 5328Tij

(15)

and r is the length scale of the cells, Tij the ambienttemperature in K at cell ij, and RHij is the relative-humidity in cell ij. The weight term for the adjacentneighbors has been taken as a = 0.88 and b= 0.12

for nonadjacent neighbors in this example. The exactvalues need to be calibrated based on experiments.

If a strong wind oriented from northeast tosouthwest were assumed, the amount of intensitytransported into the cell ij from the northeast neigh-

bors would be more than that from its southwestneighbors compared to the conditions in the absenceof any wind currents. Transporting effect is affectedby wind in our case study. Here, we do not considerthe effect of wind on pool fire. Instead, we considerthe effect of wind on thermal energy spreading. Theeffect of this factor depends on the distance betweenneighbor cell and seed cell and the direction ofwind. Thus, the magnitude of the transporting coeffi-cient may be expressed as:

ij

=

1

rn

uij, (16)

where r is distance from neighbor cell to the seedcell, n is an exponent, and uij is the directionalconstant associated with the specific direction. Thenumerical values assigned to these directional con-stants are selected according to the importance anddegree of the directionality. In this example, wehave assigned to the exponent value 1 for simplic-ity and we assume the direction of wind is northeast.So we have une > un = ue > 0, unw = use = 0, usw

cellular automata-based systematic risk analysis

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