Full Access

Cellular Automata-Based Systematic Risk Analysis Approach for Emergency Response

Corresponding Author

Xuewei Ji

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

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 University, Beijing, P. R. China; 100084; tel: +86-10-62792402; [email protected].Search for more papers by this author

Wenguo Weng,

Wenguo Weng

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

Search for more papers by this author

Weicheng Fan,

Weicheng Fan

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

Search for more papers by this author

Xuewei Ji,

Corresponding Author

Xuewei Ji

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

School of Aerospace, Tsinghua University, Beijing, P. R. China.

Wenguo Weng,

Wenguo Weng

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

Search for more papers by this author

Weicheng Fan,

Weicheng Fan

Center for Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, P. R. China.

Search for more papers by this author

First published: 20 September 2008

https://doi.org/10.1111/j.1539-6924.2008.01104.x

Citations: 18

School of Aerospace, Tsinghua University, Beijing, P. R. China.

Share a link

Email
Wechat
Bluesky

Abstract

Emergency response is directly related to the allocation of emergency rescue resources. Efficient emergency response can reduce loss of life and property, limit damage from the primary impact, 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, a cellular automata-based systematic approach for conducting risk analysis in emergency response is presented. Three general rules, i.e., diffusive effect, transporting effect, and dissipative effect, are developed to implement cellular automata transition function. The approach takes multiple social factors such as population density and population sensitivity into consideration and it also considers risk of domino accidents that are increasing due to increasing congestion in industrial complexes of a city and increasing density of human population. In addition, two risk indices, i.e., individual risk and aggregated weighted risk, are proposed to assist decision making for emergency managers during emergency response. Individual risk can be useful to plan evacuation strategies, while aggregated weighted risk can help emergency managers to allocate rescue resources rationally according to the degree of danger in each vulnerable area and optimize emergency response programs.

1. INTRODUCTION

Disasters occur frequently, taking the form of floods, hurricanes, earthquakes, fires, terrorism, and nuclear and hazardous material accidents.⁽^1–3⁾ These emergency situations can result in great loss of life and property. Public awareness of hazards, emergencies, and disasters has increased as the cost of disasters has increased dramatically. Rapid population and economy growth in the most hazardous geographical areas of the country have created increased exposure to disaster impacts. In an effort to minimize the potential and subsequent impact of disasters on life and property, emergency response has received more and more attention.⁽^4,5⁾

Emergency response is “applying science, technology, planning, and management to deal with extreme events that can injure or kill large numbers of people, do extensive damage to property, and disrupt community life.”⁽³⁾ Emergency response is directly related to the supplies of manpower and material resources for preventing accidents in an urban area, as well as the quantum of monetary resources to be committed for the purpose. Efficient emergency response can reduce loss of life and property, limit damage from the primary impact, and minimize damage from derivative impacts. An appropriate risk analysis approach in the event of accidents is one rational way to conduct efficient emergency response. Risk is defined as the likelihood that an event will occur at a given location within a given time period and inflict casualties and damage.⁽^6,7⁾ For about 10 years, many methodologies have been developed to undertake a quantitative risk assessment, e.g., MCAA (maximum credible accident analysis),⁽⁸⁾ FTA (fault tree analysis) study,⁽⁹⁾ or any other exercise in loss prevention and safety implementation whose essential inputs come from the probability and the enormity of the likely accidents. However, it has been found that a risk analysis approach to serve emergency response during accidents is still missing in literatures. The methodologies mentioned above cannot be applied to emergency response.

First, as we know, emergency response is urgent and the emergency managers need to know the risk of an accident scene as soon as possible. Accuracy and rapidity are two crucial factors for risk analysis that can determine success or failure of the emergency response. Accident modeling is the foundation of risk analysis, so simulating the accident spreading accurately and rapidly is very important. Empirical formulas⁽^10,11⁾ or partial difference equations (PDEs)⁽^12–14⁾ are usually used to model accidents in risk analysis in previous studies. However, an empirical formula method is simple but not very accurate, while the PDE method is accurate but computation time consuming. One needs to develop an approach that is both accurate and rapid.

Second, the common feature of some methodologies described above is that the accident impact is usually assumed to propagate outward from the accidental epicenter in a radically symmetrical fashion. With this basic assumption, the impact areas of these accidents are denoted with circles. The areas corresponding to, say, 100%, 50%, and 25% probability of death due to an accident are bounded by circles of increasing radii, with the accident site serving as the center of the circles. But in real situations, the conditions prevailing in the neighborhood of the accident epicenter are rarely homogeneous. The area of impact of an accident shall have an irregular shape.

Third, recently, domino accidents are more common on account of increasing congestion in industrial complexes and increasing density of human population around such complexes.⁽¹⁵⁾ However, the domino effect is often neglected or is badly dealt with due to lack of related scientific support during emergency response. The explosion in Jilin chemical plant of China in 2005 leading to a series of emergencies, which formed an emergency chain, is the best example. Therefore, in this complex emergency response decision-making process, a systematic risk analysis approach incorporating the domino effect is very necessary.

Furthermore, it is important for the emergency managers to realize that not only technical aspects but also political, psychological, and social processes all play an important role in risk analysis during emergency response.⁽⁴⁾ Without doubt, some social factors such as population density and population sensitivity can directly affect emergency response. During emergency response, a sparsely populated area with high individual risk may be not the area in most need of rescue resources. In contrast, the area with high individual risk and dense population is the most dangerous area and needs more attention. The constitution of the population is of great importance due to the vulnerability variation of different population groups to the hazards, such as children, elderly people, and patients. Accordingly, incorporation of some social factors into risk analysis is necessary.

Based on the above considerations, a cellular automata-based systematic approach is presented to assist emergency response. The approach can forecast the risk of a single accident as well as a chain of accidents (domino effect) and deal with heterogeneous environmental conditions. It can also systematically consider multiple factors such as population density and population sensitivity. To meet the requirements of accuracy and rapidity during emergency response, a cellular automata (CA) method is adopted. After analyzing the spreading mechanism of various accidents, three common rules (diffusive effect, transporting effect, and dissipative effect) are proposed to define cellular automata transition function. Besides, two risk indices are adopted, e.g., individual risk and aggregated weighted risk, to assist decision making for emergency managers. Individual risk can be used as prewarning information to help the people who are likely to be affected to select the appropriate escape routes. Aggregated weighted risk can help emergency managers to allocate rescue resources rationally according to the degree of danger in each vulnerable area and optimize emergency response programs.

CA is a class of automata defined on the simulation space divided into discrete areas called “cells,” and was developed by John von Neumann and Stanislaw Ulam in the United States.⁽^16,17⁾ Though the purpose of developing CA was said to model a self-reproducing machine or to understand the mechanism of a neural system, it is currently being employed in diverse fields such as architectural design, ecology, epidemiology, environmental hazard management, genetics, medical sciences, road traffic flow modeling, cryptography, image processing, urban dynamics modeling, and others.

2. THEORETICAL BACKGROUND

A physical quantity called accident intensity is defined here to express the common characteristic of various accidents, which describes the ability of an accident to cause losses to life and property. It expresses different meanings in different accidents, such as blast waves and shrapnel in explosions, gas concentration in toxic gas dispersion, and so on. The risk assessment here is performed by evaluating individual risk for each cell and aggregated weighted risk for a cluster of cells where population density and population sensitivity are taken into consideration. Population density reflects the population magnitude per unit area, and population sensitivity indicates the constitution of the general population. Individual risk (^t+1IR_ij) is deemed to be a function of accident intensity (^t+1AI_ij) and population sensitivity (PS_ij), while aggregated weighted risk (^t+1AWR_ij) depends on individual risk (^t+1IR_ij), population density (PD_ij), and population sensitivity (PS_ij). They can be expressed as follows:

(1)

(2)

2.1. Cell Accident Intensity State Analysis

In most accidents, such as fires and gas dispersion, the phenomenon of accident intensity spreading in an isotropic medium can be expressed by the following equation:

(3)

where ∂ϕ/∂t is the rate of transfer per unit space, ϕ is intensity of spreading accident, Γ is the diffusive coefficient describing transmissivity or conductance of the medium, U, V, and W are the convective coefficient describing the degree of convection, and S_ϕ is the source intensity of accident epicenter. The term inline image

expresses diffusive effect and the term inline image

expresses transporting effect. The above equation may be generalized as:

(4)

where i represents the coordinates in which the processes are considered.

Accident intensity spreading is dominated by two ingredients: “inner factor” and “outer factor.” The dynamics of propagation of the intensity is first controlled by the diffusive effect, which is the inner factor. This implies that intensity flux liberated from the accident epicenter travels outward to the adjoining cells and once each of these incident cells become saturated with the intensity, they in turn begin to act as new intensity sources and the intensity flux begins to diffuse from these cells into their respective neighborhoods. The intensity gradient, which expresses different meanings in different accidents, is the driving force governing this outward propagation of the intensity flux. It means concentration gradient in toxic gas dispersion and temperature gradient in heat spreading and so on. According to common sense, accident spreading is also influenced by some outer factors. For example, wind and terrain slope will affect the distribution of the toxic gas concentration and temperature difference between the ambience and the accident hazards will result in convection. We say that the intensity propagation is also governed by the transporting effect. The dissipative effect is also an important outer factor, which perhaps changes the way of the intensity spreading. While spreading, barriers such as building, river, trees, and sedimentation may all weaken the accident intensity.

Based on above analysis, three common rules can be extracted, i.e., diffusive effect, transporting effect, and dissipative effect, which the accident intensity spreading obeys. Three generalized coefficients are defined to illustrate the three rules:

1
Diffusive coefficient (Γ): the ability of intensity spreading from high intensity to low intensity. It is the intrinsic attribute of the accident intensity spreading.
2
Transporting coefficient (τ): the ability that environment transports the intensity.
3
Dissipative coefficient (α): the ability that outer factors weaken (strengthen) the intensity.

The three general coefficients are critical for simulation results, and they may be functions of other physical quantities in some complex scenarios. They express different meanings in different accidents. For example, the diffusive coefficient expresses gas diffusive coefficient in toxic gas dispersion, while it means thermal energy diffusive coefficient in heat spreading.

Under two-dimensional situations, “Moore neighborhood,” which comprises of eight immediate neighbors to each cell, is used. The amount of the accident intensity in a cell ij(^t+1AI_ij) at time step t+ 1 would depend on the magnitude of the intensity present in the cell at the time t (^tAI_ij), the magnitude of the intensity present in neighborhood cells at the time t+ 1 (Δ^t+1AI_Neighbour), and attributes of the cell and its neighborhood cells' (Γ_ij, τ_ij, α_ij). The attributes of each cell include accident intensity state, natural factors, and hazardous factors. Natural factors refer to wind velocity, wind direction, barriers, and so on. Hazardous factor expresses whether there are potential hazardous sources in the cell or not, which may cause derivative accidents. The transition function to compute accident intensity is established as follows:

(5)

(1) Diffusive effect rule.

Two types of neighbors depending upon their orientation around the central cell—the adjacent neighbors and nonadjacent neighbors—are considered.⁽¹⁸⁾ Thus:

(6)

where ω_a is the adjacent neighbor's weight to the target cell and ω_b is the nonadjacent neighbor's weight. The two coefficients obey the following relationships: ω_a > ω_b, ω_a+ω_b= 1.

(2) Transporting effect rule.

In this approach, the transporting effect is supposed to be only affected by the cell, the line between whose center and the target cell's is not orthogonal with the transporting force direction. The distance between neighborhood cells and target cell is also an impact factor. Thus:

(7)

where r_neighbor and inline image

are respectively scalar and vector indicating the distance between neighborhood cells and target cell, n is the distance impact factor, and inline image

is a vector indicating the direction of accident spreading.

(3) Dissipative effect rule.

We regard the dissipative effect as a “barrier,” which is considered to be a property of the cell. The effect of barriers is likely to be anisotropic, e.g., the effect of a wall as a barrier to toxic dispersions depends on wind direction. The anisotropy of barriers is not discussed here, and an isotropic effect of barriers is assumed. That is to say, if there is a “barrier” in the cell ij, the accident intensity increases or decreases certain amount of quantity linearly. The rule based on the above assumption is expressed as:

(8)

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

Incorporating above three rules, the cell transition function can be set up:

(9)

2.2. Domino Effect Analysis

To study the domino effect, the cells are sorted into two categories, general cells (cell^g) and hazardous cells (cell^h). General cells are the cells that do not contain the potential hazardous source, and the hazardous cells are the cells that contain the potential hazardous source and serve as potential seed cells. The domino effect is performed through two levels.⁽¹⁵⁾

At the first level, a screening of all the hazardous cells is done in order to identify hazardous cells and general cells. Then, we need to determine whether certain hazardous cell can cause accidents according to the accident intensity the cell has perceived. For this purpose, three methods have been proposed in the literatures: (1) vulnerability threshold models (the physical effect on the secondary target is higher than a threshold value for damage and then domino effect happens);⁽^19–21⁾ (2) propagation functions based on empirical decay relations for physical effects;⁽²²⁾ (3) propagation functions based on specific probabilistic models.⁽^23,24⁾

At the second level, a more detailed analysis is conducted to compute the intensity states of all cells under domino effect. After obtaining the intensity states of all cells resulting from the primary accident at a time t, we further judge which cell can be served as the seed cell based on the method referred at the first level. In the next time step, simulation is performed based on the propagation occurring from all seeds. With time going by, we will analyze the tertiary accident, the quartus accident, and so on in the same way. In the approach, the vulnerability threshold model is used. The domino effect can be expressed as:

(10)

2.3. Individual Risk and Aggregated Weighted Risk Analysis

Accident intensity provides a basis for systematic comparison of different exposure. However, in case of emergency response, the emergency managers are more concerned about human lives rather than accident intensity itself. Furthermore, accident intensity from different phenomena, e.g., thermal heat flux and toxic concentration is not directly comparable. On the other hand, the type of health damage that an exposure might cause provides a common basis that allows direct comparison.⁽²⁵⁾ In the proposed approach, we will only consider death probability of an exposed individual. The probability can be calculated from the physical effects and the estimated time of exposure using probit models for human vulnerability.⁽^26,27⁾ The probit function for fatal injuries can be expressed as:

(11)

where ^t+1P_ij is the probit value, m is the mean value of the intensity fatal to population, and σ is the standard deviation, both of which are from experiments on animals or the historical data.

Based on the assumption that the strength of the human body to accident intensity is normally distributed with mean value of 5 and standard deviation of 1,⁽²⁵⁾ the probability of loss of life in cell ij on receiving certain accident intensity AI_ij is given by:

(12)

The approach proposed here to treat a sensitive population is based on the assumption that the mean value of intensity fatal to a sensitive population is lower than the mean value of intensity fatal to a normal population, and also that the standard deviation σ of the distribution for a sensitive population is lower than the standard deviation for a normal population. Suitable probit function can be generated for the estimation of individual risk to a sensitive population through adjusting σ and m.⁽²⁸⁾

The overall individual risk due to contemporary exposition to different types of physical effects (e.g., a toxic release and a fire, and so on) is also considered. It is calculated as a combination of each related individual risk. The combination can be performed by different strategies. Individual risk is actually probability value; thus probabilistic rules are required for the combination. Four methods have been reported elsewhere.⁽²⁹⁾ In the approach, one can choose one or several methods to compute the overall individual risk referring to detailed discussions by Cozzani et al. (2005).

Aggregated weighted risk (AWR) is cited to describe the risk of a cluster of cells. It expresses “the relationship between individual risk and the number of people suffering from a specified level of harm in a given population from the realization of specified hazards.”⁽³⁰⁾ The factor of population density varies spatially and temporally, that is to say, different cells have different population density states at different times. Aggregated weighted risk is calculated by multiplying population density inside a certain area (A) with its IR_ij level in cell ij. The effect of protection due to buildings is not accounted for here, so the results are conservative.

(13)

2.4. Algorithm of the Systematic Approach

An algorithm of the systematic approach has been developed (Fig. 1), where simulation starts at t = 0 and T is the maximum time, user defined. The study area is divided into a two-dimension lattice of cells, and the attributes (hazardous factors, natural factors, and social factors) of each cell are identified. Seed cells that can cause the primary accidents are selected and accident scenarios are developed. The algorithm evaluates the intensity state of each cell in the matrix with respect to the neighborhood cells, taking into account diffusive effect, transporting effect, and dissipative effect. After obtaining the intensity state of each cell, we judge whether some cell contains a potential hazardous source; if yes, we judge whether the intensity of the cell exceeds the threshold; if yes, we take the cell as a seed cell in the next time step. Otherwise, we directly do the next simulation. During each simulation step, we will take population density state and population sensitivity state into consideration. And then, we can get individual risk state in each cell and aggregated weighted risk in a cluster of cells at time t+ 1.

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Algorithm of the cellular automata-based systematic risk analysis for emergency response.

The algorithm is run synchronously for every cell present in the lattice. The emerging scenario including domino effect in the subsequent time step is automated. The algorithm is run repeatedly in order to generate the scenarios for all subsequent time steps. This is pursued until the number of time steps becomes larger than the user-defined constant. Consequently, the algorithm is able to generate real-time individual risk and aggregated weighted risk at the end of every time step.

3. APPROACH APPLICATION: AN ILLUSTRATIVE EXAMPLE

3.1. Hypothetical Accident Scenarios

To illustrate the application of the systematic approach, we made simulations on a fictitious city based on THU-CPSR city model, which was designed to simulate a real city with the scale of 5,250 × 4,410 m. There are two commercial buildings, 10 residential buildings, two workshops, three LNG gas containers, and a petrochemical industry in the city. There are river and virescence areas to separate the industrial and residential areas. Therefore, the model can represent a complex city with a cluster of potential hazardous sources and heavy population density. The city model is shown in Fig. 2.

The fictitious city is divided into uniform grids of 35 × 35 m. As illustrated in the article, the purpose of the approach proposed here is for risk analysis during emergency response. According to Abrahamsson,⁽³¹⁾ the process of risk analysis has a lot of uncertainty and the more detailed spreading simulation might not play a greater role for the results of risk.⁽³¹⁾ Therefore, the size of cell needs not be too small. Besides, in our city model, the attribute of each cell is homogeneous when the size is 35 × 35 m. If the size is larger, the attribute of some cells may not be homogeneous. This will bring great trouble for the computations and may affect the precision of the results. Taking the above analysis into consideration, we think that the size (35 × 35 m) is appropriate in our example.

L, M, and N (see Fig. 2) are potential hazardous sources that may cause pool fires. The vulnerable areas are A to J (see Fig. 2), which represent residential areas with heavy population. A hypothetical scenario is used to illustrate the application of the approach. A gasoline leak in one of the gasholders formed a liquid pool at M and flashing of the liquid gasoline results in a pool fire. If the thermal intensity at L and N exceeds the threshold value (10 KW/m² is used here), derivative pool fires may happen.

During a fire incident, the dominant form of energy that causes maximum damage is the thermal intensity, which propagates via conduction, convection, and radiation. Therefore, accident intensity expresses thermal intensity in this situation. For pool fires, there is an initial unsteady phase in which the burning rate accelerates, a steady state where equilibrium is achieved, and finally a dying down phase in which the accident intensity dissipates to zero. The amount of thermal intensity is influenced by factors such as pool diameter, flame lip effects, the amount of fuels, and so on. In most pool fires, it passes very 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 to be constant, i.e., 100 KW/m².

A constant heat value distribution in space would be expected from a pool fire having a constant thermal intensity, but the constant value cannot be achieved as soon as the fire reaches the stable state. It needs time for each cell to achieve the constant state in the steady state. This time is vital for emergency response. If efficient emergency rescue is performed during 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 discussed.

3.2. Methods

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

(14)

where:

(15)

and r is the length scale of the cells, T_ij the ambient temperature in K at cell ij, and RH_ij is the relativehumidity in cell ij. The weight term for the adjacent neighbors has been taken as ω_a = 0.88 and ω_b = 0.12 for nonadjacent neighbors in this example. The exact values need to be calibrated based on experiments.

If a strong wind oriented from northeast to southwest were assumed, the amount of intensity transported into the cell ij from the northeast neighbors would be more than that from its southwest neighbors compared to the conditions in the absence of any wind currents. Transporting effect is affected by wind in our case study. Here, we do not consider the effect of wind on pool fire. Instead, we consider the effect of wind on thermal energy spreading. The effect of this factor depends on the distance between neighbor cell and “seed cell” and the direction of wind. Thus, the magnitude of the transporting coefficient may be expressed as:

(16)

where r is distance from neighbor cell to the “seed cell,”n is an exponent, and u_ij is the directional constant associated with the specific direction. The numerical values assigned to these directional constants are selected according to the importance and degree of the directionality. In this example, we have assigned to the exponent value 1 for simplicity and we assume the direction of wind is northeast. So we have inline image

Now, we turn to dissipative effect. Unlike in the case of an absolute vacuum, the participating media may attenuate the released thermal intensity due to absorption and scattering. Referring to Section 2, an isotropic effect of barriers is assumed. The dissipative coefficients used here obey the principle that different objects have different dissipative ability. The exact values need to be obtained from experiments.

According to F. P. Lees,⁽³²⁾ the mean value of the intensity fatal to normal population m is 7.775, the standard deviation σ is 0.3903. The individual risk is computed with Equations (11) and (12). The aggregated weighted risk in the residential areas A to J were mainly analyzed. The aggregated weighted risk can be calculated using Equation (13). Table I presents the information about the population density, and the total number of the population of each residential area. We regard population density as constant in the example for simplicity. The combination of site monitoring and a GIS database can be used to obtain the real-time data of population density in practical application.

Table I. Population Density and the Total Number of Population in Each Residential Area

Residential Area No.	Population Density (no./km²)	Total Number of Population	Residential Area No.	Population Density (no./km²)	Total Number of Population
A	31,020	4,484	F	17,143	1,323
B	29,388	4,132	G	4,082	1,323
C	31,020	3,648	H	14,694	1,188
D	31,020	4,750	I	14,694	1,512
E	33,469	5,248	J	14,694	1,584

3.3. Results and Discussions

The results under homogeneous conditions and heterogeneous conditions were computed to illustrate the CA method's advantage in treating heterogeneous conditions. Here, homogeneous conditions mean that there exist no intercepting objects in all cells (α_ij = 0). Heterogeneous conditions arise when there are intercepting objects in some cells and the conditions are different in different cells. Domino effect under the two conditions was also analyzed.

Fig. 3 gives the thermal energy varying with time at potential hazardous sources L and N. A significant difference of thermal intensity value can be observed under the two conditions. The thermal intensity under homogeneous conditions is higher than that under heterogeneous conditions at the same time. For example, at t = 600s, the thermal intensity under homogeneous conditions is 5.17 KW/m² and its counterpart is 3.32 KW/m² at L. A similar conclusion can be obtained at N, and the two values are 8.84 and 6.61 KW/m². Due to the impact from the intercepting objects, time to cause derivative accidents is also different and the existence of intercepting objects can delay the time. Under homogeneous conditions, L and N can cause derivative accidents at t = 1005s and t = 697s and the results are 1425 and 975s under heterogeneous conditions.

The contours of thermal intensity were also computed (Fig. 4). The results under homogeneous conditions are regular curves, while the impact of heterogeneous conditions on the results can be seen, which makes the curves not smooth and is closer to reality. One can also conclude that designing isolated areas to separate an industry area and a residential area, and different industry areas is advantageous to reduce accident impact and prevent domino effect. Comparing the two groups of figures, one can see that the existence of river and virescence areas greatly reduces the thermal intensity. For example, in the area G thermal intensity has been more than 10 KW/m² without intercepting objects, but under heterogeneous conditions the value is less than 10 KW/m² at t = 800s (Figs. 4(C) and 4(D)). At t = 800s, thermal intensity at N is over 10 KW/m² and a secondary accident has happened under homogeneous conditions (Fig. 4(D)). Due to the absorption of buildings, the intensity is less than 10 KW/m² at L and no secondary accident happened at t = 800s (Fig. 4(C)). The potential hazardous source L received nearly 10 KW/m² thermal intensity at 1000s (Fig. 4(F)), and the tertiary accident will occur soon, while the counterpart intensity is only about 5 KW/m² (Fig. 4(E)), which cannot cause any derivative accident. Besides, according to the results, one can determine emergency rescue time. At t = 975s, the secondary accident occurs at N. So if emergency rescue power is sent to N during this time, a secondary accident may be prevented. If not, at least one can delay the time of the secondary happening to obtain more time for people evacuation.

Individual risk is analyzed and the simulation results of individual risk contours are discussed (Fig. 5). From contours of individual risk, one can obtain the real-time information about the distribution of individual risk. As expected, for an emergency manager, individual risk is much more practical than accident intensity during emergency response. For example, at t = 800s (Fig. 5(B)), although the thermal intensity in most of the residential areas is more than 1 KW/m², the individual risk is much less than 1 × 10⁻⁶. Therefore, the manager can easily judge that at this time most of the residential areas are safe (we think that individual risk less than 1×10⁻⁶ is safe). At t = 1200s (Fig. 5(C)), the individual risk around building G is more than 1 × 10⁻⁶, and the area is not safe anymore. With time going by, the unsafe area expands gradually. At t = 2600 s (Fig. 5(D)), almost all residential buildings are in danger except building A. Besides, according to the contours of individual risk, emergency managers can issue prewarning information to guide the people to evacuate. If one neglects tertiary accidents, it is a good strategy to guide people to evacuate to the northwest area. However, a high risk source L exists in the north and it will cause an accident at t = 1425s. Comprehensively considering these factors, a west side evacuation is strongly recommended (Figs. 5(E) and 5(F)).

Aggregated weighted risks in the 10 residential areas were also computed at different time. The results are given in Table II. Some significant conclusions can be obtained to help emergency managers allocate emergency rescue resources. For example, the AWR is very low in all the 10 areas at t = 600s and t = 800s. At t = 1200s and t = 1600s, the AWR at area E, G, and J is much higher than that at other areas, especially area G where the AWR is the highest. At t = 2000s, the area E is the most dangerous area. After t = 2000s, nearly all areas have high AWR. Based on above analysis, the following resources allocation strategy is advised: (1) at the first half an hour of emergency response, more rescue resources should be sent to E, G, and J; (2) after that, D, F, H, and I gradually need more resources.

Table II. Aggregated Weighted Risk in the 10 Residential Areas at Different Times

	600s	800s	1200s	1600s	2000s	2600s
A	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	0.05801328
B	0.00000000	0.00000000	0.00000000	0.00000000	0.03297678	70.69564293
C	0.00000000	0.00000000	0.00000000	0.00000000	0.00007334	0.45263844
D	0.00000000	0.00000000	0.00000102	0.00110798	0.20017541	34.11987993
E	0.00000238	0.00072004	0.18783947	4.60474650	98.56040847	1126.08295703
F	0.00000000	0.00000000	0.00008104	0.01595472	0.70950394	27.93128237
G	0.00462710	0.07861287	1.46759059	9.16648734	35.34787203	115.56288804
H	0.00000000	0.00000000	0.00000000	0.00007405	0.01880954	3.57464209
I	0.00000000	0.00000000	0.00005910	0.02229424	1.22450960	46.84007340
J	0.00000000	0.00001079	0.01515049	1.31135140	24.86859071	316.95609140

4. CONCLUSIONS

Emergency response is applying science, technology, planning, and management to deal with extreme events. Developing a meaningful model capable of conducting emergency response is an arduous task that requires the contributions of many individuals from several disciplines. The cellular automata-based systematic risk analysis approach for emergency response presented here is a preliminary attempt to contribute to the gigantic efforts.

In this article, three cellular automata transition rules, which work through diffusion, transport, and dissipation mechanism, are proposed. The approach can take multiple factors into account such as physical and social characteristics of the site and can also handle domino accidents. As an outcome, two risk indices are proposed to assist emergency managers to make decisions. The potential application of the proposed approach for risk analysis and emergency response has been illustrated with an example. The results demonstrate that the CA method can easily treat heterogeneous conditions, and give an irregular shape of the area of impact of an accident, which is much more realistic assessment for risk analysis. Besides, according to the results, we conclude that individual risk is useful to plan evacuation strategies and aggregated weighted risk can help emergency managers to allocate rescue resources rationally and optimize emergency response programs.

In reality, before the approach is brought to bear on any complex problems, there are three issues meriting special attention. First and foremost, it must be emphasized that cellular automaton is a computational tool, whose effectiveness depends upon its accurate calibration on the basis of data from experimental results as well as those from past accident histories. Research in these areas has been continuing across the world but needs greater impetus. Besides, discussion of the size of the cells is also needed according to real problems in the future research. Secondly, the process of emergency response is very complicated, and some other social factors may also affect the results of risk assessment, such as important facility density, transportation system density, rescue power distribution, and so on. The detailed discussion of those factors should be conducted in future research. Last but not least, the merit of the approach should be judged in real-life scenarios, although it is hard. It is a good way to validate and improve the approach in future emergency response drills. The data gathered from real cases are also meaningful for this purpose.

REFERENCES

1 Ford, J. K., & Schmidt, A. M. (2000). Emergency response training: Strategies for enhancing real-world performance. Journal of Hazardous Materials, 75, 195–215.
10.1016/S0304-3894(00)00180-1
CAS PubMed Web of Science® Google Scholar
2 Haimes, Y. Y. (1999). The role of the society for risk analysis in the emerging threats to critical infrastructures. Risk Analysis, 19(2), 153–157.
10.1111/j.1539-6924.1999.tb00396.x
Web of Science® Google Scholar
3 Wulf, W. A., Haimes, Y. Y., & Longastaff, T. A. (2003). Strategic alternative responses to risks of terrorism. Risk Analysis, 23(3), 429–444.
10.1111/1539-6924.00325
PubMed Web of Science® Google Scholar
4 Lindell, M. K., Prater, C., & Perry, R. W. (2007). Introduction to Emergency Management. New York , Wiley Press.
Google Scholar
5 Dombroski, M., Fischhoff, B., & Fischbeck, P. (2006). Predicting emergency evacuation and sheltering behavior: A structured analytical approach. Risk Analysis, 26(6), 1675–1688.
10.1111/j.1539-6924.2006.00833.x
CAS PubMed Web of Science® Google Scholar
6 Kaplan, S., & Garrick, J. (1981). On the quantitative definition of risk. Risk Analysis, 1(1), 11–27.
10.1111/j.1539-6924.1981.tb01350.x
PubMed Web of Science® Google Scholar
7 Haimes, Y. Y. (2006). On the definition of vulnerabilities in measuring risks to infrastructures. Risk Analysis, 26(2), 293–296.
10.1111/j.1539-6924.2006.00755.x
PubMed Web of Science® Google Scholar
8 Khan, F. I., & Abbasi, S. A. (2002). A criterion for developing credible accident scenarios for risk assessment. Journal of Loss Prevention in the Process Industry, 15, 467–475.
10.1016/S0950-4230(02)00050-5
Web of Science® Google Scholar
9 Khan, F. I., & Abbasi, S. A. (2000). Analytical simulation and PROFAT II: A new methodology and computer automated tool for fault tree analysis in chemical process industries. Journal of Hazardous Materials, A75, 1–27.
10.1016/S0304-3894(00)00169-2
Web of Science® Google Scholar
10 Arystanbekova, N. K. (2004). Application of Gaussian plume models for air pollution simulation at instantaneous emissions. Mathematics and Computers in Simulation, 67, 451–458
10.1016/j.matcom.2004.06.023
Web of Science® Google Scholar
11 Gong, Y. W., Lin, W. S., Gu, A. Z., & Lu, X. S. (2004). A simplified model to predict the thermal response of PLG and its influence on BLEVE. Journal of Hazardous Materials, A108, 21–26.
10.1016/j.jhazmat.2004.01.012
CAS Web of Science® Google Scholar
12 Hankin, R. K. S., & Britter, R. E. (1999). TWODEE: The Health and Safety Laboratory's shallow layer model for dense gas dispersion. Part 1. Mathematical basis and physical assumptions. Journal of Hazardous Materials, 66(3), 211–226.
10.1016/S0304-3894(98)00269-6
CAS PubMed Web of Science® Google Scholar
13 Chen, H.- J., & Lin, M.- H. (1999). Modeling a boiling-liquid, expanding-vapor explosion phenomenon with application to relief device design for liquefied ammonia storage. Industrial & Engineering Chemistry Research, 38, 479–487.
10.1021/ie980216y
CAS Web of Science® Google Scholar
14 Hankin, R. K. S. (2003). Shallow layer simulation of heavy gas released on a slope in calm ambient. Part I. Continuous releases. Journal of Hazardous Materials, A103, 205–215.
10.1016/S0304-3894(03)00224-3
CAS Web of Science® Google Scholar
15 Khan, F. I., & Abbasi, S. A. (2001). An assessment of the likelihood of occurrence, and the damage potential of domino effect (chain of accidents) in a typical cluster of industries. Journal of Loss Prevention in the Process Industries, 14, 283–306.
10.1016/S0950-4230(00)00048-6
Web of Science® Google Scholar
16 Von Neumann, J. (1966). In A. Burks (Ed.), Theory of Self-Reproducing Automata. Urbana , IL : University of Illinois Press.
Google Scholar
17 Ulam, S. (1952). Random processes and transformations. Proceedings of the International Congress on Mathematics, 2, 264–275.
Google Scholar
18 Sarkar, C., & Abbasi, S. A. (2006). Cellular automata-based forecasting of the impact of accidental fire and toxic dispersion in process industries. Journal of Hazardous Materials, A137, 8–30.
10.1016/j.jhazmat.2006.01.081
CAS Web of Science® Google Scholar
19 Gledhill, J., & Lines, I. (1998). Development of Methods to Assess the Significance of Domino Effects from Major Hazard Sites. CR Report 183. London , UK : Health and Safety Executive.
Google Scholar
20 Contini, S., Boy, S., Atkinson, M., Atkinson, M., Labath, M., Banca, M., et al. (1996). Domino effect evaluation of major industrial installations: A computer aided methodological approach. In Proceedings of the European Seminar on Domino Effects. Leuven , Belgium .
Google Scholar
21 Delvosalle, C. (1998). A Methodology for the Identification and Evaluation of Domino Effects. Report CRC/MT/003, Brussels , Belgium , Belgian Ministry of Employment and Labor.
Google Scholar
22 Bagster, D. F., & Pitblado, R. M. (1991). The estimation of domino incident frequencies: An approach. Process Safety Environment, 69, 195–199.
Web of Science® Google Scholar
23 Khan, F. I., & Abbasi, S. A. (1998). Models for domino effect analysis in chemical process industries. Process Safety Progress, 17(2), 107–123.
10.1002/prs.680170207
CAS Web of Science® Google Scholar
24 Cozzani, V., & Salzano, E. (2004). The quantitative assessment of domino effects caused by overpressure. Part I. Probit models. Journal of Hazardous Materials, 107(3), 67–80.
10.1016/j.jhazmat.2003.09.013
CAS PubMed Web of Science® Google Scholar
25 Papazoglou, I. A., & Aneziris, O. N. (1999). Uncertainty quantification in the health consequences of the boiling liquid expanding vapor explosion phenomenon. Journal of Hazardous Materials, A67, 217–235.
10.1016/S0304-3894(99)00041-2
Web of Science® Google Scholar
26 Committee for the Prevention of Disasters. (1989). Methods for the Calculation of Possible Damage (Green Book). The Hague , The Netherlands : Committee for the Prevention of Disasters.
Google Scholar
27 Uijt de Haag, P. A. M., & Ale, B. J. M. (1999). Guidelines for Quantitative Risk Assessment (Purple Book). The Hague , The Netherlands : Committee for the Prevention of Disasters.
Google Scholar
28 Christou, M. D., & Mattarelli, M. (2000). Land-use planning in the vicinity of chemical sites: Risk-informed decision making at a local community level. Journal of Hazardous Materials, 78, 191–222.
10.1016/S0304-3894(00)00223-5
CAS PubMed Web of Science® Google Scholar
29 Cozzani, G., Gubinelli, G., Antonioni, G., Spadoni, G., & Zanell, S. (2005). The assessment of risk caused by domino effect in quantitative area risk analysis. Journal of Hazardous Materials, A127, 14–30.
10.1016/j.jhazmat.2005.07.003
CAS Web of Science® Google Scholar
30 Jonkmana, S. N., Van Gelder, P. H. A. J. M., & Vrijling, J. K. (2003). An overview of quantitative risk measures for loss of life and economic damage. Journal of Hazardous Materials, A99, 1–30.
10.1016/S0304-3894(02)00283-2
CAS Web of Science® Google Scholar
31 Abrahamsson, M. (2002). Uncertainty in quantitative risk analysis: Characterization and methods of treatment. Research report 1024, Lund .
Google Scholar
32 Lees, F. P. (1996). Loss Prevention in the Process Industries, 2nd ed. Oxford , UK : Butterwort-Heinemann.
Web of Science® Google Scholar
33 Centre for Chemical Process Safety (CCPS) of the American Institute of Chemical Engineers. (2000). Guidelines for Chemical Process Quantitative Risk Analysis, 2nd ed. New York : AiChE.
Google Scholar
34 Pietersen, C. M., & Huerta, S. C. (1985). Analysis of the LPG Incident in San Juan Ixhuatepec, Mexico City, 19 Nov 1984. TNO84-0222. Apeldoorn , The Netherlands : Netherlands Organization for Applied Scientific Research.
Google Scholar

Citing Literature

Volume28, Issue5

October 2008

Pages 1247-1260

Cellular Automata-Based Systematic Risk Analysis Approach for Emergency Response

Abstract

1. INTRODUCTION

2. THEORETICAL BACKGROUND