The study on the coupling model of unconventional incidents

1 Introduction

With the social development and environmental change, the frequency and size of the events in the world are constantly improving and expanding (Hang et al., 2009). At the same time, because of the increasing interrelation of the social system, events of one system could cause other events in another system. So the localized and conventional events may evolve to be serious effect and harmful emergency. This is called coupling between systems. Lack of the scientific understanding of the coupling low of emergency and its secondary derivatives disaster, we cannot distinguish the coupling transmission and variation of the emergency, so that the management will have difficulty to take effective warning and emergency action. So quantitatively describing the coupling feature of the events during the evolution and scientifically analyzing the coupling low of the events is the unconventional emergency management theory and practice of the key issues to be solved.

Now the study of the coupling of emergency concentrate on concrete emergency fields, especially in natural disaster field. In literature (Cong et al., 2006), the writer take advantage of the logistic regression model and pre‐effective rainfall into the geological disaster warning field. Based on the comprehensive analyze the rainfall and geological environmental factors, the writer raised measure of auto divide the danger level to auto warning the rainfall induced disaster. Through analyzing the environmental factors of landslip, the literature (Li et al., 2006) explained the coupling affection among geological structure, height of water before the slope, rainfall, underground water, human activities. Based on the disaster investigation of earthquake in Wenchuan, the literature (Zhang et al., 2009) summarized some main perform of inner and outer dynamic coupling during the disaster evolution, which are coupling of active faults and weathering, the coupling of the form of deformation and failure and the structure of rock and soil, the coupling of seismic forces and topography, the coupling of seismic forces and underground water, and so on. What is more, there are other studies, such as study of the coupling of rainstorm and landslip (Finlay et al., 1997; Dahal et al., 2008; Zhou and Li, 2009), flood coupling (Guo and Guo, 2009), magnetic storm coupling (Liu and Wen, 2002), fire disaster coupling (Xun et al., 2010; Yao et al., 2007), elastic supply network coupling (Liu and Ji, 2007), based on Bays net modeling of emergency coupling (Dong, 2009), the type and mechanism of the coupling (Chi and Chen, 2011), etc.

All these literature discussed the coupling during the emergency evolution from different sights, however, they can be relatively narrow range of applications, while there is little research on general coupling mechanism for emergency from the perspective of emergency management to guide different types of emergencies incident response. Therefore, the urgent need for the study on the mechanisms for different types of coupling events in‐depth is made, so that it can establish different types of coupling models to guide the complex coupling event emergency management.

Being a random network which take on the features such as straightforward and concise, logical mathematical model, Graphical Evaluation Review Technique (GERT) has a very wide range of applications (Lin et al., 2011; Wang et al., 2011; Reza et al., 2010; Manji et al., 2007). From the actual needs for the modeling, Pritsker et al. further develop the functions of the GERT network nodes and make it form a GERTS (random network simulation technology) network model. GERTS model integrates the network theory, probability theory and simulation technology, so it can well describe the relationship between the activities and status of the transfer in the process and effectively reflect the randomness of the process. If we take the state of the system in the unexpected events evolution as a node, then the connected arrows can stand for the transferred relationship between nodes, and it apparently takes on a certain probability relationship, so the network possesses the randomness in the running process. While modeling principles of the GERTS network can describe the evolution of the uncertainty of events, so event evolution based on GERTS network model can be constructed (Fang et al., 2009).

Therefore, by analyzing the types and general mechanism of emergency coupling, based on the GERTS network characteristics, the concepts of three types of coupling are put forward, and then three types of coupling operators are defined and studied, so that it could provide an effective tool for the quantitative study on unconventional incidents coupling.

2 The concept and type of emergency coupling

The events coupling in the evolution of the emergency is the phenomenon that in the evolution of disaster system the interactions and effects of two or more factors cause other emergencies or make the original coupling emergency more serious. According to different classification standards, there are different classifications of the emergency coupling. On the basis of the manifestation of coupling objects, the emergency coupling can be divided into three types of coupling which are “events‐events” coupling, “event‐factors” coupling and “factors‐factors” coupling (Chi and Chen, 2011).

Where, the “events‐events” coupling refers to the phenomenon that the mutual coupling between two or more emergencies leads to a greater emergency. For example, the coupling between the two emergencies which are earthquakes and the rain, respectively, can cause coast or debris flow that are greater harm.

The “events‐events” coupling refers to the phenomenon that the mutual coupling between the emergency and some influencing factors makes the emergency more serious or causes new emergencies. Here the difference between the “factor” and “emergency” is that “factor” is not hazardous, while the “emergency” is hazardous. For example, the dry weather itself is not hazardous, but it is the influence factor of fire.

The “factors‐factors” coupling means the mutual coupling between two or more influencing factors leads to emergency. For example, the coupling between strong winds and loose billboards will result in the falling of billboards.

According to the effect mechanism and the method of coupling objects, the emergency coupling can be divided into three types of coupling which are hybrid force coupling, mutual force coupling, driving force coupling.

Definition 1

If there are not interactions between the event A_i (i=1,2, … ,n), and the event A_i can lead to the emergence of the event C, but the common occurrence of the event A_i and the event A_j (i≠j) causes that the consequences of the event C is much larger than the sum of the two consequences which are caused by the event A_i and the event A_j, respectively, and increases the probability of that the event C induces other secondary disasters, and enhances the disaster strength of the event C, this way of coupling is called hybrid force coupling. Where, the event A_i is called induced event (also known as precursor events), and the event C is called coupling event (also known as follow‐up event). (The coupling between earthquake and rainfall lead to worse consequences of landslide, it is hybrid force coupling).

Definition 2

The interactions between the events A and B lead to more serious consequences of each other disaster events, and increases the probability of that the event A and B induces other secondary disasters, and enhances the disaster strength, this way of coupling is known as mutual force coupling. (The coupling between flood and the damage of the hydraulic structure is mutual force coupling. Floods damage the hydraulic structure, and the damage of the hydraulic structure will make floods more serious).

Definition 3

The event A_i (i=1,2, … ,n) is not the inducting factor of the event C, but the event A_i (i=1,2, … ,n) can lead to more serious disaster consequences of the event C, and increases the probability of that the event C induces other secondary disasters, and enhances the disaster strength, then the coupling between A_i (i=1,2, … ,n) and C is called driving force coupling. The event A_i is called the driving factor of the event C (such as the coupling between wind and fire coupling is driving force coupling, the factor wind results in more serious consequences of fire).

To research and analyze the impact of the coupling between events on the evolution situation of the disasters quantitatively, you need to analyze in the perspective of the output factors and the input factors of the coupling events. However, considering the differences of data attributes between the output factors and the input factors of the events (many data, contrasting), and the difficulty of obtaining data (it is difficult to obtain the details of the loss data of the disaster attributes in the literature and the network). This paper mainly use the state elements of the event (the rate of disaster evolution) to study the coupling between the events (mainly considering that this date is easier to obtain, and the elements can also reflect the overall disaster extent of the event). Therefore, the coupling referred to below is the coupling between the disaster loss rates of the disaster events.

3 Construction of three coupling model

If the event (factor) A_i (i=1,2, … ,n) is induced event (factor) of the hybrid force coupling for the event Z, and dA_i/dt stands for the changing rate of the event A_i, then: Equation 1 is called the disaster loss rate based on the hybrid force coupling event Z.

Where, T stand for the hybrid force coupling operator, while w(t) is coupling parameter, and form (1) is called a hybrid force coupling model.

If the event (factor) A_i (i=1,2, … ,n) is mutual force coupling (event factor), then T is called as the mutual force coupling operator: Equation 2 where, dA_i/dt stand for the disaster loss rate of the event (factor) A_i, V(A_j(t)) stand for the disaster loss rate of the event (factor) in the time t; (1/V(A_i(t)))∑_j=1,j≠iⁿw_ji(t) · V(A_j(t)) stand for the acceration factor of the event (factor) A_i in the effect of the mutual force coupling event (factor) in the time t; w_ji(t) stand for the acceration factor of the event A_j on the event A_i in the effect of the mutual force coupling (event factor) in the time t.

Therefore, a mutil‐ factor mutual force coupling model is built and shown in the form (2): Equation 3 Suppose A_i (i=1,2, … ,n, no considering the coupling relationship between them) is driving force coupling event (factor) of the disastrous event Z, written as A=∑_i=1ⁿA_i, then T is called as the driving force coupling operator: Equation 4 where, w_j stand for the acceration coefficient factor of the event A_j on the event Z in the effect of driving force coupling, and the form (3) is called as the driving force coupling model.

The following steps can be used to achieve the above three types of coupling model in the simulation based on GERTS network, as follows:

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  Step 1. Collect and collate for a possible emergency driving force coupled set of events.

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  Step 2. Make and set a priori the conditions for the occurrence of the driving force coupling for an emergency event and its driving force factors.

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  Step 3. If satisfy the a priori conditions, the driving force coupling occurs.

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  Step 4. Determine the solution method of the coupling parameters, and deducte and calculate the disasters results from coupling effects.

4 Case study

According to the statistics from 1949 to 2011, a total of more than 300 typhoons have influenced China, and they often act frequently between July and September. The areas, which typhoon landed through both before and after the typhoon, often appear too concentrated and wider range of heavy rain, sometimes even severe storms, so that those areas often appear flash floods, flood tide, and even embankment, reservoir and other disasters. (On August 7, 2009, the typhoon named “molake” landed in Hualien Taiwan China, and landed again on August 9 in XiaPu fujian China. From the beginning to the end of the “molake” typhoon, it only experienced nine days, but it caused serious disasters to many provinces and cities. The typhoon caused 693 deaths, 76 missing, 46 hurt, and the loss of Agricultural products as high as 4.932 billion yuan, farmland and agricultural facilities loss 5.02 billion yuan in Taiwan. In the whole process of disaster, there were 57 water conservancy facilities damaged, 57 embankment, four Seawall disaster and 25 gaging station were on the alert. In addition, there were as high as 20 fractures on railway bridge and all kinds of highway bridge, 540 buildings confronted with water problems, 11 buildings collapsed, and even more than 200 landslides happened. On the mainland, the disaster affected 13.516 million people in Fujian, Zhejiang, Jiangxi, Anhui, Jiangsu five provinces, caused nine death, three missing, 1.61 million people displaced to emergency shelters and 14,000 houses collapsed. The disaster caused direct economic loss as high as 11.45 billion yuan, at the same time also can cause mudslides, landslides and secondary disasters.

By analyzing and transformating the typhoon events and their logical, the evolution process of the typhoon events can be with described based on the GERTS network (Figure 1). Where, many houses collapsed are resulted the coupling function of water and typhoon, while the coupling function of flood and the damage of the agricultural facilities result in the damage of crops; and the flood and the damage of the water conservancy facilities are typical mutual coupling, they influence and promote each other.

In the digital experiment of scene inference, to begin with, the evolution scene of the initial disaster events (the typhoon) should be set. On the basis of the published rainfall data of “molake”, and considering the fact that the normal distribution is the theoretical basis of many statistical method. Although many statistical method are not requirements analysis index must submit to normal distribution, many real disaster is similar to the process of normal distribution characteristics, and its corresponding statistics approximate to normal distribution in the big samples. So, we assumpt the evolution scene of the initial disaster events (the typhoon) as normal distribution.

What is more, derived disaster and secondary disasters have the nature of randomness and time delayed in disaster evolution system, so quantitative representation would be needed in the scene inference process in order to describe the impact of randomness and time delayed on disaster system. As a result of the complexity of the disasters evolution system, it is difficult to obtain exact values, but it can be assignmented with the knowledge and experience of experts. For the convenience of calculation, the random of events inducing coupling is setted as 0.2 and the time of induced delay setted as two days in the following disaster scene suggesting.

At the last but not the least, due to the specificity of emergencies and the incomplete of information, it is difficult to obtain historical statistics data of the disaster losses. If a more complete history statistics data can be obtained, then the coupling parameters can be acquired through the analysis and fitting of historical statistical data. If the history statistics data are relatively poor, these parameters can be estimated with the knowledge of expert who participated in the rescue and the historical experience (if more than one estimate given by experts is inconsistent, group decision‐making and data fusion method are available for processing, thereby a satisfactory value can be obtained). The coupling coefficient in this part based on the knowledge and experience of expert is an estimated value taken as 0.5.

According to the above “Morak” typhoon disaster scenario inference GERTS network and GERTS network simulation theory, the above parameters can be obtained, then based on the Matlab, the scenarios inference result of the disaster loss rate is available and shown in Figure 2.

In Figure 2, the x‐axis (node) stands for each node of disaster system in Figure 1, while the y‐axis (time) stands for the scene inference time of disaster loss in each node, the z‐axis (disaster loss rate) said disaster losses of each node. Figure 2 shows directly the disaster loss rate of each node trends over time in disaster evolution system which showed in Figure 1. According to Figure 2, it is obvious that the disaster loss rate of node 7 (crop loss) change in a large range and is higher than other nodes in the same period (from the numerical point of view) and continued losses for the later in the typhoon disaster scenario inference GERTS network, so the subsystem of disaster evolution composed by typhoons‐agricultural facilities damage‐crops loss is the major disaster evolution process in this system. The disaster loss rate of node 2 (building collapse), and node 6 (house water) in scenario deduction changes in scope (from the numerical point of view), while enough attention should be paid to the loss of these nodes leading to large numbers of people relocated in the disaster control. The disaster loss rate of node 4 (population casualties) changes little in the initial phase of the scenario deduction, but from the beginning of the scene inference time period 4, the loss rate increases rapidly and peak at the time of stage 7. In addition, the disaster losses rate of node 7 emerged the phenomenon of more than one peaks. This phenomenon can be used effectively in risk control, that is, when relief measures can delayed the next level of disaster, people are able to raise all kinds of supplies and relief actively, and the peak of disaster loss rate will be reduced, it will reduce the relief the pressure.

5 Conclusion

Coupling, common phenomenon in unconventional incidents, is a significant factor that leads to the happen and deterioration of unconventional incidents. To deal with the weakness in research on unconventional incidents evolution, this article analyzes different type of coupling in unconventional incidents and proposes three types of coupling based on current research. The models of the three types of coupling are built, effectively making up for the method scarcity of quantitative research on unconventional incidents evolution. The academic result of this article is expected to be of practical significance to scientific unconventional incidents management and effective emergency measures. Still, what should not be neglected is that there are many areas remained to be studied in unconventional incidents evolution estimation. For instance, the coupling of different type of unconventional incidents can be modeled to explore the coupling rule. The method of getting rid of coupling factors is among our future in‐depth research.