Probabilistic model for safe evacuation under the effect of uncertain factors in fire
Introduction
Evacuating people safely in a fire is a process in which people are evacuated to safe zones when there is a fire. In current research, two parameters are generally used to determine whether people can be evacuated safely, i.e., the available safe egress time (ASET) and the required safe egress time (RSET) Kuligowski, 2013. If ASET is more than RSET, it means that people can be evacuated safely from the building to the safe zones. The parameter ASET is the duration from the start of a fire to such a disastrous fire environment in which people can no longer be evacuated. It is also the duration from the start of a fire to the time when the hazard factors in a fire can endanger the evacuation. The ASET can be determined by fire model or field simulation (Ronchi, 2013).
The parameter RSET is the time required for people to evacuate to safe zones after the occurrence of a fire, which includes the recognition time, pre-movement time and movement time. These three times are explained as follows. (1) Recognition time. An detector signal is generated when the fire detector installation is activated by the release of hot smoke or thermal radiation in case of fire. Then, people or evacuees themselves realize the occurrence of fire. This period is called the recognition time, whose duration depends on the type and layout of the detector installation, scale of fire and its growth rate. Society of Fire Protection Engineers (SFPE) has summarized the models which can predict the recognition time. They have further developed corresponding prediction models of the recognition time for stable and instable fires (Seguridad contra incendios et al., 2002). (2) Pre-movement time. The pre-movement time in an evacuation is closely related with their psychological state, behavior characteristics, age, and degree of familiarity with the buildings, sensitivity to react, and even evacuees’ cluster characteristics. All these factors have a great deal of randomness. Hence, it is difficult to use mathematical functions to describe the pre-movement time accurately. Two approaches are currently used to carry out research on people’s pre-movement time, i.e. simulation modeling and evacuation testing. For example, Gwynne et al. developed a behavior process model to simulate people’s recognition of fire, decision making and preparing for evacuation (Gwynne et al., 2001). (3) Movement time. The movement time is the time required for all the evacuees to evacuate to safe zones from the beginning of evacuation action. This period depends on the evacuation parameters such as people density, maximum indoor evacuation distance, effective width of evacuation door, and specific flow (Zhang et al., 2016). Until now, some evacuation simulation models, such as BGRAF, EXODUS, SIMULEX can be used to predict the movement time and performance of evacuations in a specific building and thus they become an important tool for doing the building evacuation analysis. In recent years, Kuligowski has classified 28 different egress models based on the level of complexity in occupant behavior (Kuligowski, 2004). Santos and Aguirre have described a critical review of emergency evacuation simulation models from the simulation methods including flow-based, cellular automata, and agent-based models (Santos and Aguirre, 2004). Tang has developed an agent-based simulation model which incorporates the fire scene and the building geometry by using a fire dynamics simulator (FDS) based on the computational fluid dynamics and geographic information system (GIS) data to model the occupant response (Tang and Ren, 2008). Braglia has proposed a new game theory based approach for the evacuees’ exit selection in emergency conditions. The model involves many other parameters and aspects attempting to obtain a satisfactory representation of the actual evacuation process and the human behavior in emergency conditions (Braglia et al., 2013).
However, in a real fire, people’s evacuation behavior is characterized by typical uncertainty features under the interaction of the fire source, people and building. For example, during the evacuation process, there can be congestion around the evacuation exit. Hence, there is uncertainty in the available exit width for evacuation before fire. Therefore, duality exists in the evacuation process, which includes determinacy and randomness (Magnusson et al., 1996). Current research on people’s safe evacuation in a thermal environment of buildings still uses the deterministic approach, while there is little research on the uncertainty and randomness of the evacuation parameters. Maclennan et al. suggested that the Weibull distribution can be used to model the probability distribution of RSET (Maclennan et al., 1999). Francisco et al. analyzed many uncertainty parameters associated with the time prediction model of a heat detector. They then utilized a probability density function to describe the uncertainty parameters, thereby developing a preliminary probabilistic analytical model on the detection time (Francisco et al., 2005). Fruin showed that the uncertainty in people’s body sizes plays a significant role in the accuracy of people’s movement time (Fruin, 1971). Helbing et al. used certain distribution to model the uncertainty in the people’s body size, thereby improving the computational accuracy and reliability of RSET (Helbing et al., 1997). However, there are few studies on the probability of people’s safe evacuation based on the effect of uncertain factors in an evacuation process.
With respect to the uncertainty in RSET, research has been carried out in this study on the randomness and determinacy in the recognition time, people’s pre-movement time and movement time. The mathematical expressions of determinacy and randomness in the evacuation process have been developed. Further, based on Latin Hypercube Sampling method, the probabilistic model for people’s safe evacuation under the effect of uncertain factors in a fire has also been developed.
Section snippets
Mathematical expression of people’s evacuation process
The required safe egress time (RSET) consists of five parts: time from fire ignition to detection, time from detection to notification of occupants of a fire emergency, time from notification until occupants decide to take action, time from decision to take action until evacuation commences and time from the start of evacuation until it is completed. Time from fire ignition to detection and time from detection to notification of occupants of a fire emergency could be collectively referred to as
Criteria for safety evacuation
When an enclosure catches fire, the personnel in the building start to evacuate after fire alarm. When the last person in the building is evacuated to the safety zone, the entire evacuation process is completed. When ASET is more than RSET, all the personnel in the building can be evacuated to the safety area before the fire danger emerges. Conversely, when ASET is less than RSET, some personnel may not be evacuated to the safety area before the fire danger emerges, and casualties may not be
Case study
Suppose a fire occurs in a 20 m long, 10 m wide, 5 m high theater, whose area is 200 m2. There are 2.5 m wide evacuation gates at the front and back of the theater, and smoke detectors have been installed in the theater. The combustibles in the theater are mainly the seats and curtains as shown in Fig. 3. There is audience in the theater when the fire occurs. The evacuation parameters are density of people, people’s pre-movement time, maximum indoor evacuation distance, effective width of the
Conclusions
Due to the uncertainties in a building fire and the evacuation behavior, the process of people’s evacuation is affected by many uncertain factors, such as the effective width of evacuation gates and evacuation speed. Although each uncertain factor shows certain random characteristics, these uncertain factors have been shown to follow certain statistical distributions. Based on this, Latin Hypercube Sampling method has been innovatively used in this study to mathematically describe the
Acknowledgments
The research presented in this paper was supported by the Key Laboratory of Building Fire Protection Engineering and Technology of MPS, China Postdoctoral Science Foundation (2016M590515) and Natural Science Foundation of Jiangsu Province (SBK2016041452).
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