# Real-Time Egress Model for Multiplex Buildings under Fire Based on Artificial Neural Network
## 2 Fire Simulation for Multiplex Building  
### Description of Fire Simulation  
The Fire Dynamics Simulator (FDS) [15], based on large eddy simulation (LES) [16], has been widely used for fire simulation and well verified by many researchers [1; 2; 3; 4]. In this study, therefore, the FDS was chosen to simulate the event of fire in multiplex buildings. As shown in Figure 3, the multiplex building has a room height of 3.2 m with a floor area of 3444 m\({}^{2}\) (82 m \(\times\) 42 m), and a mesh size of 0.62 m \(\times\) 0.62 m \(\times\) 0.72 m [15]. The mesh sizes were determined based on the \(D^{*}\) method mentioned in the FDS User Guide [15]. A nondimensional parameter (\(D^{*}/\delta x\)) was set to 4, where \(D^{*}\) is a characteristic fire diameter (m), and \(\delta x\) is the nominal size of a mesh cell (m). \(D^{*}\) can be calculated as follows:  
\[D^{*}=\left(\frac{\overset{\bullet}{Q}}{\rho_{co}c_{p}T_{\infty}\sqrt{g}} \right)^{2/5} \tag{1}\]  
where \(\dot{Q}\) is the total heat release rate of fire (kW), \(\rho_{\infty}\) is the density of air (1.204 kg/m\({}^{3}\)), \(c_{p}\) is the specific heat (1.005 kJ/kg-K), \(T_{\infty}\) is the ambient temperature (293 K), and \(g\) is the acceleration of gravity (9.8 m/s\({}^{2}\)). The type of fuels and the location of fire sources were set as the main variables for the analysis. A total of five fuel types, which include ethanol, kerosene, polystyrene foams, polyurethane foams and wood, were used, and the location of fire sources were divided into 12 compartments, as indicated by the numbers in circles, as shown in Figure 3. The values presented in the Society of Fire Protection Engineers (SFPE) handbook [17] were used as the material properties of fuels, as shown in Table 1. The combustibles were assumed to be chairs, tables, and sofas, which are mainly placed on the floor in the multiplex building, and the heat release rate (HRR) of each combustible was set by referring to the DB provided by the National Center for Forensic Science (NCFS) [18]. As shown in Figure 4, heat release rates over time were calculated using a \(t\)-squared fire curve [19]:  
\[t=\sqrt{\frac{Q}{\alpha}} \tag{2}\]  
where the fire growth rate is classified into'slow','medium', 'fast', and 'ultra fast'. \(Q\) is the HRR (kW), \(\alpha\) is the coefficient for fire growth, and \(t\) is the time (s). In the fire simulation conducted in this study, the burning area was set as 1 m \(\times\) 1 m, and the fire growth rate was assumed to be of a medium level with reference to the _Structural Design for Fire Safety_[20]. Figure 2: General structure of an egress model based on ANN. In general, factors that directly influence the safety of the occupants in the event of a fire include toxic gases, heat, and visibility [17], and the National Fire Protection Association (NFPA) presents tenability criteria, as shown in Table 2. In this study, a simulation was conducted on fire scenarios for a total of 60 cases, as shown in Table 3, and the temperature, visibility, and concentrations of oxygen (O\({}_{2}\)), carbon dioxide (CO\({}_{2}\)), and carbon monoxide (CO) at the fire compartment and nonfire compartment were measured for each scenario with the use of measurement devices placed in a total of 27 locations at intervals of 1 m, as shown in Figure 5. In order to evaluate the spread of fire and the safety of life during evacuation of occupants, the measurement devices were installed at a height of 1.8 m from the floor as suggested by NFPA. Ventilation systems can reduce concentrations of toxic gases, which keeps occupants safer under fire. The ventilation systems in multiplex buildings are in fact diverse, which makes it very difficult to conduct numerical simulations when considering all the different cases. In the simulation conducted in this study, therefore, it was assumed that there was no forced (or active) ventilation system in the multiplex