# Fire Egress System Optimization of High-Rise Teaching Building Based on Simulation and Machine Learning

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

#### 1.3. Scientific Originality

#### 1.4. Aim of This Work

## 2. Research Methodology

#### 2.1. Study Building Specification

#### 2.2. Indicators for Evaluations of the Building Egress System

#### 2.2.1. Criterion for Evaluation of the ASET

^{3}), ${\mathrm{c}}_{\mathrm{p}}$ is the air specific heat (kJ/(kg∙K)), ${\mathrm{T}}_{\infty}$ is the ambient temperature, and g is the acceleration of gravity (${\mathrm{m}/\mathrm{s}}^{2}$).

#### 2.2.2. Criterion for Evaluation of the RSET

- The speed of evacuating people decelerates when passing through obstructions such as stairs, with a certain acceleration maintained in areas with low density of passenger flow:$${\mathrm{v}}_{0}=\left\{\begin{array}{c}{\mathrm{v}}_{\mathrm{max}}\frac{\mathrm{k}}{1.4}(\mathrm{D}<0.55)\\ {\mathrm{v}}_{\mathrm{max}}\frac{\mathrm{k}-0.266\mathrm{kD}}{1.19}(\mathrm{D}\ge 0.55)\end{array}\right.$$$${\mathrm{a}}_{\mathrm{max}}=\frac{{\mathrm{v}}_{\mathrm{max}}}{\mathrm{t}}$$

- 2.
- Directional selection weights during evacuation:$$\mathsf{\omega}=\frac{\mathsf{\theta}}{2\mathsf{\pi}}$$

- 3.
- The speed and acceleration vectors in the direction of evacuation with the least probability of path selection:$$\left|\stackrel{\rightharpoonup}{\mathrm{v}}\right|=\left\{\begin{array}{c}{0(\mathrm{l}}_{\mathrm{max}}\le {\mathrm{l}}_{\mathrm{stop}})\\ {\mathrm{v}(\mathrm{l}}_{\mathrm{max}}{\mathrm{l}}_{\mathrm{stop}})\end{array}\right.$$$${\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{min}}=\left|\stackrel{\rightharpoonup}{\mathrm{v}}\right|\ast {\stackrel{\rightharpoonup}{\mathrm{l}}}_{\mathrm{min}}$$$${\stackrel{\rightharpoonup}{\mathrm{a}}}_{\mathrm{min}}=\frac{{\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{min}}-\stackrel{\rightharpoonup}{\mathrm{v}}}{\left|{\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{min}}-\stackrel{\rightharpoonup}{\mathrm{v}}\right|}{\mathrm{a}}_{\mathrm{max}}$$
^{2}).

- 4.
- The speed and place of evacuees travelling to the next location:$${\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{next}}{=\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{min}}{+\stackrel{\rightharpoonup}{\mathrm{a}}}_{\mathrm{min}}\Delta \mathrm{t}$$$${\stackrel{\rightharpoonup}{\mathrm{P}}}_{\mathrm{next}}{=\stackrel{\rightharpoonup}{\mathrm{P}}+\stackrel{\rightharpoonup}{\mathrm{v}}}_{\mathrm{min}}\Delta \mathrm{t}$$

#### 2.3. Determination of Main Independent Variables

#### 2.4. Data Deployment and Preference of Machine Learning Algorithms

#### 2.4.1. Preferential Selection of Algorithms

^{2}, MSE (Mean Square Error), RMSE (Root Mean Square Error), MAE (Mean Absolute Error), and MAPE (Mean Absolute Percentage Error) are used as assessment indices for the accuracy of the algorithm to predict the test set data. The formula is shown in Equations (11)–(15) [58]:

^{2}is to 1, the smaller the MSE, RMSE, MAE, and MAPE are, the more accurate the model is.

^{2}= 0.971, the closest to 1, and the lowest values of MSE, RMSE, MAE, and MAPE (Table 7), making this regression model the most accurate. As a consequence, this algorithm was the preferred one for predicting the outcomes of multi-factor combinatorial optimization (Figure 4).

#### 2.4.2. Parameter Combinations and Results Prediction

#### 2.5. Statistical Method

## 3. Results and Discussion

#### 3.1. Results of the Simulation

#### 3.1.1. Determining ASET: Simulating Fire Scenarios with Pyrosim

- Temperature analysis

^{2}, the electrical substation room is situated in the northwest quadrant of the floor plan. It has a high fire resistance and is removed from other principal usage rooms and the four stairwells. As a result, other areas, with the exception of the fire room and the nearby region, were not significantly affected by the temperature. The key element influencing evacuation is not temperature.

- 2.
- CO concentration analysis

- 3.
- Visibility analysis

#### 3.1.2. Determining RSET: Simulating Fire Emergency Evacuation with Pathfinder

#### 3.1.3. Comparison Results of ASET and RSET

#### 3.2. Effect of Design Parameters on Death Rate

#### 3.3. Data Analysis and Egress System Optimization

#### 3.3.1. Monofactor Analysis

^{2}= 0.499 suggested that it fitted the data quite well and can partially explain the relationship between the independent and dependent variables. As shown in Table 10, the average value of the residuals is close to 0 and the standard deviation is close to 1, indicating that the data are basically normally distributed. The VIF values for each factor are between 0 and 10 (Table 11), meaning that there is no covariance in this regression model, namely, the variables are independent of one another. Moreover, Table 11 illustrates the sensitivity and magnitude of the factors’ contributions to the effect of evacuation.

- The sensitivity factors for TET are SFW, SDW, and LDSF, all of which are design parameters of evacuation stairwells. As illustrated in Figure 12a, the stairwells are more likely to get congested than the others because they are at the end of the evacuation procedure for each level. This is in line with what the literature [55,64,65] analysis revealed.
- Additionally, the results indicates that CW and RDW are not sensitive to TET, which is inconsistent with the findings of earlier investigations [66,67]. This discrepancy results from the characteristics of building planar evacuation. The layout of the building, a series of rooms clustered around an atrium, is identical to how the rooms are arranged on the side facing the outer walkway. Furthermore, the atrium does not extend all the way to the top floor, creating a bigger area to accommodate the flow of passengers on the 6th, 8th, and 9th floors, resulting in relatively mild crowding in the corridors during the evacuation process (Figure 12b). Since there is no other crowd overlay and the evacuation burden is not particularly intense, RDW primarily affects the effectiveness of early personnel evacuation from the classroom to the corridor. As a result, its impact on TET is minimal (Figure 12c).
- SDW (Beta = −0.444) has more of an impact on TET than LDSF (Beta = −0.089). People enter the staircase by the SD and descend via the stairs. If the downstairs flight is positioned distant from the side of the stairwell door, it extends the evacuation distance for those on this floor. At the same time, they converge with the people on the upper floor. The merging behavior of the stairwell entry buffer would cut down the descending speed [38]. Meanwhile, the intensity of the behavior can be somewhat controlled by SDW, which also regulates the flow of individuals.

#### 3.3.2. Muti-Factor Combination Effect Analysis

## 4. Conclusions

- Three evaluation factors—temperature, CO concentration, and visibility—are typically used to determine the ASET. The ASET in this paper was assessed through calculations and analysis to be the moment when visibility achieved its limited value in stairwell 4.
- The three variables relating to stairwells (SFW, SDW, LDSF) are all sensitive factors for TET, with SFW contributing the most to TET and SDW the second most. These three variables should be prioritized in the architectural program.
- Although neither could reach ASET, the multi-factor combinations with a maximum reduction in TET by 29.5%, outperforms the single-factor approach in terms of enhancing evacuation performance, and TET drops to the lowest when SFW [2100, 2200], SDW [2000, 2200], CW [1800, 2400], with LDSF being close to staircase door.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SFW | Stair Flight Width |

SDW | Stairwell Door Width |

CW | Corridor Width |

RDW | Room Door Width |

LDSF | Location of the Downward Stair Flight |

TET | Total Evacuation Time |

ASET | Available Safe Evacuation Time |

RSET | Required Safe Evacuation Time |

S1 | Slice 1 |

S2 | Slice 2 |

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**Figure 2.**(

**a**) Photo of the teaching building; (

**b**) model of the teaching building; (

**c**) typical plan and fire source setting.

**Figure 5.**Temperature analysis: (

**a**) slices of room temperature at 75.4 s; (

**b**) slices of room temperature at 600 s; (

**c**) curves of temperature change in four stairwells; and (

**d**) slices of temperature in the Y-axis direction in the middle of the corridor.

**Figure 6.**CO concentration analysis: (

**a**) slice of room CO concentration at 131.8 s; (

**b**) slice of room CO concentration at 600 s; (

**c**) curves of CO concentration changes in four stairwells.

**Figure 7.**Visibility analysis: (

**a**) slice of room visibility at 43.5 s; (

**b**) slice of room visibility at 600 s; (

**c**) curves of visibility change in four stairwells.

**Figure 12.**(

**a**) Density distribution in the stairwell; (

**b**) density distribution in the corridor; (

**c**) density distribution near the room door.

**Figure 15.**Combination effect analysis: (

**a**) TET < ASET; (

**b**) larger SFW; (

**c**) smaller SFW; (

**d**) larger SDW; (

**e**) smaller SDW; (

**f**) LDSF near stairwell door; (

**g**) LDSF far from stairwell door. (Highlighted with orange square).

References | Research Tools | Scenarios | Content |
---|---|---|---|

Fang, Z.M. (2012) [38] | Empirical study | High-rise commercial building | Factors affecting the evacuation speed of stairwells |

Li, Y. (2020) [6] | Simulation | Hospital | Effect of overlap and acceleration on evacuation |

Zang, Y. (2021) [10] | Campus | Effect of obstacles on evacuation | |

Zhang, X. (2018) [23] | Subway station | Effect of floor plan on evacuation | |

Liu, Y.Q. (2021) [17] | Subway station | Fire smoke flow simulation | |

Wang, N. (2021) [19] | Underground shopping malls | Fire safety assessment | |

Tajima, Y. (2001) [36] | Effect of door size of exit on evacuation | ||

Weifeng, F. (2003) [37] | Bidirectional pedestrian movement characteristics | ||

Rostami, R. (2021) [9] | Elementary school | Effect of parameters such as exit numbers on evacuation | |

Kodur, V.K.R. (2020) [5] | High-rise office building | Effect of stair location on evacuation | |

Li, J.C. (2022) [34] | Optimal ratio of parameters for convex exit | ||

Syed Abdul Rahman, S.A.F. (2021) [35] | Campus | Evacuation emergency management | |

Wang, K. (2019) [29] | Machine learning | Evacuees’ movement pattern | |

Horii, H. (2020) [30] | Identification of crowd behavior | ||

Gu, J.L. (2022) [31] | Campus | Emergency management and evacuation simulation | |

Tkachuk, K. (2018) [32] | Prediction of the evacuation route | ||

Wang, K. (2023) [21] | Intelligent algorithm | Evacuation route optimization | |

Deng, H. (2021) [33] | Simulation, machine learning | Campus | Evacuation route planning |

Guo, K. (2022) [11] | Subway station | Evacuation optimization | |

Zhong, Y. (2021) [16] | Simulation, intelligent algorithm | Fire emergency lighting distribution |

Scenarios | Evaluation |
---|---|

ASET > RSET | Safe |

ASET < RSET | Dangerous |

Temperature (°C) | Endurance Time (min) |
---|---|

<60 | >30 |

100 | 12 |

180 | 1 |

CO Content (ppm) | Exposure Time | Harm Effect |
---|---|---|

100 | Within 8 h | No feeling |

400–500 | Within 1 h | No feeling |

600–700 | Within 1 h | Headache, nausea, breathing disorder |

1000–2000 | Within 2 h | Consciousness, breathing disorders, coma, die within 2 h |

3000–5000 | Within 20–30 min | Death |

10,000 | Within 1 min | Death |

Visibility Threshold (m) | Scenarios |
---|---|

1 | Small spaces |

10 | Large spaces |

Serial Number | Variables | Value Range |
---|---|---|

X1 | SFW | [1200, 2850] |

X2 | SDW | [900, 2550] |

X3 | CW | [1300, 2950] |

X4 | RDW | [900, 2550] |

X5 | LDSF | 0, 1 |

Serial Number | Algorithms | MSE | RMSE | MAE | R^{2} | MAPE |
---|---|---|---|---|---|---|

1 | Decision tree | 96.009 | 9.798 | 7.466 | 0.942 | 1.704 |

2 | Random Forest | 46.665 | 6.831 | 5.824 | 0.971 | 1.409 |

3 | Adaboost | 108.014 | 10.393 | 7.709 | 0.934 | 1.775 |

4 | Gradient Boosting Decision Tree (GBDT) | 85.019 | 9.220 | 7.461 | 0.948 | 1.759 |

5 | Extra Trees | 64.128 | 8.008 | 6.583 | 0.961 | 1.541 |

6 | CatBoost | 99.568 | 9.978 | 7.887 | 0.939 | 1.815 |

7 | K-Nearest Neighbor (KNN) | 67.905 | 8.240 | 6.643 | 0.959 | 1.557 |

8 | Back-Propagation (BP) neural network | 771.358 | 27.773 | 19.346 | 0.534 | 4.625 |

9 | Support Vector Machine (SVR) | 1364.423 | 36.938 | 33.006 | 0.177 | 7.960 |

10 | XGBoost | 84.082 | 9.169 | 8.035 | 0.949 | 1.887 |

11 | Light Gradient Boosting Machine (LightGBM) | 649.480 | 25.484 | 14.749 | 0.608 | 3.379 |

12 | Linear Regression (Gradient Descent) | 775.047 | 27.839 | 19.234 | 0.532 | 4.641 |

Type | Gender | Ratio (%) | Shoulder Width (cm) | Height (m) | Walking Speed (m/s) |
---|---|---|---|---|---|

Youths | Man | 53 | 40 | 1.7 | 1.55 |

Woman | 37 | 37 | 1.6 | 1.5 | |

Middle-aged | Man | 5 | 41 | 1.7 | 1.52 |

Woman | 5 | 38 | 1.6 | 1.4 |

Type | Parameter Setting |
---|---|

RDW (mm) | 1000 |

CW (mm) | 2160 |

SDW (mm) | 1#2# staircases 1500 |

3#4# staircases 1300 | |

SFW (mm) | 1#2# staircases 1530 |

3#4# staircases 1480 | |

LDSF | Away from stairwell doors |

Minimum | Maximum | Average | Standard Deviation | Number of Cases | |
---|---|---|---|---|---|

Predicted value | 297.295 | 402.385 | 363.161 | 17.873 | 4000 |

Residuals | −51.149 | 87.345 | 0.000 | 17.888 | 4000 |

Standard predicted values | −3.685 | 2.195 | 0.000 | 1.000 | 4000 |

Standard residuals | −2.858 | 4.880 | 0.000 | 0.999 | 4000 |

Serial Number | Variables | Beta | p | VIF |
---|---|---|---|---|

1 | SFW | −0.560 | 0.000 | 1.052 |

2 | SDW | −0.444 | <0.001 | 1.017 |

3 | CW | −0.030 | 0.007 | 1.008 |

4 | RDW | 0.005 | 0.674 | 1.046 |

5 | LDSF | −0.089 | <0.001 | 1.030 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhou, M.; Zhou, B.; Zhang, Z.; Zhou, Z.; Liu, J.; Li, B.; Wang, D.; Wu, T.
Fire Egress System Optimization of High-Rise Teaching Building Based on Simulation and Machine Learning. *Fire* **2023**, *6*, 190.
https://doi.org/10.3390/fire6050190

**AMA Style**

Zhou M, Zhou B, Zhang Z, Zhou Z, Liu J, Li B, Wang D, Wu T.
Fire Egress System Optimization of High-Rise Teaching Building Based on Simulation and Machine Learning. *Fire*. 2023; 6(5):190.
https://doi.org/10.3390/fire6050190

**Chicago/Turabian Style**

Zhou, Muchen, Bailing Zhou, Zhuo Zhang, Zuoyao Zhou, Jing Liu, Boyu Li, Dong Wang, and Tao Wu.
2023. "Fire Egress System Optimization of High-Rise Teaching Building Based on Simulation and Machine Learning" *Fire* 6, no. 5: 190.
https://doi.org/10.3390/fire6050190