Impact of Underground Space Height and BMI on Children’s Fatigue During Ascending Evacuation: An Experimental Study and Intelligent Assistive Implications

Abstract

With the rapid expansion of urban underground spaces, safety concerns related to ascending evacuation have become increasingly critical, particularly for children, who are more susceptible to fatigue than adults. However, most existing research focuses on adults and overlooks the unique needs of children. This study investigated two key fatigue-related factors, evacuation height and body mass index (BMI), to construct a predictive model of children’s fatigue levels and proposed a non-invasive, code-compliant assistive solution integrated into underground fire escape stairways. Data were collected from 41 child participants during an ascending evacuation under simulated emergency conditions using real-time heart rate monitoring and video analysis. Statistical correlation and regression modeling revealed a significant positive correlation between evacuation height and heart rate (p < 0.01). Female participants exhibited higher mean heart rates and greater variability, with a strong positive correlation between BMI and heart rate observed in females (p < 0.01). Regression analysis showed that heart rate increased with BMI but plateaued in the obese group. These findings demonstrate that evacuation height and BMI significantly influence children’s fatigue levels. Based on these physiological insights, this study proposes a non-invasive architectural intervention to enhance children’s evacuation performance, offering practical guidance for the design of intelligent evacuation systems. Furthermore, it provides theoretical support for child-centered assistive design and safety improvement within the boundaries of current fire protection codes.

1. Introduction

Amid rapid urban development, underground space expansion has steadily progressed and become a critical element of urban spatial growth [1,2]. With the increasing complexity of underground environments, children have emerged as a significant user group, particularly as mixed-use commercial spaces, integrated underground commercial–transit networks, and dedicated play areas for children and families continue to be developed and expanded [3,4,5,6]. Additionally, the risks associated with ascending evacuations for children, attributed to their frequent presence and activity in such spaces, have become more pronounced [7,8]. Studies have indicated that commonly used underground spaces typically extend 7–25 m below the ground, equivalent to two to six above-ground building levels [8,9] (Figure 1 and Figure 2). Under these depth conditions, children encounter greater challenges during ascending evacuation owing to their limited physical capacity and underdeveloped cognitive judgment [10,11,12].

Children have been reported to experience noticeable ascending movement fatigue due to limited physical reserves and reduced muscular endurance, resulting in significant differences compared with adults [10,11,12]. Unlike ascending evacuation, descending evacuation involves different directions of limb and muscular exertion and does not require overcoming gravitational resistance. Consequently, evacuation during descent is generally faster and places greater emphasis on impact control and fall prevention [13]. In contrast, prolonged ascending evacuation leads to increased fatigue owing to sustained muscular effort. This continuous exertion often results in observable behaviors, such as frequent use of handrails, slower movement, and a noticeable decline in evacuation speed [14,15,16,17,18]. Increased fatigue can affect children’s physical capabilities such as slower movement, poor coordination, gait instability, and physical exhaustion [8]. Moreover, children exhibit heightened sensitivity to fatigue and limited self-regulation, which can be accompanied by behavioral instability that compromises emergency responsiveness and willingness to evacuate. Sustained exertion during emergency scenarios causes a progressive decline in children’s speed, widening the gap from preceding evacuees and further disrupting evacuation flow and order [14,15]. Critically, fatigue-induced slowing not only influences individual evacuation but may also trigger chain reactions within the crowd, as trailing children or others reduce speed or pause to avoid collisions, thereby increasing pedestrian density [19]. Elevated density intensifies congestion and increases the risk of accidents during evacuation [8,14,15,18,20,21,22]. Therefore, emergency evacuation planning for children should consider the effects of physical exertion and fatigue to ensure both safety and efficiency.

Existing research on child evacuation focuses primarily on downward evacuation. Various factors, including age, body mass index (BMI), gender, and evacuation posture, have been examined for their influence on evacuation behavior [10,11,12,14,15,19,22,23,24]. For instance, studies have shown that age and weight can significantly affect downward evacuation speed, with younger or heavier children demonstrating slower movement and greater susceptibility to early fatigue [25]. These investigations commonly employ methods, such as video analysis, physiological data collection, and questionnaires, which integrate experimental observations with data analysis. However, ascending evacuation differs fundamentally from downward evacuation, and current research on children’s ascending evacuations remains limited. In particular, there is a lack of systematic studies addressing the relationship between children’s fatigue, ascending height, and BMI during evacuation.

Moreover, existing solutions for underground space evacuation primarily focus on optimizing evacuation pathways, stair configurations, and guiding systems [26,27,28,29]. The first strategy can reduce evacuation time and enhance efficiency by increasing the number of evacuation routes and optimizing stair and exit dimensions. However, its application is limited to completed underground structures and offers minimal improvement in vertical ascending evacuation efficiency. The second strategy centers on enhancing guidance systems, whereas most current systems prioritize horizontal evacuation while overlooking the requirements of vertical ascent, thereby reducing their practical effectiveness.

In studies on factors influencing the downward evacuation of children, researchers have employed video recordings and physiological data analysis to examine the effects of BMI, floor height, gender, and age on evacuation behavior. Strutzenberger et al. [30] used video recording and a three-dimensional motion analysis system on a dedicated test staircase to assess the evacuation performance of 18 obese and 17 normal-weight children aged 10–13 years. These findings indicate that obese children are more susceptible to early fatigue and joint overload due to their higher BMI and excess body weight [30]. Similarly, Song et al. [31] analyzed the downward stair movement of 16 obese boys (11.19 ± 0.66 years) and 21 normal-weight boys (11.13 ± 0.69 years) using video recordings on a controlled experimental staircase. The results showed that under identical load-bearing conditions, obese children experienced greater muscle fatigue and risk of injury than their normal-weight peers [31]. Zhang et al. [25] analyzed the evacuation behavior of 28 children aged 4–6 using wearable sensors and video recordings. The study found that boys exhibited faster movement speeds, higher physical intensity, and greater fluctuations in physiological indicators, such as electrodermal activity and skin temperature. Additionally, boys demonstrated higher physiological demands than girls during evacuation. Overall, their study revealed that boys experienced significantly higher fatigue levels than girls under the same evacuation conditions.

Similarly, Zhang et al. [23] employed motion capture equipment to investigate the effects of three evacuation postures on fatigue in 28 children aged 4–6 years (13 boys and 15 girls) in a kindergarten third-floor corridor. The knee-and-hand crawling posture (KHC) induces significantly greater fatigue, whereas no significant differences are observed between upright walking (UW) and stoop walking (SW). Zeng et al. [24] used video recordings to observe the evacuation behavior of 38 university students (equal gender ratio) in a nine-story building at the University of Science and Technology of China. The results indicated that participants using handrails completed evacuation more quickly under both full (100%) and low (12%) illumination conditions. Yao et al. [32,33] analyzed video data to examine the age-related differences in the evacuation performance among children aged 4–6 in a three-story building. The findings demonstrated that age influenced fatigue endurance and evacuation speed, confirming age as a significant factor. A similar conclusion was drawn by Kholshchevnikov et al. [34], who reported that age affected children’s evacuation speed. Existing studies have extensively examined behavioral differences and fatigue responses during downward evacuation, considering factors such as BMI, gender, and age. Through experimental approaches involving video analysis, 3D kinematic tracking, and wearable sensors, researchers have consistently suggested that obese children are more prone to fatigue, while gender and age significantly influence evacuation behavior [25,30,31]. However, current research remains predominantly focused on downward evacuation, with limited systematic investigations into children’s ascending evacuation behavior and fatigue mechanisms in underground environments, necessitating further study.

During ascending evacuation, individuals are affected by factors such as BMI, physical exertion, and oxygen consumption, which contribute to varying levels of fatigue and increase evacuation risk [8,14,15,18,22,35,36]. In existing studies on the factors influencing ascending evacuation, researchers have employed methods including subjective rating scales, video recording, physiological data collection, and simulation coupling to examine the effects of variables such as age, BMI, gender, and handrail usage frequency on evacuation performance. For instance, Li et al. [8] analyzed the ascending evacuation behavior of 67 participants in a 10-story office building using video recordings. The participants included 4 male children aged 10–18, 24 male and 16 female college students aged 18–24, 2 males aged 30–40, 2 middle-aged males, 4 females aged 40–50, and 15 elderly individuals aged 50–60. Their study found that prolonged upward movement caused significant fatigue, with fatigue increasing with floor height. Moreover, females exhibited greater fatigue than males, as indicated by a more pronounced speed reduction and subjective fatigue responses [8]. These findings, drawn from adolescent to elderly populations, do not contradict those of Zhang et al. [23], who studied preschool-aged children and observed greater fatigue among boys. Rather, the differences likely stem from variations in physiological development, metabolic levels, and fatigue mechanisms across age groups.

In a similar study, Pan et al. [35] conducted an observational experiment using video recordings at a subway station in Chongqing, China, involving 54 young students (27 male and 27 female) in an ascending evacuation scenario. The results demonstrated a significant correlation between ascent height, heart rate (HR), and fatigue. The authors developed mathematical models linking evacuation speed and HR at various ascent heights. Notably, for the male participants, once the ascent height exceeded 54.6 m, HR was no longer the primary factor influencing evacuation speed. Moreover, across all five experimental groups, the male HR curves consistently exceeded those of females, indicating gender-based differences in physiological responses during ascending evacuation. However, compared with the studies conducted by Li et al. [8] and Zhang et al. [23] this result still has limitations, as it does not incorporate stratified analysis based on relevant factors, such as height, weight, BMI, and individual physical condition. Without such subgroup comparisons, it remains difficult to determine which populations are more prone to fatigue under ascending evacuation conditions. Pan et al. [21] conducted a questionnaire-based survey using data collected from subway stations and professional websites, obtaining 555 valid responses (289 male and 266 female). The results indicated that gender, age, education level, and safety knowledge significantly affected evacuation behavior across different population groups [21].

Xie et al. [36] conducted an observational study using video recordings in the underground space of a university teaching building, analyzing the ascending evacuation behavior of 64 university students (32 males and 32 females) on a staircase. The results indicated that BMI significantly influenced fatigue levels during ascent, with individuals of higher BMI exhibiting a more rapid decline in evacuation speed, which could be due to accelerated energy consumption and earlier fatigue onset [36]. Similarly, Strutzenberger et al. [37] used a treadmill combined with an infrared camera system to examine the stair-climbing behavior of 11 obese adolescents aged 14–16 years (6 males and 5 females). Their study revealed that individuals with a higher BMI experienced increased joint load during ascent, contributing to greater fatigue [37]. Lu et al. (2021) [17] conducted an experimental study on pedestrian ascending and descending evacuation behaviors using video recordings and quantitative analysis under limited visibility conditions. Participants of various ages and genders performed ascending and descending evacuation tasks in simulated low-illumination environments. The results revealed that under such conditions, ascending evacuation was more likely to induce gait instability, path deviation, and fluctuations in movement speed, particularly in the later stages, where fatigue accumulation became more evident. Similar to the studies by Strutzenberger et al. [30] and Xie et al. [36], this research employed video tracking and a dedicated stair flight to quantify the effects of physical load on fatigue. However, Lu et al. [17] specifically highlighted the amplifying role of environmental perception constraints (such as inadequate lighting) in fatigue development during ascending evacuation, thereby contributing an environmental interaction perspective to the understanding of differences between ascending and descending evacuation. Li et al. [16] conducted a field study on ascending evacuation behavior under varying staircase slopes using video recordings and wearable sensors. The results showed that with increasing stair slope, energy consumption during ascent significantly increased, leading to greater physical load and fatigue accumulation, which in turn reduced the average evacuation speed. However, owing to limitations in the BMI data, their study did not capture the effect of BMI on fatigue [16]. These findings underscore the critical impact of BMI on ascending evacuation behavior. Individuals with higher BMI can endure greater physical strain, resulting in faster fatigue accumulation and reduced evacuation speed. Such evidence provides valuable insights into the evacuation performance of individuals with varying body types and offers empirical support for the design of evacuation strategies and safety measures in underground spaces.

Jiang et al. [18] conducted an observational experiment in a high-rise hotel building to analyze the ascending stair-climbing behavior of 16 students (8 males and 8 females) aged 22–28. The study discovered that the frequency of handrail applications significantly influenced fatigue levels during evacuation [18]. Similarly, Shi et al. [38] performed an observational study at the Yachi Center Primary School in Meishan, Sichuan, China, examining the stair movement characteristics of 131 participants: 26 children aged 4–6, 25 elementary students aged 8–10, 27 middle school students aged 12–14, 28 middle-aged adults aged 27–57, and 25 elderly individuals aged 63–81. The results indicated that age had a pronounced effect on stair-climbing speed, with elementary and middle school students exhibiting the highest speeds. In addition, the average speed was identified to be negatively correlated with age in both ascending and descending movements [38].

In summary, existing research on ascending evacuations has predominantly focused on adult populations, examining factors such as BMI, age, gender, and handrail use. Through the integration of video analysis, physiological monitoring, and survey data, these studies identified key variables influencing fatigue levels and evacuation efficiency during ascent [8,14,15,18,19,22,35,36,39]. Although these findings provide a robust foundation for understanding evacuation characteristics across different demographics, research on children remains limited, particularly regarding ascending evacuation behavior, evacuation dynamics in underground spaces, fatigue mechanisms, and related design optimization strategies. The absence of systematic and in-depth investigations in these areas highlights the need for further research.

This study employed video-based experimental methods to conduct an ascending evacuation experiment involving children on a four-story fire escape staircase. This study aimed to investigate the effects of ascending height and children’s BMI on evacuation-induced fatigue. By collecting and analyzing relevant physiological data, a predictive model for fatigue during children’s ascending evacuation in urban underground spaces was developed. The findings provide a theoretical basis, within the bounds of regulatory standards, for child-friendly stair-assistive designs and enhanced evacuation safety.

2. Methods

This section presents a detailed overview of the experimental site, participants, experimental design, and the methods used for data collection and analysis. Section 2.1 provides a detailed description of the experimental site, equipment setup, procedural workflow, and measures implemented to maintain the controlled conditions throughout the evacuation process. Section 2.2 outlines participant characteristics, including age distribution and body measurements of the child subjects involved in this study. Section 2.3 outlines the data collection process, while Section 2.4 details the analytical methods employed. According to previous studies [20,40,41,42], lighting conditions during underground evacuation can influence behavioral responses. In this experiment, adequate lighting was ensured to provide sufficient illumination throughout the evacuation process. Therefore, the potential influence of lighting-related factors was excluded from the analysis.

2.1. Experimental Site and Equipment Selection

2.1.1. Selection of Experimental Site

The experimental site was located in a three-story fireproof stairwell, with a total height of 13.8 m. Ascending evacuation data were also recorded from the third floor and above to serve as a reference for deeper underground spaces. The site selection was based on the Chinese Code for Fire Protection Design of Buildings (GB50016-2014) [43], which mandated that all evacuation staircases in high-rise and underground buildings be designed as fireproof stairwells. Accordingly, the staircases used in this study were all equipped with metal fire doors with specifications and dimensions strictly conforming to the relevant design standards. This configuration renders the staircase model suitable for simulating evacuation scenarios in underground environments [8].

As shown in Figure 3, the staircase consisted of two flights, comprising a total of 24 steps. Each flight had a width of 1.39 m, a tread depth of 0.28 m, and a riser height of 0.14 m, resulting in a stair slope of 26.5°. The intermediate landing measured 2.8 m × 1.6 m.

2.1.2. Selection of Experimental Equipment

Surveillance video equipment was used to record participants’ entire ascending process in detail. The fixed positions of the cameras are shown in Figure 3. Four digital cameras were used, each with a resolution of 1920 × 1080 pixels and a frame rate of 30 fps.

Previous studies have demonstrated that HR is a key physiological indicator for assessing pedestrian fatigue, with elevated HR levels during physical activity reflecting increased fatigue [18,20,44,45]. In this experiment, HR was monitored using a device manufactured by POLAR, featuring a sampling frequency of 1 kHz. This enabled second-by-second tracking of instantaneous HR fluctuations with high accuracy, meeting the requirements for various physical activity conditions. Detailed images of the device and the HR monitor placement method are illustrated in Figure 4.

2.2. Participant Information

A total of 41 children participated in the experiment, comprising 21 boys and 20 girls. Age, gender, height, weight, and BMI were recorded for each participant. All the children were in good physical health and exhibited no apparent motor impairments. The BMI classification was based on the Growth Standards for Children Under 7 Years of Age and the Recommended Criteria for the Physical Development of Children and Adolescents Aged 0–18 Years, both issued by the National Health Commission of China [46,47,48]. Detailed BMI classification criteria are presented in

Table 1. Basic information about the child members involved in the experiment.

Group	Personnel Quantity	Age (Mean)	BMI Range (kg/m2)			Mean Height (m)	Mean Body Weight (kg)
			Age (Years)	Male	Female
Thin Group A	Male (5), Female (5)	5.35	4	BMI < 13.6	BMI < 13.4	114.6	17.6
			5	BMI < 13.6	BMI < 13.5
			6	BMI < 13.7	BMI < 13.6
Normal Group B	Male (4), Female (7)	5.09	4	13.6 ≤ BMI < 15.7	13.4 ≤ BMI < 15.5	114.6	17.6
			5	13.6 ≤ BMI < 15.7	13.5 ≤ BMI < 15.6
			6	13.7 ≤ BMI < 15.9	13.6 ≤ BMI < 15.8
Overweight Group C	Male (7), Female (3)	5.35	4	15.7 ≤ BMI < 17.4	15.5 ≤ BMI < 17.1	119.2	23.8
			5	15.7 ≤ BMI < 17.4	15.6 ≤ BMI < 17.2
			6	15.9 ≤ BMI < 17.7	15.8 ≤ BMI < 17.5
Obese Group D	Male (5), Female (5)	5.20	4	BMI ≥ 17.4	BMI ≥ 17.1	118.2	28.0
			5	BMI ≥ 17.4	BMI ≥ 17.2
			6	BMI ≥ 17.7	BMI ≥ 17.5

.

2.3. The Experimental Procedure

To clarify the effects of floor height and BMI on fatigue during children’s ascending evacuation and to ensure experimental standardization and data comparability, the 41 participants were divided into four groups based on BMI: Group A (10 participants), Group B (11 participants), Group C (10 participants), and Group D (10 participants). In each trial, one child from each group performed the experiment individually and sequentially. The design deliberately excluded crowd interference, overtaking, and queuing behaviors to eliminate their influence on the evacuation performance.

Prior to the experiment, the staff ensured that all participants’ identification tags were securely attached and that the Polar H10 heart rate sensors were properly worn. The resting HR was recorded after standing still for 5 min to serve as a baseline. Previous studies have identified heart rate as a key physiological indicator for assessing fatigue during physical activity [20,35,44]. The experiment was conducted in rotating groups, following a pre-defined sequence. Before each round, the participants assembled in Waiting Area 1 to complete the resting HR measurements before proceeding along the designated evacuation path. During the experiment, the participants sequentially passed through the designated checkpoints: T1, P1 (1.68 m), T2, P2 (3.36 m), T3, P3 (5.04 m), T4, P4 (6.72 m), T5, P5 (8.40 m), T6, and P6 (10.08 m). The participant’s behavior at each node was recorded and analyzed using surveillance videos. Notably, all participants were unfamiliar with the experimental environment, enhancing the realism of the simulated evacuation scenario. Following each round, the participants rested for 10 min to alleviate evacuation-induced fatigue. The experimental procedure is illustrated in Figure 5.

2.4. The Data Analysis Method

This study utilized the average HR and resting HR to assess fatigue level changes during children’s ascending evacuation [35]. Data processing involved the statistical analysis of HR increase range, mean, and standard deviation, with groupings based on gender, floor height, and BMI classification. A 95% confidence interval was applied to evaluate HR variation, and Pearson correlation coefficients were used to analyze the relationships among ascending height, BMI, and HR indicators [35,36]. The participants were further grouped by BMI, and regression fitting was conducted to model HR trends with increasing ascent height across BMI categories. This method aimed to evaluate the influence of BMI on HR response and fatigue accumulation. Previous studies have confirmed that HR during physical activity can effectively reflect fatigue levels [18,20,35,44,45]. Based on these findings, the fatigue levels were quantitatively categorized according to HR values [35] as follows: ultra-low activity (HR ≤ 120): no fatigue; low activity (120 < HR ≤ 140): slight fatigue; moderate activity (140 < HR ≤ 160): moderate fatigue; high activity (160 < HR ≤ 180): severe fatigue; and ultra-high activity (HR > 180): extreme fatigue.

3. Results

3.1. Analysis of Heart Rate and Fatigue Level During Ascending Evacuation

During ascending evacuation, fatigue levels are closely associated with physiological characteristics, stamina decline, and energy consumption.

Table 2. Heart rate (HR) of all males and females.

Heart Rate (HR)	Rang (b/min)	Average HR (b/min)	SD	Resting HR (b/min)	SD
Overall participants (HR)	87–142	112.05	9.7	104.92	10.11
Male participants (HR)	91–136	109.81	8.28	105.14	10.05
Female participants (HR)	87–142	114.30	12.08	104.70	10.97

SD: standard deviation.

summarizes the HR data of all participants and presents a gender-based analysis of HR range and statistical characteristics. The results indicated that the males exhibited a lower average HR than females, with a difference of 4.49 b/min, while the resting HR showed no significant gender difference. In terms of HR fluctuations, female participants demonstrated significantly greater variability. Specifically, the minimum HR differed by 4 b/min, and the maximum HR showed a difference of 6 b/min.

This study further analyzed gender differences in average HR during both rest and exercise. The results showed that the male participants had a resting HR of 105.14 ± 10.05 b/min and the average exercise HR of 109.81 ± 8.28 b/min, while the female participants had a resting HR of 104.70 ± 10.97 b/min and an exercise average HR of 114.40 ± 12.08 b/min. Although the resting HR were similar between genders, the females exhibited significantly higher HRs during exercise, further highlighting the pronounced gender difference in the HR fluctuation range.

Table 3. Confidence interval (95%) for heart rate values.

Heart Rate (HR)	Resting HR		T1 (1.68 m)		T2 (3.36 m)		T3 (5.04 m)		T4 (6.72 m)		T5 (8.4 m)		T6 (10.08 m)
	Mean 95% Confidence Interval		Mean 95% Confidence Interval		Mean 95% Confidence Interval		Mean 95% Confidence Interval		Mean 95% Confidence Interval		Mean 95% Confidence Interval		Mean 95% Confidence Interval
	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max
Overall participant HR (b/min)	99.46	108.74	102.46	110.74	104.24	111.27	105.13	112.47	106.42	114.68	109.99	118.10	114.41	122.49
Male participant HR (b/min)	99.46	108.74	102.46	110.74	104.24	111.27	105.13	112.47	106.42	114.68	109.99	118.10	114.41	122.49
Female participant HR (b/min)	99.43	109.97	101.30	112.60	103.32	114.38	107.40	118.00	111.78	122.92	116.61	127.19	122.07	132.63

summarizes the 95% confidence interval data of heart rates for different floor heights and genders.

Figure 6 and Figure 7 illustrate the distribution of resting and average HRs for male and female participants. The resting HR for males was primarily concentrated between 95 and 105 b/min, while it ranged from 90 to 110 b/min for females. In terms of the average HR, the male participants were mainly distributed between 100 and 115 b/min, whereas the females exhibited a broader distribution, ranging from 100 to 130 b/min, which further reflected larger fluctuations and generally higher HR levels in females.

3.2. Relationship Between Ascending Height and Participants’ Heart Rate (HR) During Ascending Evacuation

Figure 8 illustrates the HR fluctuation trends of male and female participants during the ascending evacuation process as the floor height increased. Overall, the males exhibited a more moderate HR increase than females. A stage-by-stage analysis showed that prior to T2, the HR increases were similar between genders; between T2 and T4, the increase was less pronounced in males; and from T4 to the final stage, both groups experienced a marked rise. Ultimately, the average HR increased by approximately 9.07% for males and 16.42% for females. This trend is consistent with the HR response findings reported in reference [18].

Table 4. Correlation analysis between upward height of the floor and upward evacuation HR of the participants.

	Total (n = 41)	Correlation	Male (n = 21)	Correlation	Female (n = 20)	Correlation
Upward height (m)	10.73 (SD = 5.07)	0.979 **	10.70 (SD = 5.14)	0.958 **	10.75 (SD = 5.00)	0.986 **

SD: standard deviation. Pearson correlation coefficients. * p < 0.05, ** p < 0.01.

presents the correlation analysis between ascending height and HR data for all participants, illustrating the cumulative effect of vertical ascent on children’s fatigue levels. The results revealed a significant positive correlation between HR and ascending floor stage (p < 0.01), with no significant difference in this correlation observed between male and female participants.

3.3. Relationship Between BMI and Participants’ Heart Rate (HR) During Ascending Evacuation

Table 5. Comparison of average heart rates between men and women with different BMI indices.

	Male (n = 21)		Female (n = 20)
Group	Mean HR (b/min)	SD	Mean HR (b/min)	SD
Thin Group A	102.4	3.56	107.4	12.34
Normal Group B	105	5.52	110.71	4.40
Overweight Group C	112.86	7.70	110.33	9.67
Obese Group D	116.8	5.71	129	7.56

SD: standard deviation.

presents the average HR values of male and female children across the four BMI-based groups (A–D). Except for Group C (overweight), the male participants in all other groups exhibited significantly lower average HRs than their female counterparts. Additionally, a gradual increase in average HR was observed among male participants as BMI increased, with a similar pattern observed among females, albeit with fluctuations noted in Group C.

Figure 9 presents the linear relationship between BMI and HR during ascending evacuation across different genders, revealing a significant overall positive correlation.

Table 6. Correlation analysis between participants’ BMI and ascending evacuation heart rate (HR).

	Total (n = 41)	Correlation	Male (n = 21)	Correlation	Female (n = 20)	Correlation
HR (b/min)	112.05 (SD = 10.56)	0.693 **	109.81 (SD = 8.28)	0.527 *	114.3 (SD = 12.08)	0.723 **
Age (years)	5.2 (SD = 0.54)	0.007	5.26 (SD = 0.56)	−0.215	5.22 (SD = 0.55)	0.21
Weight (kg)	22.36 (SD = 5.01)	0.489 **	23.23 (SD = 4.25)	0.054	21.44 (SD = 5.67)	0.572 **
BMI (kg/m2)	16.38 (SD = 2.61)	0.693 **	16.39 (SD = 1.89)	0.527 *	16.38 (SD = 3.21)	0.723 **

SD: standard deviation. Pearson correlation coefficients. * p < 0.05, ** p < 0.01.

presents the Pearson correlation analysis results, indicating a significant positive correlation between BMI and HR for all participants (r = 0.693, p < 0.01). The gender-specific analysis demonstrated a higher correlation coefficient for females (r = 0.723, p < 0.01) than for males (r = 0.527, p < 0.05), suggesting that BMI had a more pronounced influence on HR among female participants.

3.4. Mathematical Relationship Between Participants’ BMI and Heart Rate (HR) During Ascending Evacuation

Figure 10 illustrates a comparison of HR changes in male and female children across four BMI categories, incorporating regression curves derived from the experimental data along with the corresponding predictive models. These curves reveal the relationship between BMI and HR during ascending evacuation and visually highlight the fatigue accumulation trends across different BMI groups. Similar modeling approaches were adopted in studies by Xie and Pan et al. [35,36], providing theoretical support for the methodology applied in this study. Regression analysis indicated that although the initial HR values varied noticeably among male children with different BMI classifications, their HR trends converged as ascending height increased. In contrast, female children exhibited significant differences in both initial HR and fatigue accumulation trends, indicating greater variability in baseline levels and exertion responses. Notably, in the underweight and normal BMI groups, the fitted HR curves for male and female participants followed similar trajectories. However, in the overweight and obese groups, a clear gender-based divergence emerged. Although gender influenced HR variation across BMI categories, the primary focus of this study was the effect of BMI on HR changes. These results suggested that HR trends were predominantly governed by BMI. Further analysis of the predictive models revealed a progressive increase in HR with the increasing BMI. In the obese group, the regression curve indicated a plateau in HR at higher ascending heights, reflecting a cardiovascular response approaching physiological limits. At this stage, the rate of HR increase declined significantly, suggesting that under high fatigue or near-maximal exertion, physiological thresholds rather than body mass became the primary determinant of heart rate regulation.

The following are the predictive models of children’s HR (b/min) during ascending evacuation, categorized by BMI group. The X-axis represents the ascending height, and the Y-axis represents the average HR.

Thin: Y (Male) = 96.2905 + 1.8533x + (−0.3172)x² + 0.0293x³ R² (Male) = 0.998

(1)

 Y (Female) = 96.3381 + 1.3596x + 0.2058x² + (−0.0047)x³ R² (Female) = 1

(2)

Normal: Y (Male) = 101.3452 + 1.887x + (−0.2120)x² + 0.0161 x³ R² (Male) = 0.999

(3)

 Y (Female) = 101.4805 + 1.1400x + (−0.0098)x² + 0.0134x³ R² (Female) = 0.999

(4)

Overweight: Y (Male) = 110.6188 + 1.3391x + (−0.3336)x² + 0.03175 x³ R² (Male) = 0.970

(5)

 Y (Female) = 105.7102 + (−0.2258) x + 0.2178x² + (−0.0060)x³ R² (Female) = 0.985

(6)

Obese: Y (Male) = 109.8667 + 1.4574 x + (−0.1611)x² + 0.0164 x³ R² (Male) = 0.995

(7)

Y (Female) = 117.4904 + (−0.0888)x + 0.4833 x² + (−0.0292)x³ R² (Female) = 0.985

(8)

4. Discussion

4.1. Relationship Between Ascending Height and Heart Rate (HR) During Upward Evacuation

Given that the direction of muscular exertion during ascending evacuation differs from that of descending evacuation, resulting in greater demands on both cardiopulmonary and muscular systems, and that sustained upward exertion tends to intensify fatigue compared to descent, this study adopted HR as an indicator of fatigue to analyze participants’ physiological responses throughout the ascending process [14,15,16,17].

This study found that children’s HR increased progressively with evacuation height, exhibiting a significant positive correlation with vertical ascent (p < 0.01). The average HR gradually increased in the early stages, followed by a marked increase in the final stage. On average, male participants exhibited a 9.07% increase, whereas female participants showed a 16.42% increase. Notably, the gender differences in the HR changes displayed phase-specific characteristics: during the initial stage (0–33% of the path), both groups experienced a similar HR increase; in the middle stage (34–66%), the males exhibited a slower increase than the females; and in the final stage (67–100%), both groups showed an accelerated increase in HR.

The average heart rate values and growth trends observed in this experiment differed from those reported in previous studies [35,49,50]. For instance, a study [35] reported no significant gender difference in the peak HR during the ascending evacuation, with the male and female peak HRs recorded at 145.99 and 151.48 b/min, respectively. In contrast, this study identified an 8.27% difference in peak HR between genders. Furthermore, the average HR of male participants (109.81 b/min) was 23.85% lower than their peak value (136 b/min), while the average HR (114.3 b/min) was 24.23% below their peak (142 b/min) for the females. Moreover, a study [49] reported an overall average HR of 170 b/min in both individual and group settings, which was 51.79% higher than the 112 b/min average observed in this study.

A previous study [50] reported that male participants exhibited a smoother increase in HR than females, whereas females showed a broader range of HR fluctuations, which was consistent with the results of this study. Moreover, peak heart rates of 135 b/min for males and 150 b/min for females were demonstrated in another study [50]. In comparison, the male peak HR in this study was 136 b/min, differing by only 0.74%, while the female peak HR was 142 b/min, representing a 5.63% deviation from earlier findings.

These observed differences can be attributed to several key factors. First, the participants in this study were all children, with an average age of 5.26 years for boys and 5.22 years for girls, whereas the participants in previous studies were significantly older. For example, a study [22] involved university students with average ages of 23.15 (male) and 23.52 (female); a study [50] reported averages of 18.6 (male) and 18.4 (female); and a study [49] included members of the general public aged 32 (male) and 34 (female). In addition, the stair dimensions used in those studies varied considerably: the treads measured 30 cm deep, 15 cm high, and 150 cm wide [22]; 26 cm deep, 16 cm high, and 116 cm wide [50]; and 25 cm deep and 20.5 cm high [49]. These differences in stair design and variations in experimental settings could influence the outcomes. Age-related physiological differences may contribute to the observed discrepancies [22].

Building on existing research, this study further quantified the relationship between HR changes and ascending floor height in children during stair evacuation. The findings indicated that ascending height could serve as a key indicator for evaluating physiological load during evacuation. These results could provide theoretical support for non-structural, human-centered assistive enhancements to evacuation stairways in urban underground spaces without altering code-mandated structural elements, and broaden the research perspective on evacuation safety from a child-specific human factor standpoint.

4.2. Relationship Between BMI and Participants’ HR During Ascending Evacuation

In this study, BMI was observed to be significantly correlated with the average HR during ascending evacuation (p < 0.01), with a stronger correlation observed among female participants. This gender difference may be attributed to physiological variations in fat distribution, cardiopulmonary endurance, and metabolic rate. Within each BMI category except Group C (overweight), females exhibited higher average HRs than males, and HR increased progressively with BMI in both sexes. The reversal observed in Group C may be related to gender-specific heterogeneity in fat distribution and autonomic regulation mechanisms among prepubertal children [51,52].

These differences are reflected in the following specific trends: in Group A (underweight), the average HR of females was 4.88% higher than that of males; in Group B (normal weight), 5.44% higher; in Group C (overweight), 2.24% lower; and in Group D (obese), 10.44% higher. In terms of HR changes across BMI categories, from Groups A to B, the average HR increased by 2.54% for the males and 3.08% for the females; from Groups B to C, the male HR increased by 7.49%, while the female HR decreased slightly by 0.34%; and from Groups C to D, the male HR increased by 3.49%, whereas the female HR increased significantly by 16.92%.

References [30,37] reached similar conclusions, indicating that childhood obesity is significantly associated with increased physical exertion and greater perceived fatigue. However, the limitations of their research design constrain the depth of their findings. Another study [37] included only two BMI categories (normal weight and obesity) without distinguishing between overweight and obese groups and excluded an underweight control group, thereby limiting its ability to assess correlations across a full range of body compositions. Similarly, a study [30] adopted a binary grouping approach (obese vs. normal weight) without constructing a comprehensive BMI gradient classification encompassing underweight, normal weight, overweight, and obese categories. Consequently, both studies restricted their conclusions to comparisons between obese and normal-weight groups, making it difficult to reveal the physiological response characteristics of children with diverse body types.

In contrast to previous studies, this study revealed a distinctive nonlinear relationship between BMI and HR responses in children during ascending evacuation. By employing a more balanced sample across four BMI categories, this study highlights significant gender-based disparities and a bottleneck effect in HR among overweight and obese groups. Specifically, in obese children, HR increase tended to plateau at an ascending height of approximately 10 m, indicating the emergence of a physiological threshold unique to this age group.

A similar phenomenon was observed in the study by Pan et al. [35], which, although primarily focused on adults, found that male participants experienced a stabilization in evacuation speed after reaching an elevation of 54.6 m due to fatigue, while female participants continued to show HR-driven declines in performance. This comparison suggests that children exhibit signs of fatigue much earlier, at approximately 80% of the adult evacuation distance, and that the gender-based physiological threshold may reverse with age. These observations were further corroborated by the findings of Xie et al. [36], who also identified a physiological ceiling in adult participants. However, in comparison with our results, children showed signs of fatigue approximately 73–78% earlier along the ascending evacuation route than adults, reinforcing the conclusion that children are physiologically more prone to early fatigue during such events. These findings not only extend the existing understanding that higher BMI is associated with increased physical exertion, but more importantly, they establish, for the first time, a clear inflection point in HR and fatigue responses from a child-centered perspective. This critical insight into the unique physiological features of children during evacuation has significant theoretical and practical implications for the development of child-focused evacuation strategies and the design of intelligent assistive systems.

Overall, this study addressed methodological limitations of previous research and filled a critical gap by quantifying the relationship between children’s BMI and HR variation during ascending evacuation. In particular, it identified age-specific physiological characteristics of children compared to adults, highlighting the earlier onset of fatigue and distinct HR regulation patterns unique to the pediatric population. By establishing an HR response analysis framework across multiple BMI categories, this study presents a robust data foundation for developing fatigue prediction models tailored to children of different body types for evacuation heights of 12 m or less. The proposed model facilitates the assessment of physical load risks during evacuation and offers theoretical support for parameter setting and optimization of intelligent safety-assist systems in underground stairwells designed for children.

4.3. An Exploratory Study on Intelligent Safety Assistance Design for Fire Escape Stairways

Based on the above findings, this study developed a regression-fitted mathematical model to describe the relationship between BMI and HR during ascending evacuation. By categorizing participants into BMI-based groups and fitting HR variation trends across different evacuation heights, the model aimed to predict fatigue levels across different BMI groups. Similar modeling approaches have also been applied in studies by Xie and Pan et al. [35,36], which provide theoretical support for the methodology adopted in this study. Furthermore, an exploratory investigation was conducted on the intelligent safety assistance design of fire escape stairways in urban underground spaces.

The proposed design scheme comprises the following modules: fire stairwell, Pedestrian Identification Device (PID), Weight Sensor (WS), Height Ultrasonic Detector (HUD), Central Processing Device (CPD), evacuation signage, and Alarm Device (ALD). PID, WS, and HUD were installed at the stairwell entrance to synchronously collect biometric data such as height and weight, enabling real-time BMI calculations. WS employed a compact load-cell-based sensing unit, which is highly suitable for integration within stairwell environments. The system was powered by the building’s standard electrical supply and featured an automatic switch to a backup battery to ensure continued operation during emergencies. Real-time data were analyzed by CPD, which utilizes a linear prediction model based on BMI and HR to assess children’s fatigue levels and identify potential risk zones during the ascending evacuation process. When a high fatigue risk or excessive crowd density is detected, the system autonomously activates ALD to issue visual or auditory alerts. Through wireless broadcasting, the system informed on-site evacuees to assist vulnerable children, alerted security personnel to intervene at key locations such as stair entrances, and activated evacuation signage and red warning lights to provide real-time guidance. This approach offers timely reminders to incoming evacuees, helping prevent overcrowding without changing the designated escape route, thereby alleviating localized congestion.

All modules operate collaboratively through a wireless communication-based control mechanism, enabling real-time data transmission and coordinated system responses. This integration improves evacuation efficiency and enhances safety protection for children during evacuation. Existing studies [35,36] have demonstrated that evacuation behavior can be effectively predicted using mathematical models that contribute to improved evacuation safety and efficiency when integrated into stair evacuation assistive systems.

The design consists of two main components. The first focuses on identifying the children’s basic physical characteristics using smart devices. At the evacuation stair entrance, a Pedestrian Identification Device (PID) and a Weight Sensor (WS) were installed to capture the external physical features and calculate each child’s BMI. These data were transmitted to a Central Processing Device (CPD) for centralized analysis and temporary storage. Upon the individual’s exit from the evacuation stair, the system automatically deleted the corresponding data to ensure personal privacy protection.

The second component focused on the design of an intelligent safety assistive system for protected evacuation stairs during emergencies. Basic information about children was acquired through PID and WS, and CPD was used to predict individual fatigue levels and crowd density based on a linear model established between BMI and HR. Previous studies have demonstrated that children’s BMI and HR during a stair evacuation can be represented using linear equations. Based on CPD predictions, the system identified children at a higher risk of fatigue and activated evacuation signage and alarm devices to issue real-time alerts along the same stairwell route. Rather than redirecting children to alternative paths, the system provided visual and auditory prompts to nearby adults and guardians, encouraging them to assist vulnerable individuals. Simultaneously, a notification was sent to security personnel to strengthen on-site support at critical entry points, ensuring a rapid human response without separating the children from their caregivers. This approach helps prevent secondary risks such as panic or loss of contact (Figure 11 and Figure 12).

The primary advantage of this design was its broad applicability. It not only improved the evacuation efficiency in newly constructed underground spaces but also minimized structural disruption in renovation projects. This intelligent safety-assistive system is particularly effective in complex, high-density, and deeply embedded underground transportation hubs and commercial complexes. By predicting evacuation trends for groups with varying BMI levels, the system enables the early identification of high-risk zones, allowing for the rapid localization of hazardous stair areas and facilitating targeted rescue operations. Moreover, the prediction process ensured personal privacy protection. Compared with the collection of more sensitive physiological indicators, such as age, heart rate, oxygen consumption, and muscle capacity, BMI was easier to measure and offered high predictive accuracy, supporting data analysis while preserving privacy. Given the structural isolation and complexity of underground environments, renovation projects can involve high costs, elevated risks, and technical constraints. For instance, increasing the number or width of evacuation passages in aging underground commercial streets or metro systems is both difficult and expensive. In contrast, the proposed system requires no major modifications to existing structures, thereby improving evacuation efficiency with minimal disruption and significantly reducing renovation and construction costs.

It is important to emphasize that the proposed assistive system does not involve any modification to the structural elements of stairways. Instead, it offers a human-centered auxiliary solution designed to operate fully within the existing fire protection codes. By addressing the specific needs of child evacuees, an underrepresented group in the current evacuation design standards, this study contributes to the development of inclusive and regulation-compliant safety strategies for underground evacuation.

From a broader planning perspective, the findings of this study also raise critical concerns about the evacuation challenges posed by deeply embedded underground spaces, particularly for vulnerable populations, such as children. While the proposed intelligent safety-assistive system provides a targeted and minimally invasive strategy for improving evacuation safety, it also underscores the necessity to re-evaluate acceptable evacuation distances in architectural and urban design standards. Excessive vertical evacuation demands, especially in facilities exceeding 10–12 m in depth, may surpass the physiological endurance thresholds of specific groups such as obese children, as identified in this study. Therefore, beyond technological interventions, future design guidelines should consider limiting vertical evacuation heights or incorporating features such as intermediate resting platforms, vertical circulation zoning, or multi-point surface access to reduce the physical burden during emergencies. These insights bridge micro-level device innovation with macro-level evacuation planning and offer new directions for risk-informed underground spatial design.

4.4. Limitations of This Study

This study systematically performed an experimental analysis, suggesting the influence of evacuation height and BMI on fatigue levels in children during ascending evacuation and provides a valuable reference for evacuation design in underground spaces, where several aspects remain open for further exploration and refinement. First, this study primarily focused on the impact of BMI on evacuation fatigue without conducting a detailed analysis of other physiological characteristics such as height, leg length, and limb proportions, which may influence evacuation speed and physical performance. These factors could serve as potential moderators of individual movement capacity during evacuation. Second, the experimental participants were limited to kindergarten-aged children, excluding a broader range of age groups such as primary school children and adolescents. Individuals at different developmental stages may exhibit significantly different evacuation behaviors owing to variations in their physical strength, endurance, and metabolic rate.

5. Conclusions

Through evacuation experiments involving child participants, this study investigated the impact of evacuation height and BMI on fatigue levels during children’s ascending evacuation in vertical stair spaces. The influencing patterns and underlying mechanisms were analyzed from multiple dimensions, with the comparison of the findings with existing studies. The main conclusions are as follows.

(1)

The experimental results revealed a highly significant positive correlation between ascending evacuation height and changes in children’s HR (p < 0.01). During the initial phase, HR increased gradually; in the middle phase, gender-based differences in the rate of increase began to emerge; and in the final phase, HR rose sharply, indicating rapid fatigue accumulation. Overall, the HR increase among female children (16.42%) was substantially greater than that among male children (9.07%), with the final average HR for girls exceeding that of boys by 4.09%.

(2)

This study discovered that BMI had a significant effect on fatigue levels across varying ascending evacuation heights (p < 0.01) and developed a fatigue prediction model applicable to children in different BMI categories for evacuation heights of 12 m or less. Furthermore, in the obese female group, once the evacuation height exceeded 12 m, the influence of BMI on fatigue diminished, with physiological limits becoming the dominant factor regulating HR. At this stage, BMI ceased to be the primary determinant.

Based on the above findings, this study further explored a design scheme for intelligent safety assistance in fire escape stairways within urban underground spaces. The proposed system incorporates an assistive device that initially measures the BMI of evacuating children to estimate their fatigue levels during ascending evacuation. This enables the prediction of high-risk zones within the stairwell, thereby allowing timely mitigation of evacuation flow pressure and the activation of broadcast and alarm systems to alert nearby adults and security personnel to provide assistance. This design offers a feasible and innovative solution to enhance the efficiency of ascending evacuation and reduce casualties, particularly in protecting vulnerable groups, such as children, in urban underground environments.

Future research can be improved in the following aspects: conducting multidimensional analyses of individual physical characteristics to examine how variations in height, weight, stride length, and other factors within similar body types influence fatigue levels and evacuation speed; further exploring the patterns and mechanisms of fatigue variation during downward evacuation to establish a more comprehensive evacuation prediction model; and expanding the experimental scope through comparative studies involving broader age groups of children to systematically analyze differences in heart rate response, fatigue accumulation, and evacuation performance. These efforts will contribute to more universally applicable design guidelines for evacuation systems that address the needs of diverse populations. Additionally, future studies will incorporate assistive design optimization from a child-centered perspective, as well as emergency scenario testing or simulation-based validation of the alarm-based support system. This will help quantify its effectiveness in optimizing evacuation performance and enable timely fatigue management during ascending evacuation.