Analysis of the Effect of Outdoor Thermal Comfort on Construction Accidents by Subcontractor Types

Abstract

The impact of climate on construction site safety varies significantly depending on subcontractor types due to the diverse nature of workplaces and work methods. This study introduces a novel approach by categorizing construction work according to subcontractor types and assessing accident risk probabilistically through the Physiologically Equivalent Temperature (PET), an outdoor thermal comfort index. Additionally, a Hidden Markov Model (HMM)-based clustering methodology was proposed to classify new groups using PET and accident probability. This study proceeded in the following sequence: (i) collection and classification of data, (ii) PET calculation, (iii) calculation of accident probability, and (iv) clustering and Pearson correlation coefficient analysis. As a result of clustering, each group was classified according to the workplace. Groups 2 and 3 demonstrated a strong positive correlation between accident probability and PET, with correlation coefficients of 0.837 and 0.772, while Group 1 exhibited a moderately positive correlation of 0.474. This study quantitatively evaluated the impact of climate on workers for each subcontractor type using PET, an outdoor thermal comfort index for construction work, and accident probability, resulting in the identification of new groups. The findings of this study may serve as novel benchmarks for safety management in construction worker safety based on PET.

1. Introduction

Climate change is an emerging environmental concern that introduces various risk factors affecting outdoor construction workers, including heightened temperatures at industrial sites, increased ultraviolet exposure, and susceptibility to diseases [1]. Given the predominantly outdoor nature of construction work, these workers are consistently exposed to climatic conditions, thereby facing heightened risks, especially in extreme climates [2]. Environmental factors such as extreme temperatures, humidity, and precipitation increase human error rates, consequently affecting worker safety and productivity [3,4]. To comprehensively address these environmental factors, thermal comfort indices like the Predicted Mean Vote (PMV), Physiological Equivalent Temperature (PET), Thermal Sensation Vote (TSV), and Universal Thermal Climate Index (UTCI) have been utilized in previous research to analyze their influence on construction accidents [5,6]. Among these indices, PET stands out as it can account for individual characteristics and environmental factors such as air temperature, relative humidity, and wind velocity. PET is particularly suited to assessing the thermal comfort of indoor and outdoor construction work [7].

Analyzing the risk of construction accidents requires careful consideration of the unique characteristics of each construction project. Factors such as workplaces and work methods vary significantly based on subcontractor types, including interior work, high-rise concrete construction, and civil engineering work such as roads and ports. These differences significantly influence the risk factors associated with injuries [8]. Li et al., have emphasized that the regions affected by climate and factors contributing to worker injuries or fatalities differ depending on the nature of construction work [9]. In particular, subcontractor types focusing on outdoor work have been identified as more hazardous than indoor work, especially under the influence of high temperatures [10]. While many previous studies have analyzed construction accidents based on industry-specific characteristics like subcontractor types or facility types, they often lacked a comprehensive examination of environmental factors using thermal comfort indices [11,12,13,14,15]. Against this backdrop, this study aims to analyze the risk of construction accidents according to the distribution of the PET index by subcontractor type.

To effectively analyze construction accidents based on subcontractor type, it is imperative to categorize subcontractors into distinct groups through cluster analysis, which identifies similarities among them. Cluster analysis is a widely utilized method across various disciplines, such as medicine, finance, life sciences, and social sciences, and identifies groups with shared characteristics [16]. Notably, researchers have utilized cluster analysis to streamline the analysis process in studies analyzing climate factors. For instance, Zheng et al., categorized age groups based on thermal comfort for older individuals, aiming to identify everyday physiological stressors within each cluster [17]. Similarly, Bhandari et al., examined thermal comfort in classroom zones, employing clustering to simplify analysis by grouping zones with similar responses to thermal conditions [18]. These studies utilized clustering to investigate the relationship between the PET and the risk of accidents across different subcontractor types.

Additionally, conducting quantitative risk analysis is crucial for effective risk management in the construction industry, facilitating a systematic approach to risk mitigation [19]. Therefore, this study aimed to assess the impact of outdoor thermal comfort on construction accidents among various subcontractor types from a probabilistic standpoint, leveraging the thermal comfort index. Furthermore, we propose a clustering methodology to devise tailored safety management standards for each subgroup, aiming to enhance safety protocols within the construction sector.

In summary, this study presents a unique approach to assessing the impact of outdoor thermal comfort on construction accidents by subcontractor type. By leveraging the PET index and HMM-based clustering, we aim to provide a systematic and quantitative analysis that can serve as a benchmark for safety management in the construction industry.

2. Literature Review

Previous research was conducted in three categories, as shown in

Table 1. Literature review.

Research Subject	Reference	Purpose	Difference
Outdoor thermal comfort index in construction	[20]	This study established a human body heat prediction method, a thermal comfort adaptation model, and a thermal comfort area with an acceptable temperature range for prefab construction site offices.	Thermal comfort index analyzed in the construction industry could not be explained in relation to accident probability.
	[21]	This study identified the sensitivity of thermal parameters at construction sites, investigated correlations between thermal indicators, and analyzed the change in heat storage in the human body.
	[6]	This study proposed a reasonable outdoor thermal comfort model to explain both the heat balance and heat adaptation of the human body based on the PET and UTCI.
Outdoor thermal comfort associated with construction accidents	[23]	This study presented research results on the effect of the climate environment on scaffolding workers at construction sites based on the UTCI.	When construction accidents were analyzed using thermal comfort indices, construction work was not classified into sub-classes for analysis.
	[22]	This study analyzed the death and injury accidents in the construction industry by setting the PET as the thermal comfort index and using uncertainty analysis to identify relative importance in consideration of injury and death accidents using a neural network.
	[10]	Based on previous studies, this study analyzed the correlation between the risk of occupational injuries (OI) and the change in heat that affects workers.
Analysis of construction accidents by subcontractor types	[13]	The work breakdown structure (WBS) was established, and the high-risk accident events of each structural work were analyzed according to the construction process.	Construction projects were analyzed by dividing them into sub-classes, but no study related to thermal comfort existed.
	[14]	This study facilitated the transfer of knowledge for recognizing high-risk factors in the construction stage by investigating the frequency of accidents for nine construction stages and the resulting factors.
	[15]	This study proposed a new approach called integrated WBS and risk breakdown structure (RBS) (i-WRBS) to identify this hierarchy structure in the construction industry.

: (i) outdoor thermal comfort index in construction [6,20,21], (ii) outdoor thermal comfort associated with construction accidents [10,22,23], and (iii) analysis of construction accidents by subcontractor type [13,14,15].

The first research subject is the outdoor thermal comfort index used in the construction industry. Chuhao Fu et al., investigated the thermal comfort in prefab construction site offices and attempted to set and analyze a model that can reflect indoor and outdoor environmental factors [20]. Consequently, they proved a difference between the comfort range of thermal sensation felt by construction site workers and the comfort range of thermal sensation commonly used. They provided an indicator of the comfortable climate felt by workers in temporary buildings in regions with temperatures similar to those in the study [20]. Tang et al., calculated the mean thermal sensation vote through a survey of construction site workers and analyzed its correlations with thermal comfort indices [21]. Consequently, they presented acceptable temperature ranges by workers for the PET, UTCI, WBGT, and Tropical Summer Index (TSI) [21]. Zhang et al., aimed to propose a reasonable outdoor thermal comfort model to explain both the heat balance and heat adaptation of the human body based on the PET and UTCI [6]. They presented new standards using the PET and UTCI and verified whether they accurately reflected thermal impact through a survey with 1063 construction site workers [6].

The second research subject is the outdoor thermal comfort associated with construction accidents. Szer et al., analyzed the effect of the climate environment on scaffolding workers based on the UTCI and insisted that the risk of accidents is high [23]. They also presented solutions for managers under extreme climate conditions [23]. Lee et al., used the PET as a thermal comfort index and analyzed the relative importance of climate factors in construction work for injury and death accidents [22]. They presented risk types and climate factors with strong correlations according to the PET range [22]. Fatima et al. [10] investigated to prove that exposure to hot weather conditions increases the risk of occupational injuries (OI) based on 24 studies between 2005 and 2020. They found that the risk of OI increased by 1% as the temperature increased by 1 °C above the standard level. These studies revealed that climate factors affect construction accidents using thermal comfort indices [10].

The final research subject is the analysis of construction accidents by subcontractor type. Elsye et al., established the work breakdown structure (WBS) and analyzed the high-risk accident events of each structural work according to the construction process [13]. Through this, they aimed to develop a method of documenting safety management plans based on the WBS standard [13]. Antoniou and Merkouri investigated the frequency of accidents by construction stage and corresponding contribution factors and analyzed high-risk and low-risk factors using the Relative Importance Index [14]. They finally determined the most dangerous stages and factors that cause risks for each construction type to provide indicators to construction site workers and managers [14]. Jeong et al., proposed integrated WBS and RBS (i-WRBS) to identify the hierarchy structure in the construction industry and attempted to quantitatively set the risk of each activity according to the project type [15]. According to their work, a high frequency of accidents cannot be simply considered dangerous, and it is necessary to calculate the probability of construction accidents considering the number of simultaneous workers or working time [15]. Studies in this field emphasize the need to analyze construction accidents considering the characteristics of construction work according to the subcontractor type for each stage of the hierarchy structure through big data. They also attempted to analyze the risk of construction accidents from a probabilistic perspective rather than simply using the frequency.

The previous studies revealed that each subcontractor type in the field has different risks. Construction work has various characteristics based on subcontractor type; thus, it is necessary to consider the characteristics of each subcontractor type for analysis. Studies on the analysis of construction accidents based on the thermal comfort that was mentioned above, however, could not provide explanations by subcontractor type because they conducted an analysis based on the entire construction industry. In addition, studies that analyzed detailed risks by classifying construction work into sub-classes did not explain the effects of climate factors. Therefore, this study aims to quantitatively analyze the impact of climate factors on construction accidents through a thermal comfort index and present integrated groups by classifying the analysis results according to the subcontractor type and considering their characteristics. In addition, the risk of accidents was analyzed from a probabilistic perspective, considering the frequency of accidents in the construction industry and the time of climate conditions to provide indicators for quantitative and systematic risk management.

3. Materials and Methods

This study was conducted in four steps, and the process is as follows: (i) collection and classification of data, (ii) PET calculation, (iii) calculation of accident probability, and (iv) clustering and Pearson correlation coefficient (PCC) analysis. Figure 1 shows the research framework.

First, data on construction accidents and corresponding climate conditions were collected and categorized by subcontractor types. Second, the PET was calculated using data on air temperature, relative humidity, and wind velocity. Third, accident probabilities were computed based on the PET values and the occurrence of accidents for different subcontractor types. Fourth, a Hidden Markov Model (HMM) was used to cluster the data, and Pearson correlation coefficients were calculated to identify the relationship between the PET and accident probabilities.

3.1. Collection and Classification of Data

This study collected construction accident data and information on climate conditions at the accident sites at the time of the accidents to explain construction accidents in relation to climate. The data of 18,129 construction accident cases that involved deaths and injuries were collected for 1279 days from 1 July 2019, to 31 December 2022. Previously, Chi et al., conducted a statistical analysis of construction accidents between 2002 and 2011 [24]. They identified the relationships between the causes of accidents and injury characteristics by accident type through 9358 accident cases in the United States [24]. Wong et al., conducted research based on 7497 construction accident cases in Hong Kong [25]. The logistic regression of the 7497 accident cases revealed the fact that the accidents caused by human factors were related to work patterns [25]. Based on these, 18,129 cases of construction accidents used in this study were considered sufficient for the analysis of construction accidents. The dataset of the 18,129 cases was collected from the Construction Safety Management Integrated Information System (CSI) [26]. CSI, a system operated by the Ministry of Land, Infrastructure, and Transport of South Korea, provides information on accidents during construction work. Additionally, 5,525,280 cases of data on the air temperature (Ta), relative humidity (Rh), and wind velocity (V) observed from 180 monitoring stations in South Korea during the same period were collected through the Korea Meteorological Administration (KMA) [27]. The climate data at the accident sites were extracted by comparing the collected weather data with the accident data from CSI.

Many previous studies had difficulty setting standards for classifying construction work into sub-classes. They mainly used the following methods: type classification through expert interviews or type classification specified in the Building Act. Salimi et al., designated the five most representative subcontractor types through expert interviews [28]. Zou et al., classified construction work into eight subcontractor types based on the Department of Buildings [29]. In this study, construction work was classified into 12 subcontractor types based on the Framework Act on the Construction Industry of South Korea, which specifies subcontractor types [30].

Since construction includes indoor and outdoor work, distinguishing between indoor and outdoor work is essentially required. Gies et al., measured the degree of solar exposure for workers in each subcontractor type and distinguished outdoor and indoor types based on the measurement results [31]. Al-Bouwarthan et al., surveyed workers at 10 construction sites and distinguished indoor and outdoor types by analyzing the workers’ workplaces based on the survey [32]. In this study, workplaces were divided into indoor, outdoor, and semi-outdoor types based on the indoor subcontractor type and outdoor subcontractor type classified in previous studies, as well as the information on each type specified in the Framework Act on the Construction Industry [30].

From the collected data, entries lacking clear information regarding the precise area, time, climate conditions, and subcontractor type associated with accidents were excluded from the analysis. Landscape planting and facility construction (54 cases) and railroad track construction (60 cases), which had fewer accident cases compared to other subcontractor types, were also excluded from the analysis due to the difficulty in the probabilistic approach. Consequently, the accident data of 14,331 cases were used by excluding 3798 cases, and a code name was assigned to each type. The results are shown in

Table 2. Number of accidents by subcontractor types.

Code	Subcontractor Type *	Workplace	N **
A	Scaffolding and structure demolition work	Outdoor	2269
B	Metal doors and windows, and roofing prefabrication work	Semi-Outdoor	436
C	Machinery and gas facility construction work	Indoor	1730
D	Painting, wet construction, waterproofing, and stonework	Semi-Outdoor	910
E	Waterworks and sewerage work	Semi-Outdoor	492
F	Underwater and dredging work	Outdoor	277
G	Interior architectural work	Indoor	921
H	Site formation and pavement work	Outdoor	1936
I	Steel structure construction work	Outdoor	791
J	Reinforced concrete work	Outdoor	4569
	Total		14,331

* The Framework Act on the Construction Industry. 2023. ** Number of accidents.

.

3.2. Calculation of PET

Previous studies have found that many types of outdoor thermal comfort indices have been used to measure the thermal stress felt by construction site workers. Among them, the PET can calculate the thermal comfort felt by individuals using only the data that can be easily obtained from KMA, such as the air temperature (Ta), relative humidity (Rh), and wind velocity (V). It can also be easily compared with the temperature used daily, as it uses the Celsius (°C) unit. The analysis results through the PET were consistent with the perceptions of field workers, meaning that the PET provides better results than other thermal comfort indices [33]. Therefore, in this study, the PET was used as a thermal comfort index.

The PET represents thermal comfort as a quantitative value using environmental factors (Ta, Rh, V, and Tmrt) and personal factors (metabolic rate and clothing) as variables. These variables are used for PET calculation based on ‘the heat balance equation for the human body’ in Equation (1).

$$M+W+R+C+E_D+E_{Re}+E_{Sw}+S=0$$

(1)

$M$ is the metabolic rate, $W$ is the physical work output, $R$ is the net radiation of the body, $C$ is the convective heat flow, $E_D$ the latent heat flow to evaporate water into water vapor diffusing through the skin, $E_{Re}$ the sum of heat flows for heating and humidifying the aspirated air, $E_{Sw}$ the heat flow due to the evaporation of sweat, and $S$ is the storage heat flow for heating or cooling the body mass [7].

The value of clothing (Clo), which is the personal factor required to obtain the PET, was set to 0.5 Clo for summer, 0.9 Clo for spring and autumn, and 1 Clo for winter, according to ASHRAE Standard 55 [34]. Each season was distinguished, as shown in

Table 3. Start date of season.

Season	Definition *	Start Date of Season
		2019	2020	2021	2022
Spring	The first day when the average daily temperature does not drop below 5 °C	25 March	17 March	4 March	8 March
Summer	The first day when the average daily temperature does not drop below 20 °C	23 May	29 May	5 June	15 June
Falling	The first day when the average daily temperature does not rise above 20 °C	5 October	29 September	9 October	4 October
Winter	The first day when the average daily temperature does not rise above 5 °C	18 December	12 December	22 December	30 November

* Season definition criteria on KMA [27].

. The metabolic rate (M) was fixed at 80 W. As for the mean radiant temperature (Tmrt), the value at the time of the accident was obtained using the Rayman Pro program [35].

Since this study intends to consider environmental factors, the height and weight of the targets among individual characteristics were assumed to be 175 cm and 75 kg, which are the averages of adult males in South Korea, and the location was set to Seoul, South Korea, at 127° E 37° N. The PET was calculated using the Rayman Pro program by substituting Ta, Rh, V, and Tmrt at the time of the accident.

3.3. Calculation of Accident Probability

Accident probability was calculated using a probabilistic approach to analyze the relationship between the thermal comfort index and accidents that occurred by subcontractor type.

After determining the PET period rate based on the occurrence frequency of each PET value (°C) and obtaining the accident rate based on the frequency of accidents at each PET value by subcontractor type, the accident probability by PET according to the subcontractor type was obtained by dividing the accident rate by the PET period rate Equations (2)–(4).

$$Accident rate at {PET}_k on{ ST}_i=\frac{accident number at {PET}_k on {ST}_i}{{\sum }_{k=n}^{m}accident number at {PET}_k on{ ST}_i}$$

(2)

where ${ST}_i$ represents $i$ among the 10 subcontractor types, and ${PET}_k$ indicates a PET value of $k (C°)$.

$$Period rate {PET}_k=\frac{occurrence frequency {PET}_k}{{\sum }_{k=n}^{m}occurrence frequency {PET}_k}$$

(3)

$$Accident probability at {ST}_i=\frac{{AR}_{{ST}_i}}{PR}$$

(4)

In Equation (4), ${AR}_{{ST}_i}$ is the $Accident rate at {PET}_k on {ST}_i$, and $PR$ is the $Period rate {PET}_k$.

An accident probability of 1 means that the frequency of accidents at a certain PET value is identical to the occurrence frequency of the PET value. If the accident probability is higher than 1, it means that the probability of accidents is relatively high because the frequency of accidents at a certain PET value is higher than the occurrence frequency of the PET value [36].

3.4. Clustering and Pearson Correlation Coefficient Analysis

Clustering was performed to reduce the complexity of analyzing accident probability by subcontractor type and to present better benchmarks in terms of management by classifying risks that depend on PET into subcontractor-type groups [16]. The Hidden Markov model (HMM), a method of modeling hidden states from a single matrix in stages based on Bayesian probability, is mainly used in biology and financial engineering. The main purpose of HMM is not clustering groups, but it has been developed as a methodology for clustering based on changes according to the sequence in many previous studies [37,38,39]. The methodology was used to integrate and classify multiple sequence matrices that show various patterns. The simple and effective K-Nearest Neighbor (KNN) algorithm has been used to classify multiple groups with various patterns [40]. However, Piyathilaka et al., revealed that the HMM exhibits better modeling performance than KNN through research [41]. According to the PET, this study used the HMM to cluster the subcontractor types into groups with similar accident probability patterns. In this study, the HMM was used for clustering the subcontractor types into groups with similar patterns of accident probability according to the PET.

The clustering method based on the HMM is as follows [37,39]:

(1)

Accident probability of each type is expressed as a hidden state through the computation process based on the HMM and arranged as a one-dimensional matrix.

(2)

After calculating the distance between the matrices of each type, agglomeration hierarchical clustering (AHC) is performed based on the results.

(3)

Differences in the characteristics of each cluster are analyzed.

Using this method, the accident probabilities of the clustered subcontractor-type groups are calculated again. The correlation between the PET and accident probability in each subcontractor type group is analyzed to express the difference between the groups.

3.4.1. Process of HMM

The HMM was originally used for time-series analysis. However, in this study, it was intended to be used to analyze the accident probability matrix according to continuous PET changes. Therefore, the calculation was performed by converting the time variable in the HMM calculation algorithm to the PET. In this study, one sequence matrix was defined as a series of accident probabilities according to the PET calculated from one subcontractor type. In addition, each hidden state represents an increase or decrease in accident probability at the PET.

The initial state probabilities ${\pi }_i$ is the probability of starting in state $i$. Find the hidden state through the process of Forward algorithm Equation (5) and Backward algorithm Equation (6) using the calculated transition probabilities and emission probabilities.

$$F_P\left(j\right)=\left({\sum }_{i=1}^N{F}_{P-1}\left(i\right)·T_{ij}\right)·E_j\left(S_P\right)$$

(5)

In this, $T_{ij}$ is the transition probability from state $i$ to state $j$, and $E_j\left(S_P\right)$ is emission probability, which is the probability of observing symbol $p$ in sequence $S_P$ on state $j$. $F_P\left(j\right)$ is the probability of being in state $j$ to PET value $P$ and observing the sequence $S_1$, $S_2$, $S_P$

$$B_P\left(i\right)={\sum }_{j=1}^N{T}_{ij}·E_j\left(S_{P+1}\right)·B_{P+1}\left(j\right)$$

(6)

$B_P\left(i\right)$ is the probability of observing the sequence $S_{P+1}$, $S_{P+2}$, given that the system is in state $i$ at PET value $P$.

The Baum–Welch algorithm is an Expectation Maximization (EM) algorithm that iteratively estimates the parameters by performing the Expectation-step, which computes the expected value of the hidden states given the observations. The Maximization-step updates the parameters to maximize the likelihood of the observations given in the model. It was used to find the transition and emission probabilities [42]. The Viterbi algorithm was also used in the HMM to compute the most likely sequence of states by maximizing the probability of combining observations with hidden states.

The HMM needs to determine the optimal number of states before accident probabilities for each subcontractor type to make a matrix using hidden states. In several previous studies, it was found that the Akaike Information Criterion (AIC) or Bayes information criterion (BIC) was used to determine the optimal number of states for HMM [43,44,45]. Previous studies were conducted to prove that the BIC showed better results in the HMM process than the AIC [46]. For this reason, this research decided to determine the optimal number of states through the BIC.

3.4.2. Clustering of Subcontractor Type Using Dendrogram

After expressing the one-dimensional matrix for the 10 subcontractor types as hidden states through the HMM, the distance of each matrix was compared through $L_1$ distance. Using the AHC algorithm, $L_1$ distance yields better results with a higher probability than $L_2$ distance [47]. In this study, the Manhattan distance, $L_1$ distance, was used instead of $L_2$ distance because the AHC algorithm was intended to be used. The Manhattan distance between each subcontractor type is obtained using Equation (7).

$$Manhattan distance(A,B)={\sum }_{i=n}^m\left|A_i-B_i\right|$$

(7)

$A_i$ and $B_i$ are the $i$-th values in one sequence matrix for each A and B subcontractor type, respectively. $n$ is the start of the matrix, and $m$ is the end of it.

Therefore, the $L_1$ distance between 10 matrices is calculated, and then clusters between subcontractor types with a close distance are selected using dendrogram, an AHC algorithm. The AHC algorithm may be subjectively selected to determine the appropriate cluster number [48]. For algorithms that are used for clustering, such as the AHC algorithm, selecting an optimal number of clusters is important for obtaining good results. In previous studies that analyzed clustering through the AHC algorithm, the silhouette score was used as a method to quantitatively determine the optimal number [49,50]. Accordingly, the silhouette score was used in this study to determine the optimal number of clusters to exclude subjective selection.

3.4.3. Pearson Correlation Coefficient Analysis

Pearson correlation coefficient (PCC) analysis was conducted to examine the effect of the PET change on accident probability. The PCC expresses the correlation between two variables as an R value ranging from −1 to +1. An R value close to 1 represents a strong positive correlation, and an R value close to −1 indicates a weak negative correlation. An R value close to zero means there is no correlation between the two variables. If the absolute value of the R value is 0.19 or less, it indicates a very low correlation. If it ranges from 0.2 to 0.39, it means a low correlation. A PCC from 0.4 to 0.59 represents a moderate correlation, a PCC from 0.6 to 0.79 has a high correlation, and a PCC higher than 0.79 has a very high correlation [51]. Since this study aims to analyze the correlation between the PET and accident probability, groups with a low PCC value suggest that they are subcontractor types less affected by climate factors. Groups with a high PCC value indicate that they are subcontractor types whose accident probability is significantly affected by climate factors. This quantitatively represents that a high level of safety management is required if such construction is performed under unfavorable climate conditions.

4. Results

4.1. Results of PET Calculation

According to the data collected through KMA, the subcontractor type with the highest average T and Rh values among the environmental factors required for PET calculation was type B (metal doors and windows and roofing prefabrication work). A high PET distribution could be predicted for the subcontractor type because the PET value increases as Ta and Rh increase and the V value decreases.

Table 4. The average temperature, relative humidity, and wind velocity at each subcontractor type.

Subcontractor Type	T (°C)	Rh (%)	V (m/s)
A	16.481	59.760	2.222
B	17.760 *	61.179 *	2.198
C	16.425	60.244	2.250
D	16.737	60.485	2.125
E	17.433	57.955	2.288
F	17.095	61.076	2.387
G	16.542	60.161	2.262
H	16.541	59.878	2.207
I	16.846	58.641	2.090 *
J	16.622	59.097	2.210

* Factors influencing PET increase: highest T, highest Rh, lowest V.

shows the environmental factors measured for the 10 subcontractor types.

When the PET was calculated using the environmental factors and the personal factors based on ASHRAE Standard 55, it was found that construction accidents occurred in the PET range from −23.3 to 48.7 °C in South Korea. As shown in Figure 2, the average PET was highest (15.403 °C) for type B (metal doors and windows, and roofing prefabrication work) and lowest (13.201 °C) for type G (interior architectural work).

4.2. Results of the Calculation Accident Probability

The unit of 1 °C was used for the PET index in previous studies that analyzed the influence of climate factors using outdoor thermal comfort indices, and the accident rate and accident probability were calculated using the same method in this study [52]. In addition, calculating accident probability makes it difficult to determine effective values as the PET increases to an extreme value because the period rate shows a value close to zero and the accident probability significantly increases (See Figure A1). Therefore, the range from −19 to 41 °C in which the PET period rate is higher than 0.001 was set as a significant range.

Figure 3 shows the accident probability distribution for all subcontractor types in the PET range. Most subcontractor types except for type B and type I showed probability values of less than 1 for the PET from −19 to 6 °C but exhibited accident probability higher than 1 for the PET from 7 to 14 °C. After that, the accident probability decreased until 20 °C and then increased as the PET increased.

Table 5. The maximum, average, standard deviation value of accident probability in each type.

	A	B	C	D	E	F	G	H	I	J
Max.	2.071	3.254	1.987	2.251	1.935	3.043	1.722	1.956	2.566	1.921
Aver.	1.026	0.964	1.054	1.006	0.904	0.868	0.969	1.020	1.035	1.048
St.D	0.335	0.607	0.325	0.434	0.528	0.637	0.351	0.319	0.477	0.312

shows the maximum, average, and standard deviation values of accident probability in the entire PET range for each type. Among the subcontractor types, type B had a maximum accident probability of 3.254 at PET 30 °C, and type C exhibited the highest average accident probability of 1.054 in the entire range. Type F showed the highest standard deviation of 0.637.

4.3. Results of the Clustering and PCC Analysis

4.3.1. Calculate the HMM

According to the BIC result, the number of states was determined to be six. A total of 6 hidden state steps were set from State 0 to State 5. Based on this, initial state probabilities and transition probabilities were calculated (See

Table A1. Average of estimated initial state probabilities on every subcontractor type.

State Grade	${\mathit{\pi }}_{\mathit{i}}$
State 0	0.4
State 1	0.2
State 2	0.2
State 3	0.2
State 4	0
State 5	0

and

Table A2. Average of estimated transition probabilities on every subcontractor type.

	To	State 0	State 1	State 2	State 3	State 4	State 5
From
State 0		0.000	0.020	0.548	0.332	0.000	0.100
State 1		0.061	0.473	0.141	0.000	0.106	0.220
State 2		0.420	0.037	0.217	0.195	0.066	0.065
State 3		0.004	0.112	0.277	0.386	0.141	0.080
State 4		0.048	0.148	0.000	0.071	0.193	0.539
State 5		0.154	0.029	0.176	0.075	0.203	0.364

). Most of the subcontractor types had the highest initial state probability at State 0, and transition probabilities to State 2 and State 3 were the highest.

For all subcontractor types, the estimated transition probabilities from State 0, with the highest initial state probability, to State 2 and State 3 were 54.8% and 33.2%, respectively.

Based on the calculated two probabilities, the 1-dimensional matrix was expressed like the matrix of $\left[\begin{array}{ccc}0& 1& 1\end{array} \dots \begin{array}{ccc}4& 5& 5\end{array}\right]$ in the effective PET range from −19 to 41 °C (see

Table A3. Matrix of each subcontractor type based hidden state.

PET	A	B	C	D	E	F	G	H	I	J
−19	2	0	3	0	1	0	2	1	0	3
−18	0	2	2	3	1	2	2	0	2	0
−17	2	0	0	4	1	0	2	2	0	2
−16	3	2	3	5	1	2	0	3	2	0
−15	3	0	2	0	0	0	3	2	0	2
−14	3	2	0	3	5	2	2	3	2	0
−13	3	0	3	4	2	0	1	2	3	2
−12	3	2	1	1	2	2	5	3	2	2
−11	3	5	5	2	2	0	3	2	3	0
−10	3	2	5	2	2	2	1	3	2	3
−9	3	3	5	2	4	0	5	2	3	3
−8	3	3	5	2	0	2	5	3	2	3
−7	3	3	2	2	5	5	3	2	0	3
−6	3	3	4	2	0	5	4	3	1	3
−5	3	3	4	2	5	5	4	2	1	3
−4	3	3	4	2	0	2	4	2	1	3
−3	3	3	4	2	5	3	4	3	1	3
−2	3	3	4	2	0	3	4	2	1	3
−1	3	3	4	2	5	3	4	3	1	3
0	3	3	4	2	0	3	4	2	1	3
1	3	3	4	2	5	3	4	3	1	3
2	3	3	4	2	0	3	4	2	1	3
3	3	3	4	2	5	3	4	3	1	3
4	3	3	4	2	2	3	4	2	1	3
5	3	3	4	2	4	3	4	3	1	3
6	3	3	4	2	3	3	4	2	1	3
7	3	3	4	2	5	3	4	3	1	3
8	3	3	4	2	2	3	4	2	1	3
9	3	3	4	2	2	3	4	3	1	3
10	3	3	4	2	2	3	4	2	1	3
11	3	3	4	2	4	3	4	3	1	3
12	3	3	4	2	0	3	4	2	1	3
13	3	3	4	2	5	3	4	3	1	3
14	3	3	4	2	0	3	4	2	1	3
15	3	3	4	2	5	3	4	3	1	3
16	3	1	4	2	2	3	4	2	1	3
17	3	4	4	2	2	3	4	3	1	3
18	3	1	4	2	2	3	4	2	1	3
19	3	4	5	2	2	3	4	3	1	3
20	3	1	5	2	2	3	4	2	5	1
21	1	4	5	2	2	3	4	3	4	1
22	1	1	5	2	4	3	4	2	5	1
23	1	1	5	2	3	3	4	3	4	1
24	1	4	5	5	5	3	4	2	5	1
25	4	1	5	0	2	3	4	3	4	1
26	5	1	5	3	4	1	4	2	5	1
27	5	1	5	4	3	1	4	3	1	1
28	5	1	5	5	5	4	0	4	1	1
29	5	1	5	0	2	1	3	5	4	1
30	5	1	5	3	2	1	1	4	5	1
31	5	4	5	4	2	1	5	5	4	1
32	5	1	5	5	2	4	3	4	5	1
33	5	4	5	0	4	5	4	5	4	1
34	5	5	5	3	3	5	4	4	5	5
35	5	2	5	4	5	2	0	5	4	5
36	4	5	5	5	2	5	3	4	5	5
37	5	5	5	0	2	2	1	5	1	5
38	4	2	5	3	4	0	2	4	1	5
39	5	5	5	4	3	2	1	5	0	4
40	0	5	5	5	1	0	2	4	2	5
41	2	2	2	0	1	2	0	5	0	5

).

As seen from the matrix, most subcontractor types except for Subcontractor Type G had a high hidden state of 4 or 5 as the PET exceeded 21 °C. In addition, Types C and G had a higher hidden state (State 4) than other subcontractor types in the PET range from −15 to 21 °C.

4.3.2. Result of the Clustering

In the silhouette score results, the highest score of 0.2293 was observed at number 3 (See

Table A4. Result of silhouette score.

Number	Silhouette Score
2	0.1309
3 *	0.2293 *
4	0.1517
5	0.1892
6	0.1729
7	0.1030
8	0.0638
9	0.0623

* The most value of silhouette score.

). Therefore, the number of clusters was determined to be three. Based on this, the cutting line of the dendrogram was set at a matrix distance of 160. The results of the dendrogram are shown in Figure 4.

In the clustering results that used the AHC algorithm, the subcontractor types were classified as shown in

Table 6. Subcontractor types in each group.

Group	Code	Subcontractor Type	Workplace
Group 1	C	Machinery and gas facility construction work	Indoor
	G	Interior architectural work	Indoor
Group 2	A	Scaffolding and structure demolition work	Outdoor
	B	Metal doors and windows, and roofing prefabrication work	Semi-Outdoor
	F	Underwater and dredging work	Outdoor
	H	Site formation and pavement work	Outdoor
	J	Reinforced concrete work	Outdoor
Group 3	D	Painting, wet construction, waterproofing, and stonework	Semi-Outdoor
	E	Waterworks and sewerage work	Semi-Outdoor
	I	Steel structure construction work	Outdoor

. Group 1 was composed of Types C and G, which had indoor workplaces. In Group 2, all types were found to be outdoor, except for Type B, semi-outdoor workplaces. In the case of Group 3, two subcontractor types had semi-outdoor workplaces, and only Type I had outdoor workplaces.

The results of calculating the accident probability for each group are as follows. Figure 5 shows the accident probability of each of the three subcontractor-type groups according to the PET.

Group 1 had a high accident probability at both ends, with values of 1.645 and 1.783 at PET −16 °C and PET 38 °C, respectively. For Groups 2 and 3, however, the accident probability gradually increased as the PET increased, unlike in Group 1. Group 2 had a maximum value of 1.730 at PET 40 °C while Group 3 had the highest accident probability of 1.841 at PET 35 °C.

Group 2 showed an accident probability lower than 1 in the PET range from −19 to 6 °C but exhibited values higher than 1 in the 7 to 41 °C range, except for the 16 to 21 °C range. Group 3 showed a tendency similar to Group 2, but it showed no clear pattern and maintained an accident probability higher than 1, unlike Group 2, for which accident probability tended to increase linearly alongside the increase in temperature after 22 °C.

Since all groups showed different accident probability trends according to the PET, the PET range was divided for analysis in this study. According to a previous PET survey, nine grades were determined at intervals of 5 or 6 °C [7]. Based on this, the PET range was divided in this study, as shown in

Table 7. PET range according to the PET grade.

PET Range		PET Grade
Cold range	<4 °C	Very cold
	4–8 °C	Cold
	8–13 °C	Cool
	13–18 °C	Slightly cool
Comfort range	18–23 °C	Neutral
Hot range	23–29 °C	Slightly warm
	29–35 °C	Warm
	35–41 °C	Hot
	>41 °C	Very hot

.

In the entire range, the average accident probability was highest (1.028) in Group 2 and lowest (0.994) in Group 3. In the cold range, unlike the entire range, the average accident probability was highest (0.728) in Group 1 and lowest (0.813) in Group 3. In the hot range, the average accident probability was highest (1.368) in Group 3 and lowest (1.218) in Group 1. These results confirmed that the average accident probability was different in each range.

4.3.3. Correlation between PET and Accident Probability

This study attempted to analyze the PET increase (from the PET cold range to the PET comfort range and from the PET comfort range to the PET hot range) on accident probability. Therefore, an analysis was conducted for the following three ranges: total range (PET −19 °C to 41 °C), cold-to-comfort range (PET −19 °C to 23 °C), and comfort-to-hot range (PET 18 °C to 41 °C).

When regression was performed for accident probability according to the PET in each range, the R² value of Group 1 was found to be very low as it could not exceed 0.3 for all of the three ranges (See Figure A2, Figure A3 and Figure A4). For Groups 2 and 3, the R² values in the total range (0.727 and 0.603, respectively) were higher compared to Group 1.

Table 8. Result of PCC.

	Total Range (PET −19–41 °C)	Cold-To-Comfort Range (PET −19–23 °C)	Comfort-To-Hot Range (PET 18–41 °C)
Group 1 PCC Sig.(two-tail)	0.474	0.221	0.280
	0.000	0.154 *	0.185 *
Group 2 PCC Sig.(two-tail)	0.837	0.591	0.771
	0.000	0.000	0.000
Group 3 PCC Sig.(two-tail)	0.772	0.628	0.463
	0.000	0.000	0.023

* Correlation is not significant over the 0.05 level.

shows the PCC analysis between accident probability and PET for each group. The PCC in the total range was 0.474 for Group 1, 0.837 for Group 2, and 0.772 for Group 3. This means that Group 1 has a moderate correlation, while Group 2 and Group 3 have very high and high positive correlations, respectively. The p-value of significance probability for the PCC was 0.000 for all of Group 1, Group 2, and Group 3, indicating a significant linear relationship.

In the cold-to-comfort range, the R-value was 0.221 for group 1, indicating a low correlation. The p-value was 0.154, showing no significant linear relationship between PET and accident probability. The R-value of Group 2 was 0.591, indicating a moderate correlation. Group 3 had the highest correlation among the groups, with an R-value of 0.628.

In the comfort-to-hot range, the R-value of Group 1 was 0.280, showing a low correlation. The p-value was also 0.185, indicating no significant linear relationship. The R-value of Group 2 was 0.771, showing a high correlation. The R-value of Group 3 was 0.463, indicating a moderate correlation. Consequently, it was found that PET had no impact on accident probability in all three ranges for Group 1. For Group 2, there was a high or very high correlation in each of the three ranges. In particular, the correlation was found to be higher in the comfort-to-hot range. In the case of Group 3, the correlation between the PET and accident probability was higher in the cold-to-comfort range compared to the comfort-to-hot range. A low correlation was observed between the comfort-to-hot range. When the accident probability of Group 3 was analyzed in the total range, the correlation with the PET was found to be higher than that of Group 1 and lower than that of Group 2.

5. Discussion

Among the 10 subcontractor types classified by the Framework Act on the Construction Industry in South Korea, machinery and gas facility construction work and interior architectural work are representative indoor subcontractor types in which most work is performed in buildings without direct solar exposure. These two subcontractor types were clustered into a group when clustering was performed using the HMM. This explains that there is a significant difference in accident probability between indoor and outdoor subcontractor types and that such characteristics were clustered through the HMM.

Lee et al., insisted that the probability of construction accidents increases beyond the PET comfort range [22]. In addition, the presence of a clear correlation between outdoor thermal comfort and accidents was observed in studies that analyzed the correlation [23,53,54]. However, in this study, Group 1, composed of indoor subcontractor types, showed a lower correlation than Group 2 and Group 3 in the PET total range. This indicates that accident probability is not significantly affected by the PET change, i.e., climate factors, for indoor subcontractor types, while accident probability is affected by changes in climate factors for outdoor subcontractor types. In Group 2, composed of outdoor workers, the correlation coefficient was higher in the comfort-to-hot range compared to the PET cold-to-comfort range. In Group 3 with semi-outdoor workplaces, the PCC was low in the comfort-to-hot range, but a strong positive correlation was observed in the total range from PET −19 °C to PET 41 °C. This shows that safety management must be performed for each subcontractor type. Finally, the three groups clustered through the HMM have different correlations between the PET and accident probability, which explains why they were significantly clustered according to subcontractor-type characteristics.

In addition, the results of this study enable the efficient distribution of limited safety management resources in the construction stage through the analysis of outdoor thermal comfort and construction accidents by subcontractor type. They can be used as indicators for implementing different levels of safety management by subcontractor type according to the outdoor thermal comfort measured in the construction stage. Figure 6 shows an example of actually applying the results of this study. When construction work was performed, the PET calculated through the temperature, humidity, and wind velocity of the day was 27 °C. According to the results of this study, the accident probability of Group 2 is lower than that of Group 3 at PET 27 °C, but Group 2 has the highest correlation between PET and accident probability among the groups. Therefore, if the PET is expected to increase after that day, a high level of safety management will be required. In the case of interior architectural work, on the other hand, a low level of safety management will be required compared to other groups. The results of this study can be used as guidelines for safety managers in systematically selecting types that require intensive management for construction accident-related safety management according to the outdoor environment.

6. Conclusions

This study presented the risk of accidents from a probabilistic perspective, using the PET as the thermal comfort index to quantitatively evaluate the risk by climate factors for each subcontractor type. In addition, subcontractor types were clustered through a HMM-based methodology. Finally, accident probability according to the PET range was analyzed for each group using the PCC.

This study was conducted in four steps, and the process is as follows: (i) collection and classification of data, (ii) PET calculation, (iii) calculation of accident probability, and (iv) clustering and PCC analysis.

The subcontractor type that showed the highest average PET value (15.403 °C) at the time of the accident was metal doors and windows, roofing prefabrication work, and interior architectural work, which showed the lowest value (13.201 °C). Accident probability according to the PET value was calculated by dividing the accident cases for 10 subcontractor types into PET periods. Based on the clustering results, the subcontractor types were classified into three groups. While Group 2 and Group 3 had a strong positive correlation between accident probability and the PET with correlation coefficients of 0.837 and 0.772, respectively, Group 1 showed a moderately positive correlation with 0.474. In addition, Group 2 exhibited a strong positive correlation (0.771) in the hot range of the PET, while Group 3 showed a strong positive correlation (0.628) in the cold range. This shows that there are significant differences between the groups clustered through the HMM.

This study has contributions as follows. First, the effects of climate factors on accidents were analyzed and quantitatively evaluated by subcontractor type for construction work with many outdoor tasks to present guidelines on safety management for outdoor workers. Second, the subcontractor types affected by thermal comfort in the cold, comfort, and hot ranges according to the PET grade were classified into groups. Finally, it was quantitatively verified that there is a difference in the influence of climate factors on the risk of accidents between indoor and outdoor subcontractor types. Based on this, it is possible to present a framework that allows safety managers to identify the groups of subcontractor types in the climate during construction work and reinforce safety measures accordingly.

This study has a few limitations. First, only the PET was considered, even though there are various indices for evaluating outdoor thermal comfort other than PET, such as the UTCI and SET*. Second, the HMM was used as a clustering method, but the clustering results for subcontractor-type groups can be different if other methods are used. Third, the PET was calculated based on the climate information provided by the KMA, and it was substituted for accidents, but the information can be different from the climate information at actual construction sites.

Therefore, in future research, the effects of climate factors on construction accidents will be investigated using indices for evaluating outdoor thermal comfort in addition to PET. In addition, other clustering methods for subcontractor-type groups will be used to present a more accurate method through comparative analysis.