A multi-period comprehensive evaluation method of construction safety risk based on cloud model

Abstract

The construction industry has long been seen as a high-risk industry, and the risk evaluation method is the core of safety risk management. Complex construction environments can lead to risk evolution over time, leading to uncertainty in risk assessment. Therefore, it is necessary to establish a risk evaluation method for multi-period group decision, which can also deal with uncertain information reliably. This study defines the risk evaluation indicators for construction safety and adopts the cloud model to deal with the uncertain information of experts’ evaluations. A cloud-based aggregation algorithm is also employed for group decision. Then, a cloud-based Minkowski distance function is proposed to enhance the ability of TOPSIS to deal with the uncertain information. Finally, an optimization algorithm is used to calculate the multi-period comprehensive evaluation value to define the risk priority. A real case is used for demonstration and the results show that the proposed method can effectively deal with the risk evaluation problem of multi-project, multi-period and group decision with uncertain information.

Keywords

Construction safety risk cloud model TOPSIS uncertain information

1. Introduction

The construction industry has long been seen as a high-risk industry in the world [50]. Many scholars have devoted into the research of construction safety risk management, including the construction risk evaluation. Some effective mathematical models have been introduced into the field of construction safety risk evaluation and obtained well achievements.

AHP is an effective tool to deal with the complexity in construction risk evaluation. It can provide a systematic approach to structure risk evaluation problems [5 , 13]. Bayesian network-based fault tree analysis (FTA) can prioritize construction safety incidents and evaluate accident rates [15 , 49]. The Monte Carlo Method (MCM), the Failure Model and Effect Analysis (FMEA) are also commonly used to assess construction safety risk effectively [22 , 51]. In addition, fuzzy set theory can deal with uncertainty in the evaluation process [10 , 33].

However, AHP is based on expert experience, which leads to personal bias and uncertainty in the evaluation process [36]. Moreover, construction safety risks evolve dynamically over time [4, 24], but the above methods can only statically assess risks within a certain period, and cannot reflect comprehensive risks in multiple periods. In addition, the risk level is usually represented by numerical value in the current methods. Thus, fuzzy set theory can only solve the uncertainty of the data itself, and cannot deal with the uncertainty of the data source. In fact, human evaluation is vague and not suitable for expression in accurate numbers, so it is better to use linguistic variables to describe evaluation [38].

Therefore, the main task of construction risk evaluation is still to establish a risk evaluation mathematical model that is robust and reliable and can describe uncertain information. This study adopts the cloud model to deal with the uncertainty of experts’ evaluations, which can effectively describe the ambiguity and randomness of the uncertain information. The ability of describing the uncertain information can improve the reliability of construction risk evaluation. Then, an aggregation algorithm based on cloud model is established to integrate group evaluations and build the cloud risk evaluation matrix. In the single-period risk evaluation, the cloud-based Minkowski distance function is proposed to enhance the ability of TOPSIS for uncertain information. Thus, the cloud-based distance can be used to measure the closeness of the ideal solution. Finally, an optimization algorithm is used to calculate comprehensive evaluation value of the multi-period to define the risk priority.

In summary, this study uses cloud model to describe linguistic variable evaluation and process uncertainty from data source. C-TOPSIS (Cloud-based TOPSIS) based on Minkowski distance function is established to improve the robustness of TOPSIS. An optimization algorithm is used to aggregate multi-period evaluation values to solve the problem that construction safety risks evolve with time. A real case of construction safety risk evaluation is used to verify the feasibility and practicability of the proposed method, and also to demonstrate the solution of multi-period group risk evaluation with uncertain information.

The paper is organized as follows: Section 2 reviews the methods used in this paper. Section 3 describes the proposed method in detail; Section 4 shows the illustrative example and discussion of the proposed method. The paper concludes in Section 5.

2. Related works

2.1. Construction risk evaluation

Risk evaluation is the core of the construction risk management. Generally, construction risk indicators are firstly defined to identify the construction risk impact factors, and the construction risk can be measured qualitatively or quantitatively. An effective evaluation algorithm is then built to calculate the construction risk situation to further control it. In addition, an appropriate technique to deal with uncertain information can enhance the reliability and flexibility of the risk evaluation results. Many studies have been conducted in different steps of construction risk evaluation and have achieved well results.

In the identification of construction risk indicators, Hinze et al. proposed [12] leading indicators, which are different from the traditional lagging indicators of construction risk evaluation, and verified that the leading indicators can be used to distinguish the differences in project safety performance. Pinto established [34] the occupational safety risk evaluation model for the construction industry and defined the construction risk evaluation indicators into four aspects: safety climate, severity factors, possibility factors, and safety barriers. Wu et al. defined [43] construction risk evaluation as 26 indicators and classified them into five aspects: safety climate, safety culture, safety attitude, safety behavior, and safety performance. The structural equation model (SEM) was used to verify the effectiveness. Lingard et al. investigated [18] the relationships among the safety performance indicators, including the lagging indicators and the leading indicators, and indicated that the leading indicators can be more effective. Gunduz and Ahsan ranked [9] the risk indicators, considering both their importance and frequencies, and defined the priority.

In the related methods of construction risk evaluation, commonly used methods such as AHP, FTA, MCM, etc. Zhang et al. proposed [48] a probability decision method, based on triangular fuzzy numbers, for subway construction risk analysis in complex engineering environment. Taylan et al. used [37] fuzzy analytic hierarchy process (FAHP) to measure the weights of fuzzy linguistic variables of the project risks, and adopted the fuzzy TOPSIS method to solve the group decision problem in the fuzzy environment. Zhang et al. proposed [47] a hybrid approach, which merges Fuzzy Matter Element (FME), Monte Carlo (MC) simulation technique, and Dempster-Shafer (DS) evidence theory, to calculate the risk degree at the early construction stage. Gao et al. established [6] a comprehensive risk evaluation model of tunnel collapse based on entropy weight and grey relational degree. Huang et al. integrated [13] AHP and grey relational analysis to build an AHP-Grey Model for construction safety evaluation. Koulinas et al. used [5] the Fuzzy Extended Analysis Hierarchy Process (FEAHP) to prioritize construction site risks for presenting a quantifiable analyze method of risk evaluation.

In the methods of describing uncertain information, Qiu et al. used [35] the fuzzy Delphi analytic hierarchy process (FDAHP) and the grey relational analysis (GRA) method to build a combination method to assess the risk of water inrush. Peng and Liu used [31] grey system theory to calculate objective weights to compensate for the uncertainty of subjective weighting. Peng et al. used [27] the cloud model to build a method for multi-criteria group decision making with uncertain pure linguistic information. Peng and Garg proposed [30] an interval valued fuzzy soft decision algorithm based on Weighted Distance Based Approximation (WDBA), COmbinative Distance-based ASsessment (CODAS) and similarity measure. It can obtain the optimal alternative without counterintuitive phenomena. Liu et al. used [19] interval grey fuzzy uncertain linguistic set to establish a ranking model for construction project risk factors. Gunduz et al. applied [10] the fuzzy set theory and the Structural Equation Model (SEM) to develop a construction safety performance indicator evaluation software. Liu et al. integrated [20] the cloud model, the Failure Model and Effect Analysis (FMEA) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to propose a risk ranking method. In addition, Pythagorean fuzzy set is often used to deal with the uncertainty of multi-attribute decision making [32]. As discussed in the above mentioned literatures, multi-attribute decision-making (MADM) models are often used in the risk evaluation, such as TOPSIS, AHP and grey relational analysis, to evaluate the risk degree of the construction site. Fuzzy numbers, gray numbers and cloud models are mostly used to deal with the uncertain information, and the cloud model can simultaneously deal with the ambiguity and randomness of uncertain information. Cloud model has also demonstrated its practicability in related applications.

2.2. Cloud model

The cloud model establishes a transformation model between the qualitative concept (based on semantic description) and the quantitative representation (through a specific algorithm), which can simultaneously deal with the ambiguity and randomness of uncertain information. Let U be an universe which is represented by exact number, corresponding to the qualitative concept $\tilde{A}$ . For any element x in the universe, there is a transformation function y = μ (x), which is called the membership of x for $\tilde{A}$ , and the distribution of y is called as the cloud droplet.

The cloud model is composed of three parameters, as shown in Fig. 1, including the expectation value (Ex), the entropy (En), and the super entropy (He). is the expectation of the distribution of cloud droplets in the universe, i.e., the most representative qualitative concept value. En is a measure of the randomness and ambiguity of qualitative concepts, reflecting the degree of dispersion of cloud droplets. He is the entropy of En, which is a measure of the uncertainty of entropy, reflecting the thickness of the cloud. The overall shape of the cloud reflects the characteristics of the uncertain information. When a large number of cloud droplets is producing, the regularity of the concept will be clearer.

Fig. 1

The parameters of cloud model.

Since the cloud model can well deal with the uncertain information, it has been widely used in many fields and has achieved good results. Wang et al. proposed [42] a decision-making method based on cloud model, which can solve the multi-standard group decision problem with known indicators’ weights, unknown decision makers’ weights and the interval linguistic variables. Wang et al. used [40] the cognitive cloud model with the probability statistics and the fuzzy set theory to build a water quality evaluation method. Wu et al. used [44] the cloud model to construct a Cloud Choquet Integral (CCI) operator to evaluate the Waste-to-Energy (WtE) performance to select the best site. Peng et al. used [28] a cloud model to process probabilistic language terminology and established a hotel decision support model to assist tourists in choosing the most suitable hotel. Liu et al. proposed [21] a cloud model-based safety evaluation method for prefabricated building construction to control the accidents in the production process of prefabricated buildings.

2.3. TOPSIS

TOPSIS proposed by Hwang and Yoon [14] is a commonly used method in multi-attribute decision making. The ranking of the scheme is calculated by measuring the distance between the alternatives and the ideal solution (and the negative ideal solution) to calculate the closeness of the ideal solution. The TOPSIS algorithm is as follows [7 , 39]:

Step 1. Develop the decision matrix X.

Let x_ij be the evaluation value of the i-th alternative on the j-th indicator, then the decision matrix is built as $X = [\begin{matrix} x_{11} & x_{12} & . . . & x_{1 m} \\ x_{21} & x_{22} & . . . & x_{2 m} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ x_{n 1} & x_{n 2} & . . . & x_{nm} \end{matrix}]$ (1) where i = 1, 2, . . . , n and j = 1, 2, . . . , m.

Step 2. Define the standardized decision matrix R.

In order to make the evaluation values comparable between the indicators, the decision matrix needs to be standardized. The unit vector method is the commonly used standardized method in TOPSIS. Let r_ij be the standardized evaluation value of x_ij, then $r_{ij} = \frac{x_{ij}}{\sqrt{\sum_{j = 1}^{m} x_{ij}^{2}}}$ (2)

Step 3. Define the ideal solution and the negative ideal solution.

The ideal solution defined as the maximum value of the larger-the-better indicator set (J₁) and the minimum value of the smaller-the-better indicator set (J₂). The negative ideal solution is opposite. Therefore, the positive ideal solution (A⁺) and the negative ideal solution (A^-) can be defined as ${\begin{matrix} A^{+} = {(max_{i} r_{ij} | j \in J_{1}), (min_{i} r_{ij} | j \in J_{2})} \\ A^{-} = {(max_{i} r_{ij} | j \in J_{2}), (min_{i} r_{ij} | j \in J_{1})} \end{matrix}$ (3)

Fig. 2

Framework of the proposed method.

Step 4. Calculate the distance from the alternative to the positive ideal solution and the negative ideal solution.

Euclidean distance function is used to calculate the distance ( $d_{i}^{+}$ ) to the positive ideal solution and the distance ( $d_{i}^{-}$ ) to the negative ideal solution distance. The calculation formula is $d_{i}^{+} = \sqrt{\sum_{j = 1}^{m} (r_{ij} - r_{j}^{+})^{2}} and d_{i}^{-} = \sqrt{\sum_{j = 1}^{m} (r_{ij} - r_{j}^{-})^{2}}$ (4) $r_{j}^{+}$ and $r_{j}^{-}$ are the positive ideal solution and the negative ideal solution of the j-th index, respectively.

Step 5. Calculate the closeness of the ideal solution.

The closeness of the ideal solution ( $c_{i}^{+}$ ) can be then defines as $c_{i}^{+} = \frac{d_{i}^{-}}{d_{i}^{+} + d_{i}^{-}}$ (5)

The larger the value, the closer it is to the ideal solution. The corresponding alternative is ranked higher.

TOPSIS’s algorithm is clear in logic and simple in calculation. Hence, it is widely used in many fields, including construction risk evaluation issues. Barros and Wanke used [1] the TOPSIS method to evaluate the African airlines efficiency. Mir et al. applied [23] a modified TOPSIS methodology for Municipal Solid Waste (MSW) problems. Peng and Dai used [29] TOPSIS to deal with the real MADM problems. It can efficaciously solve decision-making problems with the inconsistent information which exist commonly in real world. Yurdakul and İç developed [46] a multi-level performance measurement model for manufacturing companies using a modified version of the fuzzy TOPSIS approach. Oz et al. extended TOPSIS model with Pythagorean fuzzy sets to assess occupational health and safety (OHS) risk in natural gas pipeline project [26]. Gul and Ak combined Pythagorean fuzzy analytic hierarchy process (PFAHP) with fuzzy technique to rank hazards by the similarity and ideal solution (FTOPSIS) method [8]. Colak et al. used type-2 fuzzy AHP and hesitant fuzzy TOPSIS methods to prioritize risks to help manufacturing industry transition [3].

3. Methodology

3.1. Framework

In order to deal with the uncertain information caused by the complex environment of the construction site and to solve the problem of multi-period group decision making, this paper combines the cloud model, TOPSIS and the optimization algorithm to propose a multi-period construction risk evaluation method under the uncertain information. The framework of the method is shown as Fig. 2.

First, in order to describe the uncertainty of the expert’s evaluation, this study uses the risk semantic evaluation and the golden section method based on cloud model to transform qualitative semantics to quantitative values. Then, to aggregate the experts’ evaluations, the cloud model is also adopted to build the cloud risk aggregation evaluation matrix. Subsequently, this paper proposes a cloud-distance function, which is integrated with the cloud model and the Minkowski distance function, to extend TOPSIS to C-TOPSIS (cloud-based TOPSIS) to deal with risk ranking in an uncertain information environment.

Finally, a multi-period aggregation algorithm is proposed, which combines the multi-period evaluation results to give a reliable evaluation and ranking.

3.2. Construction risk evaluation indicators and cloud membership functions

Chou summarized [2] a large number of literatures and collected a complete hierarchy of construction risk evaluation indicators, which were divided into 6 categories and 23 indicators. In addition, an investigation based on the analytic hierarchy process was conducted to define the weights of the indicators. Chou provided a reasonable indicators system of construction risk evaluation. Therefore, this paper develops the multi-period risk evaluation method based on these indicators, as shown in Table 1.

Table 1
Construction risk evaluation indices and weights

Category Weight Indices Weight Final weight

U₁: Personnel 0.316 U₁₁: Lack of construction expertise and safety awareness 0.299 0.094

U₁₂: The degree of proficiency of the workers 0.201 0.064

U₁₃: The workers were not trained in construction safety 0.137 0.043

U₁₄: Special operation without license 0.245 0.077

U₁₅: Physical health quality 0.118 0.037

U₂: Machinery and equipment 0.102 U₂₁: Mechanical handling 0.311 0.032

U₂₂: Reliability test of vertical transport machinery 0.392 0.040

U₂₃: Maintenance and repair of mechanical equipment 0.297 0.030

U₃: Machinery and equipment 0.147 U₃₁: Preparation of construction materials 0.461 0.068

U₃₂: Handling of construction materials 0.316 0.046

U₃₃: Construction material stacking 0.223 0.033

U₄: Machinery and equipment 0.208 U₄₁: Construction organization design 0.366 0.076

U₄₂: Branch safety technology disclosure 0.281 0.058

U₄₃: Procedure for construction design 0.206 0.043

U₄₄: The adoption of new technology and method 0.147 0.031

U₅: Machinery and equipment 0.123 U₅₁: Weather conditions 0.295 0.036

U₅₂: Geologic condition 0.207 0.025

U₅₃: Construction site environment 0.363 0.045

U₅₄: Cultural and social environment 0.135 0.017

U₆: Machinery and equipment 0.104 U₆₁: Safety operation regulations 0.331 0.028

U₆₂: Safety management organization and position setting 0.285 0.026

U₆₃: Report system of accident of safe production 0.113 0.024

U₆₄: Accident emergency rescue system 0.271 0.022

Category	Weight	Indices	Weight	Final weight
U₁: Personnel	0.316	U₁₁: Lack of construction expertise and safety awareness	0.299	0.094
		U₁₂: The degree of proficiency of the workers	0.201	0.064
		U₁₃: The workers were not trained in construction safety	0.137	0.043
		U₁₄: Special operation without license	0.245	0.077
		U₁₅: Physical health quality	0.118	0.037
U₂: Machinery and equipment	0.102	U₂₁: Mechanical handling	0.311	0.032
		U₂₂: Reliability test of vertical transport machinery	0.392	0.040
		U₂₃: Maintenance and repair of mechanical equipment	0.297	0.030
U₃: Machinery and equipment	0.147	U₃₁: Preparation of construction materials	0.461	0.068
		U₃₂: Handling of construction materials	0.316	0.046
		U₃₃: Construction material stacking	0.223	0.033
U₄: Machinery and equipment	0.208	U₄₁: Construction organization design	0.366	0.076
		U₄₂: Branch safety technology disclosure	0.281	0.058
		U₄₃: Procedure for construction design	0.206	0.043
		U₄₄: The adoption of new technology and method	0.147	0.031
U₅: Machinery and equipment	0.123	U₅₁: Weather conditions	0.295	0.036
		U₅₂: Geologic condition	0.207	0.025
		U₅₃: Construction site environment	0.363	0.045
		U₅₄: Cultural and social environment	0.135	0.017
U₆: Machinery and equipment	0.104	U₆₁: Safety operation regulations	0.331	0.028
		U₆₂: Safety management organization and position setting	0.285	0.026
		U₆₃: Report system of accident of safe production	0.113	0.024
		U₆₄: Accident emergency rescue system	0.271	0.022

In the definition of cloud membership function, this paper defines the effective universe is U = (x_min, x_max). Risk is classified into five levels, i.e., absolutely low (al), low (l), moderate (m), high (h), and absolute high (ah). Then, the golden section method [16] is used to define the five cloud membership functions of risk levels as $C = {\begin{matrix} c_{ah} = ({Ex}_{ah,} {En}_{ah}, {He}_{ah}) = (x_{max} - 3 {En}_{ah}, \frac{{En}_{h}}{0.618}, \frac{{He}_{h}}{0.618}) \\ c_{h} = ({Ex}_{h,} {En}_{h}, {He}_{h}) = ({Ex}_{m} + 0.382 ({Ex}_{ah} - {Ex}_{m}), \frac{{En}_{m}}{0.618}, \frac{{He}_{m}}{0.618}) \\ c_{m} = ({Ex}_{m,} {En}_{m}, {He}_{m}) = (\frac{x_{max} + x_{min}}{2}, \frac{0.382 (x_{max} - x_{min}}{3 (n + 1)}, {He}_{m}) \\ c_l = ({Ex}_{l,} En_l, He_l) = ({Ex}_{m} + 0.382 ({Ex}_{m} - {Ex}_{al}), \frac{{En}_{m}}{0.618}, \frac{{He}_{m}}{0.618}) \\ c_{al} = ({Ex}_{al,} {En}_{al}, {He}_{al}) = (x_{min} + 3 {En}_{al}, \frac{En_l}{0.618}, \frac{He_l}{0.618}) \end{matrix}$ (6)

In Equation (6), the value of He_m should be set in advance according to the indicator characteristics and the evaluation requirements.

3.3. Algorithm

In the risk evaluation algorithm of multi-period group under the uncertain information environment, there are three problems needed to be solved: the synthetic cloud evaluation matrix of experts’ evaluations; the distance function based on cloud model to calculate the closeness degree in the synthetic cloud evaluation matrix; the multi-period aggregate evaluation algorithm to provide a reliable comprehensive evaluation. The algorithms of the above three problems are described as follows.

3.3.1. The algorithm of the synthetic evaluation cloud matrix

Let ⊗X^p be the cloud risk evaluation matrix given by the p-th expert. $\otimes X^{p} = [\begin{matrix} \otimes x_{11}^{p} & \otimes x_{12}^{p} & . . . & \otimes x_{1 m}^{p} \\ \otimes x_{21}^{p} & \otimes x_{22}^{p} & . . . & \otimes x_{2 m}^{p} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ \otimes x_{n 1}^{p} & \otimes x_{n 2}^{p} & . . . & \otimes x_{nm}^{p} \end{matrix}]$ (7)

$\otimes x_{ij}^{p}$ is the cloud evaluation given by the p-th expert for the i-th alternative in the j-th index, which is described as $\otimes x_{ij}^{p} = {{Ex}_{ij}^{p}, {En}_{ij}^{p}, {He}_{ij}^{p}}$ . There are many methods to build the synthesis cloud model. Wang and Feng established [41] the aggregation algorithm of floating clouds to generate floating cloud between two adjacent clouds. Yang et al. proposed [45] two kinds of cloud aggregation algorithms. One is the synthetic cloud aggregation algorithm, and the other one is the weighted average cloud aggregation algorithm. This paper adopts the synthetic cloud aggregation algorithm as ${\begin{matrix} {Ex}_{ij} = \frac{1}{P} \sum_{i = 1}^{P} {Ex}_{ij}^{p} \\ {En}_{ij} = \frac{1}{6} [max_{i} {{Ex}_{ij}^{p} + 3 {En}_{ij}^{p}} - min_{i} {{Ex}_{ij}^{p} - 3 {En}_{ij}^{p}}] \\ {He}_{ij} = \frac{1}{P} \sum_{i = 1}^{P} {He}_{ij}^{p} \end{matrix}$ (8)

Fig. 3

Cloud model synthesis.

The concept of cloud model synthesis is shown in Fig. 3. Equation (8) can be used to integrate experts’ cloud evaluations into a synthetic cloud.

3.3.2. Cloud-based TOPSIS (C-TOPSIS)

C-TOPSIS is proposed in this paper to extend TOPSIS in the cloud environment and several problems need to be solved in C-TOPSIS applications. The first problem is the definitions of the ideal solution and the negative ideal solutions. The definitions of traditional TOPSIS are as shown in Equation (3). However, in C-TOPSIS, the evaluation value is extended from the exact number to the cloud model, which is composed of three parameters. Under this condition, the definitions of the ideal solution and the negative ideal solution also need to be modified. The ideal solution and the negative ideal solution of cloud model can be defined as follows. Let the effective universe U = (x_min, x_max), then ${\begin{matrix} A^{+} = {((x_{max}, 0, 0) | j \in J_{1}, (x_{min}, 0, 0) | j \in J_{2})} \\ = (\otimes x_1^{+}, \otimes x_2^{+}, . . ., \otimes x_{m}^{+}) \\ A^{-} = {((x_{min}, 0, 0) | j \in J_{1}, (x_{max}, 0, 0) | j \in J_{2})} \\ = (\otimes x_1^{-}, \otimes x_2^{-}, . . ., \otimes x_{m}^{-}) \end{matrix}$ (9)

The second problem is the calculation of distance between cloud models. This paper extends the distance functions proposed by Lin et al. [17] and Liu et al. [20]to combine the cloud model and the Minkowski distance function to redefine $\otimes d_{i}^{+}$ and $\otimes d_{i}^{-}$ as ${\begin{matrix} \otimes d_{i}^{+} = \sqrt{\frac{1}{3} \sum_{j = 1}^{m} w_{j} [({Ex}_{ij} - x_{max})^{2} + ({En}_{ij})^{2} + ({He}_{ij})^{2}]} \\ \otimes d_{i}^{-} = \sqrt{\frac{1}{3} \sum_{j = 1}^{m} w_{j} [({Ex}_{ij} - x_{min})^{2} + ({En}_{ij})^{2} + ({He}_{ij})^{2}]} \end{matrix}$ (10)

Table 2

Semantic risk evaluations of the foundation engineering period

E	S	U₁					U₂			U₃			U₄				U₅				U₆
		U₁₁	U₁₂	U₁₃	U₁₄	U₁₅	U₂₁	U₂₂	U₂₃	U₃₁	U₃₂	U₃₃	U₄₁	U₄₂	U₄₃	U₄₄	U₅₁	U₅₂	U₅₃	U₅₄	U₆₁	U₆₂	U₆₃	U₆₄
E₁	S₁	H	M	M	L	H	M	M	H	M	L	M	H	M	M	M	H	H	M	M	AH	H	M	M
	S₂	M	L	L	H	M	L	M	L	L	AL	M	M	M	L	M	L	L	L	M	M	M	L	M
	S₃	AH	M	H	H	M	AH	H	H	M	H	M	H	H	M	M	M	M	H	M	H	H	AH	M
	S₄	M	AH	H	L	L	L	M	H	H	AH	M	M	M	H	H	H	H	H	H	H	H	M	M
	S₅	H	M	M	AH	H	M	L	M	AH	M	M	M	M	H	AH	L	L	M	H	AH	H	H	M
E₂	S₁	H	M	L	L	H	H	M	H	M	H	M	H	M	L	M	H	M	M	M	H	AH	M	M
	S₂	L	M	AL	AL	L	AL	L	L	AL	AL	M	L	AL	M	L	AL	L	AL	M	L	L	M	M
	S₃	AH	H	H	M	AH	M	H	H	H	L	M	H	M	M	M	H	H	M	M	M	H	AH	M
	S₄	M	L	H	H	M	M	L	M	AH	H	M	AH	H	M	M	H	H	AH	M	H	M	L	M
	S₅	M	H	M	L	H	H	M	H	M	M	M	L	M	M	M	H	M	AH	AH	H	AH	AH	M
E₃	S₁	L	M	M	L	H	M	H	L	M	H	H	H	M	H	M	H	H	M	M	H	AH	AH	M
	S₂	L	L	AL	M	M	M	L	L	L	L	M	L	L	L	M	H	M	L	L	AL	L	L	M
	S₃	H	H	M	L	H	H	M	H	H	L	M	M	H	AH	H	H	M	M	M	M	H	M	M
	S₄	AH	AH	M	M	H	AH	AH	H	M	AH	H	M	M	M	M	H	AH	M	M	H	AH	M	M
	S₅	M	H	M	M	H	M	H	H	H	L	M	AH	H	M	H	M	M	M	M	L	H	M	M

Note. There are five construction sites (S₁ to S₅) and three experts (E₁ to E₃).

Where w is the weights of the evaluation indicator,

\otimes d_{i}^{+}

and

\otimes d_{i}^{-}

are the distance of i-th alternative between the ideal solution and the native ideal solution, respectively. After completing the cloud distance calculation, the risk evaluation closeness of single period can be obtained according to Equation (5).

Table 3

Expert evaluation cloud matrix of the foundation engineering period

P₁			…	P₃
	S₁	…	S₅	...	S₁	…	S₅
U₁	U₁₁	(6.274,0.343,0.032)	…	(6.274,0.343,0.032)	…	(3.726,0.343,0.032)	…	(5.000,0.212,0.020)
	U₁₂	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(6.274,0.343,0.032)
	U₁₃	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)
	U₁₄	(3.726,0.343,0.032)		(8.335,0.555,0.052)		(3.726,0.343,0.032)		(5.000,0.212,0.020)
	U₁₅	(6.274,0.343,0.032)		(6.274,0.343,0.032)		(6.274,0.343,0.032)		(6.274,0.343,0.032)
U₂	U₂₁	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)
	U₂₂	(5.000,0.212,0.020)		(3.726,0.343,0.032)		(6.274,0.343,0.032)		(6.274,0.343,0.032)
	U₂₃	(6.274,0.343,0.032)		(5.000,0.212,0.020)		(3.726,0.343,0.032)		(6.274,0.343,0.032)
U₃	U₃₁	(5.000,0.212,0.020)		(8.335,0.555,0.052)		(5.000,0.212,0.020)		(6.274,0.343,0.032)
	U₃₂	(3.726,0.343,0.032)		(5.000,0.212,0.020)		(6.274,0.343,0.032)		(3.726,0.343,0.032)
	U₃₃	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(6.274,0.343,0.032)		(5.000,0.212,0.020)
U₄	U₄₁	(6.274,0.343,0.032)		(5.000,0.212,0.020)		(6.274,0.343,0.032)		(8.335,0.555,0.052)
	U₄₂	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(6.274,0.343,0.032)
	U₄₃	(5.000,0.212,0.020)		(6.274,0.343,0.032)		(6.274,0.343,0.032)		(5.000,0.212,0.020)
	U₄₄	(5.000,0.212,0.020)		(8.335,0.555,0.052)		(5.000,0.212,0.020)		(6.274,0.343,0.032)
U₅	U₅₁	(6.274,0.343,0.032)		(3.726,0.343,0.032)		(6.274,0.343,0.032)		(5.000,0.212,0.020)
	U₅₂	(6.274,0.343,0.032)		(3.726,0.343,0.032)		(6.274,0.343,0.032)		(5.000,0.212,0.020)
	U₅₃	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)
	U₅₄	(5.000,0.212,0.020)		(6.274,0.343,0.032)		(5.000,0.212,0.020)		(5.000,0.212,0.020)
U₆	U₆₁	(8.335,0.555,0.052)		(8.335,0.555,0.052)		(6.274,0.343,0.032)		(3.726,0.343,0.032)
	U₆₂	(6.274,0.343,0.032)		(6.274,0.343,0.032)		(8.335,0.555,0.052)		(6.274,0.343,0.032)
	U₆₃	(5.000,0.212,0.020)		(6.274,0.343,0.032)		(8.335,0.555,0.053)		(5.000,0.212,0.020)
	U₆₄	(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)		(5.000,0.212,0.020)

Table 4

Synthetic evaluation cloud matrix of the foundation engineering period

		S₁	S₂	S₃	S₄	S₅
U₁	U₁₁	(5.425,0.539,0.032)	(4.151,0.305,0.028)	(7.648,0.493,0.045)	(6.112,0.648,0.031)	(5.425,0.305,0.024)
	U₁₂	(5.000,0.071,0.020)	(4.151,0.305,0.028)	(5.849,0.305,0.028)	(6.799,0.918,0.045)	(5.849,0.305,0.028)
	U₁₃	(4.575,0.305,0.024)	(2.352,0.493,0.045)	(5.849,0.305,0.028)	(5.849,0.305,0.028)	(5.000,0.071,0.020)
	U₁₄	(3.726,0.114,0.032)	(4.313,0.918,0.035)	(5.000,0.539,0.028)	(5.000,0.539,0.028)	(5.687,0.918,0.035)
	U₁₅	(6.274,0.114,0.032)	(4.575,0.305,0.024)	(6.536,0.684,0.035)	(5.000,0.539,0.028)	(6.274,0.114,0.032)
U₂	U₂₁	(5.425,0.305,0.024)	(3.464,0.684,0.035)	(6.536,0.684,0.035)	(5.687,0.918,0.035)	(5.425,0.305,0.024)
	U₂₂	(5.425,0.305,0.024)	(4.151,0.305,0.028)	(5.849,0.305,0.028)	(5.687,0.918,0.035)	(5.000,0.539,0.028)
	U₂₃	(5.425,0.539,0.024)	(3.726,0.114,0.032)	(3.726,0.114,0.032)	(5.849,0.305,0.028)	(5.849,0.305,0.028)
U₃	U₃₁	(5.000,0.071,0.020)	(3.039,0.493,0.039)	(5.849,0.305,0.028)	(6.536,0.684,0.035)	(6.536,0.684,0.035)
	U₃₂	(5.425,0.539,0.032)	(1.665,0.185,0.052)	(3.888,0.918,0.039)	(7.648,0.493,0.045)	(4.575,0.305,0.024)
	U₃₃	(5.425,0.305,0.024)	(5.000,0.071,0.020)	(5.000,0.071,0.020)	(5.425,0.305,0.024)	(5.000,0.071,0.020)
U₄	U₄₁	(6.274,0.114,0.032)	(4.151,0.305,0.028)	(5.425,0.305,0.024)	(6.536,0.684,0.035)	(5.687,0.918,0.035)
	U₄₂	(5.000,0.071,0.020)	(3.464,0.684,0.035)	(5.849,0.305,0.028)	(5.425,0.305,0.024)	(5.425,0.305,0.024)
	U₄₃	(5.000,0.539,0.028)	(4.151,0.305,0.028)	(6.112,0.684,0.031)	(5.425,0.305,0.024)	(5.425,0.305,0.024)
	U₄₄	(5.000,0.071,0.020)	(4.575,0.305,0.024)	(5.425,0.305,0.024)	(5.425,0.305,0.024)	(6.536,0.684,0.035)
U₅	U₅₁	(6.274,0.114,0.032)	(3.888,0.918,0.039)	(5.849,0.305,0.028)	(6.274,0.114,0.032)	(5.000,0.539,0.028)
	U₅₂	(5.849,0.305,0.028)	(4.151,0.305,0.028)	(5.425,0.305,0.024)	(6.961,0.493,0.039)	(4.575,0.305,0.024)
	U₅₃	(5.000,0.071,0.020)	(3.039,0.493,0.039)	(5.425,0.305,0.024)	(6.536,0.684,0.035)	(6.112,0.684,0.031)
	U₅₄	(5.000,0.071,0.020)	(4.575,0.305,0.024)	(5.000,0.071,0.020)	(5.425,0.305,0.024)	(6.536,0.684,0.035)
U₆	U₆₁	(6.961,0.493,0.039)	(3.464,0.684,0.035)	(5.425,0.305,0.024)	(6.274,0.114,0.032)	(6.112,0.918,0.039)
	U₆₂	(7.648,0.493,0.045)	(4.151,0.305,0.028)	(6.274,0.114,0.032)	(6.536,0.684,0.035)	(6.961,0.493,0.039)
	U₆₃	(6.112,0.684,0.031)	(4.151,0.305,0.028)	(7.223,0.684,0.041)	(4.575,0.305,0.024)	(6.536,0.684,0.035)
	U₆₄	(5.000,0.071,0.020)	(5.000,0.071,0.020)	(5.000,0.071,0.020)	(5.000,0.071,0.020)	(5.000,0.071,0.020)

3.3.2. Multi-period aggregation algorithm

Most risk evaluations are often conducted based on single period records. However, the condition of construction risk changes with progress and the aggregation evaluation of multi-period would provide more reliable results. Therefore, this paper adopts the multi-period aggregation algorithm [17] to complete the multi-period cloud-based risk evaluation method. Let v (t) denote the weight of the t-th period (t = 1, 2, . . . , T) and then the stage weight vector is $v = (v (1), v (2), . . ., v (T)) and \sum_{t = 1}^{T} v (t) = 1$ (11) $v (t) \otimes d_{i}^{+} (t)$ and $v (t) \otimes d_{i}^{-} (t)$ respectively represent the weighted cloud distance to the ideal solution and the weighted cloud distance to the negative ideal solution at the t-th period. Let u_i be the multi-period aggregation ideal solution closeness, then is the multi-period aggregation negative ideal solution closeness. The multi-period weighted distance function can be defined as $F (u) = \sum_{t = 1}^{T} {[u_{i} v (t) \otimes d_{i}^{+} (t)]^{2} + [[(1 - u_{i}) v (t) \otimes d_{i}^{-} (t)]^{2}}$ (12)

The stable solution of u_i can be obtained when $\frac{\partial F (u)}{\partial_{u_{i}}} = 0$ , i.e.,

$\begin{matrix} \frac{\partial F (u)}{\partial_{u_{i}}} = \sum_{t = 1}^{T} {^{2} + [[(1 - u_{i}) v (t) \\ \otimes d_{i}^{-} (t)]^{2} [- v (t) \otimes d_{i}^{- (t)}] = 0} . \end{matrix}$ (13)

Then, u_ican be defined as $\begin{matrix} u_{i} = \frac{\sum_{t = 0}^{T} [v (t) \otimes d_{i}^{-} (t)]}{\sum_{t = 1}^{T} {[v_{u_{i}} (t) \otimes d_{i}^{+} (t)]^{2} + \sum_{t = 1}^{T} v (t) \otimes d_{i}^{-} (t)]^{2}}} \end{matrix}$ (14)u_i can be used as a basis of risk ranking. Larger value means higher risk level.

4. Illustrative example

4.1. Case background

A real case in Chengdu, China is used for demonstration. Five construction projects are chosen and three experts are invited to conduct risk evaluation in three periods (the foundation engineering period, the main structural engineering period, and the roofing engineering & installation period). They evaluate the construction risk situation based on the indicators listed in Table 1. Five semantic risk levels are used, i.e., absolutely low (AL), low (L), moderate (M), high (H), absolute high (AH). According to experts’ opinions, the period weights are set as equal.

4.2. Results

Take the first period (foundation engineering) as example, the semantic risk evaluation matrix is obtained in Table 2.

Then the semantic evaluation matrix is converted into the cloud-based evaluation matrix. Let U = (0, 10) and He_m = 0.020, then the following semantic evaluation cloud is obtained $C = {\begin{matrix} c_{ah} = ({Ex}_{ah}, {En}_{ah}, {He}_{ah}) = (8.335, 0.555, 0.052) \\ c_{h} = ({Ex}_{h}, {En}_{h}, {He}_{h}) = (6.274, 0.343, 0.032) \\ c_{m} = ({Ex}_{m}, {En}_{m}, {He}_{m}) = (5.000, 0.212, 0.020) \\ c_{l} = (Ex_l, En_l, He_l) = (3.726, 0.343, 0.032) \\ c_{al} = ({Ex}_{al}, {En}_{al}, {He}_{al}) = (1.665, 0.555, 0.052) \end{matrix}$ (15)

Therefore, the semantic evaluation cloud can convert the qualitative semantic evaluation into the quantitative evaluation cloud, and obtain expert evaluation cloud matrix, as shown in Table 3.

Then, experts’ evaluations can be integrated according to the group cloud synthetic algorithm described in 3.3.2, and the synthetic evaluation cloud matrix for foundation engineering period is obtained, as shown in Table 4

4.2.1. C-TOPSIS calculations

The indicators for this study are the smaller-the-better type, so the positive and negative ideal solutions, according to Equation (9), are A⁺ = (0, 0, 0) and A^- = (10, 0, 0), respectively. Therefore, the distance from the evaluation cloud matrix to the ideal solution and the negative ideal solutions are calculated according to Equation (10). Then the C-TOPSIS ranking results of the five project in the foundation engineering period are shown in Table 5, and the risk ranking can be determined as 2 ≻ 1 ≻5 ≻ 3 ≻4.

Table 5
C-TOPSIS calculations of the foundation engineering period

Site $\otimes d_{i}^{+}$ $\otimes d_{i}^{-}$ $c_{i}^{+}$

S₁ 3.14 2.72 0.46

S₂ 2.27 3.60 0.61

S₃ 3.40 2.48 0.42

S₄ 3.50 2.37 0.40

S₅ 3.29 2.56 0.44

Site	$\otimes d_{i}^{+}$	$\otimes d_{i}^{-}$	$c_{i}^{+}$
S₁	3.14	2.72	0.46
S₂	2.27	3.60	0.61
S₃	3.40	2.48	0.42
S₄	3.50	2.37	0.40
S₅	3.29	2.56	0.44

Fig. 4

Robustness analysis results.

Fig. 5

Effectiveness analysis results.

In the same way, the C-TOPSIS results of the main structural engineering period (2-Period) and the roofing engineering & installation period (3-Period) can be obtained, as shown in Table 6. The risk rankings of the main structural engineering period and the roofing engineering & install period are 4 ≻ 2 ≻5 ≻ 1 ≻3 and 2 ≻ 3 ≻1 ≻ 5 ≻4, respectively.

Table 6

The multi-period comprehensive evaluation results

	1-Period	2-Period	3-Period	u _i
	$\otimes d_{i}^{+}$	$\otimes d_{i}^{-}$	$\otimes d_{i}^{+}$	$\otimes d_{i}^{-}$	$\otimes d_{i}^{+}$	$\otimes d_{i}^{-}$
S₁	3.14	2.72	3.16	2.69	3.19	2.67	0.42
S₂	2.27	3.60	3.00	2.93	2.70	3.17	0.60
S₃	3.40	2.48	3.42	2.44	2.96	2.95	0.39
S₄	3.50	2.37	2.77	3.09	3.39	2.46	0.40
S₅	3.29	2.56	3.26	2.59	3.29	2.56	0.38

4.2.2. Multi-period aggregation calculations

Risk evaluation is often conducted by single period. Although the cloud model can be used to solve the ambiguity and randomness caused by the uncertain information, C-TOPSIS is still used in single period. Therefore, the multi-period aggregation algorithm in Section 3.3.2 can be used to calculate the comprehensive evaluation.

The weight vector of periods is assumed equal. According to the Equation (13), the multi-period comprehensive evaluations are calculated as Table 8: The construction safety risk ranking of these five projects is 2 ≻ 1 ≻4 ≻ 3 ≻5.

In order to evaluate the safety risk of the construction project more intuitively, C-TOPSIS and aggregation algorithm are calculated for the semantic evaluation indicator cloud in 4.1, and the ideal solution closeness of the semantic evaluation indicators is obtained. Therefore, an evaluation standard based on the representation of the ideal solution closeness is established, as shown in Table 7.

Table 7
The evaluation standard based on the ideal solution closeness

Evaluation standard Cloud model u _i

Absolutely Low (AL) (1.665,0.555,0.052) 0.96

Low (L) (3.726,0.343,0.032) 0.74

Moderate (M) (5.000,0.212,0.020) 0.50

High (H) (6.274,0.343,0.032) 0.26

Absolutely High (AH) (8.335,0.555,0.052) 0.04

Evaluation standard	Cloud model	u _i
Absolutely Low (AL)	(1.665,0.555,0.052)	0.96
Low (L)	(3.726,0.343,0.032)	0.74
Moderate (M)	(5.000,0.212,0.020)	0.50
High (H)	(6.274,0.343,0.032)	0.26
Absolutely High (AH)	(8.335,0.555,0.052)	0.04

Table 8

The application case weights of robustness analysis

Period	Current	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
	case
1	0.33	0.314	0.345	0.339	0.363	0.297	0.303
2	0.33	0.342	0.320	0.343	0.304	0.356	0.338
3	0.33	0.344	0.335	0.318	0.333	0.347	0.359

Tables 6 and 7 can be further compared to obtain the following conclusions:

Most of the projects in the evaluation sample are between medium risk and high risk, with relatively high construction safety risks. It can be inferred that the construction safety risk of the projects in Chengdu is poor. The relevant management departments should organize large-scale inspections to confirm the construction safety risks of the projects, and order the rectification of unqualified projects.

The ideal solution of project 2 is 0.60, which is between medium risk and low risk. Compared to the other four projects, project 2 has a lower construction safety risk. The safety risk management method of project 2 construction site is analyzed to provide reference for other project rectification.

4.3. Discussion

In order to verify the robustness and reliability of proposed method, the period weights are adjusted to verify the effect of weights on the results. First, we adjust the period weights within 5% and 10% to verify robustness. The weight distributions are shown in Table 8: the weights of case 1 3 vary within 5% and the weights of case 4 6 vary within 10%. The results shown in Fig. 4 indicate that within 10%, the changes of the period weights don’t affect the ranking order. The proposed method can deal with the uncertainty caused by period weights. Thus, the proposed method is proved to be robust within 10%.

Table 9
The application case weights of effectiveness analysis

Period Current case Case 7 Case 8 Case 9 Case 10

1 0.33 0.8 0.2 0.2 0.4

2 0.33 0.1 0.7 0.2 0.4

3 0.33 0.1 0.1 0.6 0.2

Period	Current case	Case 7	Case 8	Case 9	Case 10
1	0.33	0.8	0.2	0.2	0.4
2	0.33	0.1	0.7	0.2	0.4
3	0.33	0.1	0.1	0.6	0.2

We also conduct five common distributions of construction safety risk based on expert suggestions to analyze the situation of the weights more than 10%. The specific weight distributions are shown in Table 9. The current case represents the equal distribution of risks in three periods, case 7 9 represent the risks of one of the three periods are higher than the other two, and case 10 represents the risks of the three periods have difference but not too large. The comparison of results were shown in Fig. 5. The weights of case 1 indicate that the accident probability in 1-Period is large. The results of case 1 are the same as the results of 1-Period C-TOPSIS. Furthermore, case 2 and case 3 show the same trends. In addition, the current case and case 4 both have a relatively even weight, and the results of the above two also show similar trends. The above results show that when the period weights change more than 10%, the proposed method can effectively reflect the timing-based risk relationship. The proposed method is reliable.

5. Conclusions

In the field of construction safety risk evaluation, the uncertainty of objective environment in construction site determines the uncertainty of subjective cognition of experts’ evaluation. These two uncertainties greatly reduce the accuracy of construction safety risk evaluation. In addition, construction safety risks evolve over time leading to instability in the evaluation results. This research attempts to resolve the above questions, and the research results are as follows:

The cloud-based TOPSIS technology (C-TOPSIS) is established to conduct construction safety risk evaluation, and semantic evaluation is used instead of mathematical expression to increase evaluation elasticity, thus reducing the uncertainty caused by the objective environment.

The aggregation algorithm of multi-expert evaluation is used to reduce the data fluctuation caused by the subjective difference of individual evaluation and reduce the uncertainty of subjective cognition.

The multi-period aggregation algorithm is established to realize the dynamic evolution based on the construction life cycle and improve the robustness of the risk evaluation for construction safety.

Establish the multi-dimensional (alternative-indicator-group-time) evaluation method for construction risk under uncertain information. On the basis of establishing a robust risk evaluation method of construction safety, a solution scheme is provided for regional construction safety risk management.

The current study has some limitations as follows: (1) The proposed method can carry out effective risk evaluation, but lacks risk prediction. In the future, a prediction algorithm can extend the practicability; (2) the weights of periods are equal in this study. Future research may consider to use expert judgment to allocate the elasticity of weights; (3) The indices in this study come from the literature review, but each construction site has its own particularity. Thus, the future research can integrate knowledge map and data mining technology to build a risk index library, and develop recommendation algorithms to customize evaluation indices.

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A multi-period comprehensive evaluation method of construction safety risk based on cloud model

Abstract

Keywords

1. Introduction

2. Related works

2.1. Construction risk evaluation

2.2. Cloud model

3.1. Framework

3.2. Construction risk evaluation indicators and cloud membership functions

3.3.1. The algorithm of the synthetic evaluation cloud matrix

4.1. Case background

4.2. Results

Table 5 C-TOPSIS calculations of the foundation engineering period Site ⊗ d i + ⊗ d i - c i + S1 3.14 2.72 0.46 S2 2.27 3.60 0.61 S3 3.40 2.48 0.42 S4 3.50 2.37 0.40 S5 3.29 2.56 0.44

Table 9 The application case weights of effectiveness analysis Period Current case Case 7 Case 8 Case 9 Case 10 1 0.33 0.8 0.2 0.2 0.4 2 0.33 0.1 0.7 0.2 0.4 3 0.33 0.1 0.1 0.6 0.2

References

Table 5
C-TOPSIS calculations of the foundation engineering period

Site $\otimes d_{i}^{+}$ $\otimes d_{i}^{-}$ $c_{i}^{+}$

S₁ 3.14 2.72 0.46

S₂ 2.27 3.60 0.61

S₃ 3.40 2.48 0.42

S₄ 3.50 2.37 0.40

S₅ 3.29 2.56 0.44

Table 9
The application case weights of effectiveness analysis

Period Current case Case 7 Case 8 Case 9 Case 10

1 0.33 0.8 0.2 0.2 0.4

2 0.33 0.1 0.7 0.2 0.4

3 0.33 0.1 0.1 0.6 0.2