Research on Safety Performance Evaluation and Improvement Path of Prefabricated Building Construction Based on DEMATEL and NK

Abstract

To address the common issues of lacking indicator system identification, causal relationship quantification, and path simulation analysis in the current research on safety performance in prefabricated construction, a method for improving safety performance in prefabricated construction based on the decision-making trial and evaluation laboratory (DEMATEL) and NK model is proposed. Firstly, through theoretical analysis and literature review, the indicator system for safety performance in prefabricated construction is identified using the grounded theory. Secondly, expert research and quantitative analysis are combined to analyze the causal relationship of the indicators using the DEMATEL method. Then, the DEMATEL method is integrated with the NK model to carry out a key indicator adaptability modeling analysis and three-dimensional simulation. Finally, a case study is conducted to validate the usability and effectiveness of the proposed model and method. The results show that X₆ (construction and implementation of safety management system) had the highest impact on the other indicators, and X₁₄ (quality and safety status of prefabricated components) was most influenced by other indicators. X₆ (construction and implementation of safety management system), X₁ (personnel safety awareness and attitude), X₁₄ (quality and safety status of prefabricated components), and X₁₂ (construction site working environment) were identified as key performance indicators. “X₆ (construction and implementation of safety management system) → X₁ (personnel safety awareness and attitude) → X₁₄ (quality and safety status of prefabricated components) → X₁₂ (construction site working environment)” was considered the optimal path to improve construction safety performance.

1. Introduction

As an important form of the integrated development of green, intelligent, and industrialized construction, prefabricated buildings aim to promote the green and low-carbon transformation and upgrading of the construction industry [1]. However, with the rapid development and large-scale application of prefabricated buildings, compared with traditional construction, new situations and problems in construction safety, such as “unsafe behavior of personnel”, “unsafe state of equipment”, “unstable environmental factors”, and “unreasonable management measures”, have become increasingly prominent. Therefore, evaluating the influencing factors of the construction safety performance of prefabricated buildings and exploring ways to improve the construction safety performance of prefabricated buildings have become fundamental theoretical issues to support the sustainable development of prefabricated buildings.

In recent years, numerous scholars have conducted research on various aspects of construction safety in prefabricated buildings. In the field of construction safety accident analysis, Chen Wei et al. [2] first constructed a system dynamics and multi-objective planning model to analyze key elements of accident safety investment and optimal resource allocation plans. Zhang et al. [3], to reduce construction safety accidents in prefabricated buildings, conducted a simulation analysis of the evolutionary game process under dynamic supervision strategies using system dynamics. Fard et al. [4] analyzed the injury types and root causes of 125 safety accidents to improve construction safety performance in prefabricated buildings. In the field of construction safety risk analysis, Wang Qiankun et al. [5] first introduced a fusion model of interaction matrices and fuzzy cognitive maps to identify key safety risks in prefabricated building construction and predict evolutionary trends. Wang et al. [6] constructed a dynamic control system for construction risks based on entropy to explore the dynamic laws of construction safety risks in prefabricated buildings. Liu et al. [7] first constructed a safety risk assessment method for prefabricated building construction based on the cloud model. Overall, these studies provide theoretical support and methodological foundations for research on the safety performance of prefabricated building construction. However, the current research at home and abroad mainly focuses on accident analysis and risk assessment, lacking systematic research on the evaluation and improvement paths of safety performance in prefabricated building construction.

Decision-making trial and evaluation laboratory (DEMATEL) is a methodology proposed to understand complex and difficult problems in the real world. It is a systematic analysis method using graph theory and matrix tools. DEMATEL can calculate the impact of each element on other elements through the logical relationships between elements in the system and the direct influence matrix, thereby calculating the causal relationship and centrality of each element as the basis for building models and determining the causal relationship between elements and the position of each element in the system. This is an important step and the key means of quantitative analysis of indicator factors. Therefore, based on the construction of a safety performance evaluation index system for prefabricated buildings, the DEMATEL method is adopted to evaluate the safety performance of prefabricated buildings in order to quantify the causal relationship and importance of construction safety performance index factors. This will be a key step in evaluating the safety performance of prefabricated building construction, and it also lays an important foundation for planning the path to improve the safety performance of prefabricated buildings.

The NK model is a mathematical model used to study complex adaptive systems, originally proposed by biologist Stuart Kaufman in 1993. The purpose of this model is to simulate the complexity of biological evolution and study the properties of solution space through network structure and interactions. The NK model provides a powerful tool for studying complex adaptive systems, enabling researchers to understand the structure of the solution space, the performance of search algorithms, and the dynamic characteristics of the evolutionary process. This model has a wide range of applications and provides important theoretical support for interdisciplinary research. The flexibility of the NK model allows for multiple extensions and variations, including multi-landscape models and dynamic NK models. Among them, the multi-landscape model is composed of multiple independent NK models, each with its own network structure. In a dynamic NK model, over time, the network structure and interactions may change, simulating the dynamic evolution process of the system. The NK model has been widely applied in fields such as biology, evolutionary computation, and genetic algorithms. In the study of complex systems, it is used to explore the structure and properties of the solution space in complex systems, as well as the dynamics of the search process.

With the integration of research methods and the expansion of application scenarios, the DEMATEL method and the NK model have been widely used in factor evaluation and path exploration [8]. In the study of factor relationships, Fontela et al. [9] first proposed the DEMATEL method to address the causal relationships and interactions of complex factors. Kuzu et al. [10] combined fuzzy logic with DEMATEL to analyze the causal relationships among ship operation risk factors. Mohandes et al. [11], based on an improved DEMATEL model, explored the interaction relationships among accident causes on construction sites by identifying key factors. In the study of implementation path decisions, Kauffman [12] first proposed the NK model to find optimal solutions through a comprehensive evaluation and decision analysis of complex systems. Liu et al. [13] proposed a risk coupling analysis method based on an improved NK model to quantify the risk of subsea blowout accidents. Bull [14], based on the NK model paradigm, proposed an improved decision-making approach for distributed control structures in complex systems. These studies demonstrate the feasibility of the DEMATEL method and the NK model in causal relationship analysis and path simulation research, providing a theoretical foundation and methodological support for the evaluation and improvement paths of safety performance in prefabricated building construction (PBC).

In summary, this paper views the evaluation and path of decision-making of prefabricated building construction safety performance as a complex system and proposes a performance evaluation and improvement path method based on DEMATEL and NK models. Through grounded theory, a performance evaluation indicator system is constructed. The DEMATEL method is used to analyze causal relationships and identify key performance evaluation indicators. Subsequently, the NK model simulation of key indicator fitness is conducted to explore the optimal improvement path. This approach provides a reference for the management of prefabricated building construction safety performance.

2. Evaluation Indicators

2.1. Sample Collection

To obtain a comprehensive indicator system for evaluating the safety performance of prefabricated building construction, this paper collected raw data through survey interviews, policy review, and literature analysis. During the survey interviews, which lasted from August 2022 to August 2023, 25 experts and scholars from government safety supervision departments, China State Construction Engineering Corporation (CSCEC) Science and Technology Development Co., Ltd., Huazhong University of Science and Technology, and Wuhan University of Technology were interviewed, yielding 200 pieces of raw data. In the policy review phase, 18 documents were collected, including the “Building Law of the People’s Republic of China”, the “Regulations on the Administration of Construction Project Safety Production”, the “Evaluation Standards for Prefabricated Buildings”, and the “Technical Specifications for the Safety of Prefabricated Building Construction”, resulting in 134 pieces of raw data. In the literature analysis phase, 10 articles on the theme of prefabricated building construction safety from databases such as WOS and CNKI were reviewed, yielding 52 pieces of raw data.

2.2. Substantive Coding

Substantive coding was directed by “unsafe behavior of personnel”, “unreasonable management measures”, “unstable environmental factors”, and “unsafe state of equipment”. Open coding and axial coding were applied to the 386 pieces of raw data. The open coding aimed to process raw data through the “raw data—labeling—initial conceptualization” procedure, categorizing, comparing, and eliminating initial concepts with frequencies lower than three. The axial coding aimed to clarify the relationships between conceptual layers through the “initial conceptualization—conceptualization—categorization” procedure, forming conceptual indicators. The process of the substantive coding of raw data is shown in

Table 1. The process of substantial encoding of the original corpus.

No.	Original Corpus	Open Coding		Axis Coding
		Labeling	Initial Conceptualization	Conceptualization	Categorization
A001	Workers engaged in prefabricated building construction generally exhibit issues such as weak safety awareness, indifference to safety protection, and insufficient safety consciousness. It is necessary to strengthen safety training and education to enhance the safety awareness and skills of practitioners.	Weak safety awareness Indifference to safety protection Insufficient safety consciousness Workers’ safety awareness and skills	Safety Awareness Safety attitude Safety skills	Safety awareness and attitude Safety technical level	Personnel factors
		Strengthening safety training and education	Safety education Safety training	Safety education and training	Management factors
		—	—	—	Environmental factors
		—	—	—	Equipment factors
A002	Necessary emergency rescue equipment and devices should be equipped at the construction site for regular inspection and maintenance to ensure the safety and stability of the construction site, and to promptly identify and address potential safety hazards.	—	—	—	Personnel factors
		Regular inspection and maintenance	Security system	Security management system situation	Management factors
		Safety at the construction site Stability of construction site Potential safety hazards	Natural environment Surrounding environment Work environment	Natural environment of construction site Construction site yard environment Construction site working environment	Environmental factors
		Emergency rescue equipment and devices	Safety equipment	Equipping with protective and rescue equipment	Equipment factors
……	……	……	……	……	……

.

An analysis of Table 1 indicates that the raw data labeled A001, upon preliminary analysis, involved “personnel factors” and “management factors”. In the open coding analysis, labeling was carried out in four aspects: “personnel, management, environment, and equipment”, forming labeled concepts, such as “weak safety awareness”, “indifference to safety protection awareness”, and “strengthening safety training and education”, which were distilled into initial conceptual indicators, such as “safety awareness”, “safety attitude”, and “safety training”. In the axial coding analysis, similar expressions within the initial conceptual indicators were merged, forming a categorical system of factors, such as “personnel”, “management”, and “equipment”. Similarly, the remaining 385 pieces of raw data were analyzed using substantive coding, ultimately summarizing 93 conceptual indicators corresponding to four categories.

2.3. Saturation Test

By summarizing and consolidating similar expressions within these 93 conceptual indicators, four core categories—personnel factors (Z₁), management factors (Z₂), environmental factors (Z₃), and equipment factors (Z₄)—corresponding to 16 main categories (X₁–X₁₆) were systematically distilled. Based on this, the constructed indicator system was verified using randomly sampled new data, and no new categories emerged, indicating that the indicator system passed the saturation test. The final prefabricated building construction safety performance indicator system is shown in

Table 2. Evaluation index system for safety performance of PBC.

Core Category	Main Category	Abbreviation
Personnel factors Z1	Personnel safety awareness and attitude	X1
	Personnel safety knowledge and technical proficiency	X2
	Personnel compliance with safety management systems	X3
	Personnel physiological and psychological health	X4
Management factors Z2	Safety education, training, and promotion	X5
	Construction and implementation of safety management system	X6
	Safety technical disclosure and construction organization design	X7
	Formulation and implementation of safety emergency plans	X8
Environmental factors Z3	Natural environment at the construction site	X9
	Surrounding environment of the construction site	X10
	Storage environment at the construction site	X11
	Construction site working environment	X12
Equipment factors Z4	Safety status of construction machinery and equipment	X13
	Quality and safety status of prefabricated components	X14
	Monitoring and maintenance of machinery and equipment	X15
	Provision of protective and rescue equipment	X16

.

3. Methodology

3.1. Research Framework of DEMATEL Method and NK Model

To evaluate the safety performance of prefabricated building construction and explore the improvement paths for safety performance, this paper proposes a method for safety performance evaluation and path selection based on DEMATEL and the NK model. First, a performance evaluation indicator system for prefabricated building construction safety is established through grounded theory coding analysis. Then, the DEMATEL method is used to quantify the centrality and causality of the safety performance indicators, analyzing the causal relationships between the indicators. Finally, the DEMATEL method is combined with the NK model, transforming the results into modeling parameters for the NK model, generating a fitness landscape map, and determining the optimal climbing path through simulation to improve the safety performance level of prefabricated building construction. The detailed steps are described in Section 2.2 and Section 2.3.

3.2. Exploring the Causal Relationship of Indicators Using the DEMATEL Method

Field experts are invited to evaluate the indicator system, and the DEMATEL method is used to quantify the direct relation matrix, indirect relation matrix, and comprehensive relation matrix of the indicators, exploring the causal relationships of safety performance through centrality and causality. The main steps are as follows:

(1) Invite m experts to use a Likert 5-point scale to evaluate the direct positive correlation between indicator X_i and X_j, with the evaluation results represented as the original relation matrix A = (a₁, a₂, …, a_m). To reduce subjective influence, use the combination ordered weighted averaging (COWA) operator to sort matrix A in descending order, starting from 0, resulting in the descending order matrix B = (b₀, b₁, b₂, …, b_h, …, b_m−1), with b₀ ≥ b₁ ≥ b₂ ≥ … ≥ b_h ≥ … ≥ b_m−1. The weighted weight vector of b_h is ψ = (ψ₁, ψ₂, …, ψ_m). The direct relation matrix T = [t_ij]_16×16 is obtained by weighted calculation of ψ_h+1 and b_h. The calculation formulas for ψ and T are shown in Equations (1) and (2):

$${\psi }_{h+1}={\displaystyle \frac{C_{m-1}^h}{{\sum }_{h-0}^{m-1} C_{m-1}^h}}={\displaystyle \frac{C_{m-1}^h}{2^{m-1}}}$$

(1)

$$T={\psi }_1{b}_0+{\psi }_2{b}_1+\cdots +{\psi }_m{b}_{m-1}=\sum _{h=0}^{m-1} {\psi }_{h+1}{b}_h$$

(2)

where ψ_h+1 is the weighted weight of b_h, $C_{m-1}^h$ is the combination number, and h is the number of elements in the descending order matrix B, h = 0, 1, …, m⁻¹.

(2) Normalize the direct relation matrix T = [t_ij]_16×16 to obtain the normalized direct relation matrix G = [g_ij]_16×16 [15]. According to the principle of Markov chain absorption, construct the indirect relation matrix Y = [y_ij]_16×16 [16]. The calculation formulas for g_ij and Y are shown in Equations (3) and (4):

$$g_{ij}=T\cdot min[{\displaystyle \frac{1}{maxi{\sum }_{i=1}^{16} t_{ij}}},{\displaystyle \frac{1}{maxj{\sum }_{j=1}^{16} t_{ij}}}]$$

(3)

$$Y=G(I-G{)}^{-1}=[y_{ij}{]}_{16\times 16}$$

(4)

(3) Add Equations (3) and (4) to establish the comprehensive relation matrix Q = [q_ij]_16×16. The calculation formula for q_ij is as follows:

$$q_{ij}=g_{ij}+y_{ij}(i,j=1,2,\dots ,16)$$

(5)

(4) Sum the row and column elements of the comprehensive relation matrix Q = [q_ij]_16×16 to obtain the influence degree (O_i) and the impact degree (P_i) of the indicators [17]. The calculation formulas for O_i and P_i are shown in Equations (6) and (7):

$$O_i={\left[{\sum }_{i=1}^{16}{q}_{ij}\right]}_{16\times 1}={\left[q_{i.}\right]}_{16\times 1}(i,j=1,2,\dots ,16)$$

(6)

$$P_i={\left[{\sum }_{i=1}^{16}{q}_{ij}\right]}_{1\times 16}={\left[q_{.i}\right]}_{1\times 16}(i,j=1,2,\dots ,16)$$

(7)

(5) Calculate the centrality (W_i) and causality (R_i) values of indicators X₁ to X₁₆. According to the DEMATEL principle [18], W_i indicates the position and importance of indicator X_i in the evaluation indicator system X₁ to X₁₆. The larger the W_i value, the more important X_i is [19]. R_i can distinguish between cause factors and effect factors [20]. If R_i ≥ 0, it is a cause factor; otherwise, it is an effect factor [21]. The calculation formulas for W_i and R_i are shown in Equations (8) and (9):

$$W_i=O_i+P_i(i,j=1,2,\dots ,16)$$

(8)

$$R_i=O_i-P_i(i,j=1,2,\dots ,16)$$

(9)

3.3. Simulation of Fitness Landscape Graph Based on NK Model

By integrating the DEMATEL method with the NK model, key indicators are identified through centrality threshold values, constructing a fitness allele set for the key indicators, mapping them into three-dimensional space, and improving the selection of the optimal path for prefabricated building construction safety performance based on the simulation results. The main steps are as follows:

(1) By setting a centrality threshold ξ to filter key indicators, the DEMATEL method and NK model can be integrated, converting the number of key indicators into the parameter N of the NK model. The calculation formula for ξ is as follows:

$$\mathsf{\xi }=\mathsf{\omega }max\left\{W_i\right\}(i,j=1,2,\dots ,16)$$

(10)

where ω represents the maximum centrality percentage of the indicators, 0 < ω ≤ 1, and the value of ω depends on the historical experience of the project manager. A larger value of ω indicates a higher centrality threshold ξ for extracting key indicators, resulting in fewer key indicators being ultimately extracted.

(2) Quantify the safety performance improvement effect when implementing specific strategies individually. Retain the rows and columns of the key indicators X_i (i = 1, 2, …, 16) in the comprehensive relation matrix Q = [q_ij]_16×16 to obtain the comprehensive relation matrix C = [c_αβ]_S×S for the key indicators, where α, β∈{1, 2, …, S}. Aggregate the row and column elements of C = [c_αβ]_S×S in the NK model to quantify the fitness value E_α when implementing the key indicators individually [22]. The calculation formula for E_α is as follows:

$$E_{\alpha }={\displaystyle \frac{{\left[{\sum }_{\alpha =1}^S c_{\alpha \beta }\right]}_{\alpha \times 1}}{{\sum }_{\alpha =1}^S c_{\alpha \beta }+{\sum }_{\beta =1}^S c_{\alpha \beta }}}={\displaystyle \frac{{\left[C_{\alpha 1}\right]}_{\alpha \times 1}}{{\sum }_{\alpha =1}^S c_{\alpha \beta }+{\sum }_{\beta =1}^S c_{\alpha \beta }}}$$

(11)

(3) Quantify the safety performance improvement effect when implementing combination strategies comprehensively. In the NK model of C = [c_αβ]_S×S (α, β∈{1, 2, …, S}), the interdependencies within the system are influenced by the interactions between the indicators. The fitness value d_α of the key indicator combination strategy and the overall fitness value F can be quantified through the effect of the key indicator combination configuration. The calculation formulas for d_α and F are shown in Equations (12) and (13):

$$d_{\alpha }=E_{\alpha }+\sum _{\beta \in \{\beta |c_{\beta }=1\mid \beta \mid \le \mathrm{K}\}}{c}_{\alpha }{E}_{\alpha },\alpha \ne \beta$$

(12)

$$F=\sum _{a=1}^s d_a \alpha ,\beta \in \{1,2,\dots ,S\}$$

(13)

For example, in the NK model [23], if there are four key indicators S = 4 and they all interact with each other, then N = 4 and K = 4 − 1 = 3. The fitness value when implementing the key indicator c₁ individually is $E_1=\left[c_{1·}\right]/({\sum }_{\alpha =1}^4{c}_{\alpha \beta }+{\sum }_{\beta =1}^4{c}_{\alpha \beta })$. The overall fitness value when c₁ and c₂ interact is as follows: when c₁ acts on c₂, the fitness value is d₁ = E_1×c₁₂+E₁; when c₂ acts on c₁, the fitness value is d₂ = E_2×c₂₁+E₂; and when c₁ and c₂ interact, the overall fitness value is F = d₁₂+d₂₁.

(4) In the NK model of C = [c_αβ]_S×S, if each key indicator makes a decision to implement or not (0 or 1), there are 2^S configurations of 0 or 1 for the S key indicators. Establish a set of allele configurations and fitness values for key indicators, map it into three-dimensional space to construct a fitness landscape map, and simulate the selection process of performance improvement paths through fitness landscape climbing simulations. Combine the quantitative analysis results to identify the optimal improvement path.

In summary, based on the quantitative identification of key indicators using the DEMATEL method, the DEMATEL is integrated with the NK to construct a set of fitness alleles for the key indicators. A method for evaluating and selecting improvement paths for PBC safety performance based on the DEMATEL and NK models is proposed to evaluate the safety performance of PBC and explore the improvement path of PBC safety performance.

4. Empirical Analysis

4.1. Case Introduction

In WH City, a prefabricated building project has a total land area of 43,541 square meters and a net land area of 42,336 square meters. The total building area is no more than 112,500 square meters, including 97,500 square meters for residential buildings and 15,000 square meters for commercial buildings, with a plot ratio of 2.58. This project relies on an intelligent construction planning scheme, focusing on safety management during the construction phase as an important control objective. According to the safety control plan, the project aims to promote the informatization and process-oriented management of construction site safety, comprehensively enhancing construction safety performance.

4.2. Causal Relationship Analysis Based on DEMATEL

Seventeen field experts with at least two years of management and research experience in prefabricated buildings were invited, including government personnel (3), industry professionals (11), and some university experts (3). Using a Likert 5-point scale (0 = “very unimportant”, 1 = “unimportant”, 2 = “no impact”, 3 = “important”, 4 = “very important”), they evaluated the direct positive correlation between indicators X_i and X_j (i, j = 1, 2, ..., 16). The survey lasted nearly three months, resulting in 13 valid questionnaires with an effective response rate of 76.47%. Due to space limitations, only the evaluation of X₁ against X₁ to X₁₆ in the 13 valid questionnaires is used as an example, with the results shown in

Table 3. Scoring results of safety performance indicator X₁ to X₁~X₁₆ in PBC.

Valid Questionnaire	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	X12	X13	X14	X15	X16
1	0	2	3	3	3	3	2	2	0	0	1	2	3	3	1	3
2	0	2	3	3	2	3	2	2	0	1	0	3	3	3	1	3
3	0	3	3	3	2	3	3	3	0	1	1	3	3	3	3	3
4	0	3	2	2	2	4	3	3	0	0	1	3	3	3	3	3
5	0	3	2	2	3	4	3	3	0	1	0	2	3	2	3	2
6	0	2	2	2	3	4	2	3	0	1	1	2	2	2	2	2
7	0	2	2	2	3	4	2	3	0	0	1	2	2	2	2	2
8	0	3	4	2	3	4	2	2	0	1	0	2	2	2	2	2
9	0	3	4	2	3	4	2	2	0	1	1	2	2	2	2	2
10	0	3	2	2	3	4	2	2	0	0	1	2	2	2	2	2
11	0	3	2	2	3	3	2	2	0	1	0	2	2	2	2	2
12	0	4	1	2	3	3	2	2	0	1	1	2	2	2	2	2
13	0	2	3	3	3	3	2	2	0	0	1	2	3	3	1	3

.

Using the COWA operator to calculate the score of indicator X₁ against X₂, the 13 valid questionnaires were listed as the initial matrix A = (2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 4, 2). Matrix A was sorted in descending order to obtain matrix B = (4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2). The weight vector ψ was calculated using Equation (1) as ψ = (1/2¹², 12/2¹², 66/2¹², 220/2¹², 495/2¹², 792/2¹², 924/2¹², 792/2¹², 495/2¹², 220/2¹², 66/2¹², 12/2¹², 1/2¹²), and the direct relation matrix element t₁₂ was calculated using Equation (2) as t₁₂ = Bψ^T = 2.9302. Similarly, the direct relation matrix of the safety performance indicators for PBC was calculated using the COWA operator, T_16×16; see

Table 4. Direct correlation matrix of safety performance indicators in PBC.

T16×16	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	X12	X13	X14	X15	X16
X1	0.0000	2.9302	2.1938	2.0193	2.9807	3.6128	2.0193	2.1938	0.0000	0.8062	0.9270	2.0193	2.1938	2.0730	2.0161	2.0730
X2	3.9968	0.0000	1.0730	0.9807	0.0000	3.9968	0.3904	3.0730	0.0000	0.0000	0.0000	1.1938	2.0193	3.0730	1.8062	0.9270
X3	2.6128	1.6128	0.0000	1.0730	0.8062	4.0000	1.2449	2.9968	0.0000	0.0000	0.0000	0.9807	2.0730	2.9270	1.9270	1.9807
X4	3.1938	1.0730	2.0730	0.0000	0.3872	3.9968	1.3872	2.0762	0.0000	0.0000	0.0000	0.9807	0.0000	3.0193	1.2131	1.1938
X5	3.9270	2.9807	2.6160	0.6128	0.0000	3.9807	0.0000	2.1460	0.0000	0.0000	0.0000	1.0386	2.0193	3.0029	1.0193	0.9270
X6	3.9807	3.0032	2.9839	2.0063	2.1938	0.0000	2.0032	3.6128	0.0000	1.1938	2.0000	1.0000	3.1938	4.0000	2.1938	2.0730
X7	3.3872	1.3872	1.8062	0.0000	1.1938	3.0032	0.0000	1.9270	0.0000	0.6128	0.9270	3.0000	1.0193	2.9807	2.0193	1.6128
X8	3.0193	2.9807	2.1938	1.8062	1.1938	2.0730	1.0193	0.0000	0.0000	0.0000	0.0000	2.0730	1.0730	2.9270	2.0000	1.0730
X9	0.0000	0.0000	0.0000	0.0000	0.1938	1.0000	0.9270	1.0000	0.0000	1.9270	1.9807	2.9968	1.0193	3.0730	2.0193	1.1938
X10	0.0000	1.9807	1.9968	1.9270	1.0032	2.0193	0.1938	0.8062	0.6128	0.0000	0.0193	2.9807	1.1938	2.8062	2.0000	1.0193
X11	1.0000	1.9270	1.6128	2.0000	1.1941	2.0000	1.0032	1.0730	0.6128	0.9807	0.0000	2.9968	0.9968	3.0000	2.0000	0.0000
X12	3.9270	0.0000	0.0000	0.0000	2.0032	2.1208	2.0032	0.0000	0.0000	2.6128	2.0730	0.0000	1.8062	3.6128	2.9270	2.9968
X13	3.0032	1.0193	1.0032	0.0000	1.0762	2.0000	1.0032	0.0000	0.9807	0.9270	0.9807	2.0000	0.0000	4.0000	1.9807	0.9807
X14	2.9968	1.9270	2.9968	1.0000	2.8062	1.6128	1.6128	2.9807	0.0000	0.0000	0.9807	3.9968	2.9807	0.0730	0.0032	0.0032
X15	3.0032	1.0032	1.0730	0.0000	1.0195	2.0000	0.9807	0.6128	0.0000	0.0000	0.0000	1.9807	0.0000	2.6128	0.0000	1.6128
X16	3.0730	0.0730	0.9807	0.0000	0.6128	2.0000	0.8062	0.9807	0.0000	0.0000	0.0000	2.9937	1.0193	3.0730	2.0730	0.0000

.

The direct relation matrix in Table 4 was normalized using Equation (3) to obtain the normalized matrix G_16×16. Based on Equation (4), the indirect relation matrix Y_16×16 was constructed. Using Equation (5), the comprehensive relation matrix of the safety performance indicators for PBC was determined, Q_16×16; see

Table 5. Comprehensive correlation matrix of safety performance indicators in PBC.

Q16×16	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	X12	X13	X14	X15	X16
X1	0.0896	0.1755	0.1455	0.1137	0.1680	0.2299	0.1211	0.1489	0.0030	0.0498	0.0594	0.1424	0.1433	0.1748	0.1360	0.1283
X2	0.2373	0.0429	0.0887	0.0664	0.0377	0.2269	0.0478	0.1747	0.0022	0.0129	0.0177	0.0966	0.1270	0.1964	0.1160	0.0720
X3	0.1844	0.1126	0.0448	0.0700	0.0719	0.2305	0.0843	0.1738	0.0022	0.0128	0.0178	0.0904	0.1308	0.1946	0.1231	0.1176
X4	0.1991	0.0857	0.1285	0.0227	0.0509	0.2241	0.0876	0.1322	0.0012	0.0113	0.0160	0.0840	0.0396	0.1887	0.0878	0.0813
X5	0.2405	0.1726	0.1567	0.0528	0.0384	0.2335	0.0324	0.1416	0.0023	0.0131	0.0181	0.0917	0.1320	0.1989	0.0857	0.0742
X6	0.2672	0.1878	0.1875	0.1191	0.1430	0.0904	0.1263	0.2164	0.0040	0.0673	0.1064	0.1122	0.1926	0.2667	0.1503	0.1326
X7	0.2169	0.1032	0.1209	0.0251	0.0905	0.1905	0.0322	0.1282	0.0023	0.0413	0.0584	0.1773	0.0881	0.1981	0.1291	0.1042
X8	0.1986	0.1668	0.1345	0.0993	0.0860	0.1506	0.0733	0.0458	0.0017	0.0124	0.0164	0.1330	0.0868	0.1908	0.1242	0.0787
X9	0.0463	0.0261	0.0279	0.0150	0.0340	0.0805	0.0602	0.0687	0.0025	0.0941	0.0979	0.1648	0.0707	0.1783	0.1144	0.0727
X10	0.0611	0.1161	0.1188	0.0998	0.0716	0.1368	0.0335	0.0714	0.0281	0.0117	0.0156	0.1655	0.0851	0.1776	0.1188	0.0716
X11	0.1079	0.1188	0.1069	0.1059	0.0835	0.1416	0.0705	0.0866	0.0284	0.0552	0.0163	0.1707	0.0801	0.1909	0.1221	0.0309
X12	0.2364	0.0449	0.0467	0.0248	0.1254	0.1529	0.1161	0.0451	0.0034	0.1256	0.1063	0.0556	0.1199	0.2249	0.1666	0.1605
X13	0.1863	0.0793	0.0798	0.0202	0.0795	0.1369	0.0696	0.0393	0.0441	0.0526	0.0585	0.1294	0.0375	0.2282	0.1189	0.0703
X14	0.2051	0.1281	0.1717	0.0678	0.1580	0.1386	0.1012	0.1734	0.0030	0.0165	0.0610	0.2178	0.1719	0.0801	0.0472	0.0382
X15	0.1765	0.0720	0.0755	0.0164	0.0706	0.1274	0.0636	0.0584	0.0010	0.0098	0.0129	0.1175	0.0310	0.1573	0.0280	0.0924
X16	0.1838	0.0347	0.0736	0.0171	0.0568	0.1298	0.0590	0.0744	0.0015	0.0119	0.0150	0.1638	0.0760	0.1815	0.1189	0.0265

.

Based on the comprehensive relation matrix Q_16×16 in Table 5, the influence degree (O_i), impact degree (P_i), centrality (W_i), and causality (R_i) of indicators X₁ to X₁₆ were calculated using Equations (6), (7), (8), and (9), respectively. The results are shown in

Table 6. DEMATEL calculation results of safety performance indicators in PBC.

Influencing Factors	Oi	Oi Rank	Pi	Pi Rank	Ri	Ri Rank	Si	Factor Types
X1	2.0292	2	2.8369	2	4.8662	2	−0.8077	Resultant Factors
X2	1.5630	9	1.6672	8	3.2302	7	−0.1042	Resultant Factors
X3	1.6617	7	1.7079	7	3.3696	6	−0.0463	Resultant Factors
X4	1.4406	11	0.9360	13	2.3766	13	0.5047	Causal Factors
X5	1.6844	6	1.3659	10	3.0502	8	0.3185	Causal Factors
X6	2.3699	1	2.6207	3	4.9907	1	−0.2508	Resultant Factors
X7	1.7061	5	1.1787	12	2.8848	11	0.5275	Causal Factors
X8	1.5988	8	1.7788	6	3.3776	5	−0.1800	Resultant Factors
X9	1.1541	15	0.1309	16	1.2850	16	1.0232	Causal Factors
X10	1.3831	13	0.5984	15	1.9814	15	0.7847	Causal Factors
X11	1.5164	10	0.6935	14	2.2099	14	0.8228	Causal Factors
X12	1.7549	4	2.1126	4	3.8676	4	−0.3577	Resultant Factors
X13	1.4304	12	1.6125	9	3.0429	9	−0.1821	Resultant Factors
X14	1.7796	3	3.0276	1	4.8072	3	−1.2480	Resultant Factors
X15	1.1101	16	1.7870	5	2.8970	10	−0.6769	Resultant Factors
X16	1.2243	14	1.3519	11	2.5762	12	−0.1276	Resultant Factors

.

An analysis of Table 6 reveals that in terms of influence degree, indicator X₆ (construction and implementation of safety management systems) has the highest influence degree, indicating that X₆ is most likely to trigger and affect other performance indicators. It is followed by X₁ (personnel safety awareness and attitude) and X₁₄ (quality and safety status of prefabricated components). Regarding the degree of being influenced, X₁₄ (quality and safety status of prefabricated components), X₁ (personnel safety awareness and attitude), and X₆ (construction and implementation of safety management systems) are the top three indicators, suggesting they are most susceptible to being affected by other performance indicators. Based on this, using the centrality values R_i from

Table 7. Comprehensive correlation matrix of key safety performance indicators in PBC.

C4×4	X1	X6	X12	X14	Cα•	Eα
X1	0.0896	0.2299	0.1424	0.1748	0.6368	0.1186
X6	0.2672	0.0904	0.1122	0.2667	0.7365	0.1372
X12	0.2364	0.1529	0.0556	0.2249	0.6698	0.1247
X14	0.2051	0.1386	0.2178	0.0801	0.6416	0.1195
C•β	0.7983	0.6118	0.5281	0.7464	∑Cα• = ∑C•β = 5.3694	—

as the horizontal axis and the causality values S_i as the vertical axis, a causality diagram is plotted, as shown in Figure 1.

An analysis of Figure 1 shows that, in terms of cause classification and effect classification, quadrants I and II belong to the cause group, while quadrants III and IV belong to the effect group. In terms of the influence degree and being influenced degree, quadrants I and IV belong to the influence group, while quadrants III and II belong to the influenced group. In the cause group, X₅ (safety education and training) has the highest centrality value (3.0502), followed by X₇ (safety technical disclosure and construction organization design) and X₄ (physiological and psychological health of personnel). In the effect group, X₆ (construction and implementation of safety management systems) has the highest centrality value (4.9907), followed by X₁ (personnel safety awareness and attitude) and X₁₄ (quality and safety status of prefabricated components). The results indicate that X₆ is easily affected by other performance indicators, causing fluctuations in the safety performance of prefabricated building construction. Notably, the top four performance indicators in centrality ranking are all in the effect group, suggesting that X₆ (construction and implementation of safety management systems), X₁ (personnel safety awareness and attitude), X₁₄ (quality and safety status of prefabricated components), and X₁₂ (construction site working environment) play significant roles in the entire prefabricated building construction safety performance system and should be given focused attention.

4.3. Fitness Modeling Simulation Based on NK Model

Based on the DEMATEL calculation results, using Equation (10) with ω = 0.7, ξ = 3.4935, the top four key performance indicators in centrality values (R_i) from Table 6 are identified as key performance indicators, namely, X₆ (construction and implementation of safety management systems), X₁ (personnel safety awareness and attitude), X₁₄ (quality and safety status of prefabricated components), and X₁₂ (construction site working environment). By integrating the DEMATEL method with the NK model, the number of key indicators 4 (S = 4) is converted to the parameter of the NK model (N = 4). Retaining the rows and columns of the key indicators in the comprehensive relation matrix Q_16×16, the comprehensive relation matrix for the key indicators C = [c_αβ]_4×4 is obtained, as shown in Table 7.

An analysis of Table 7 shows that by aggregating the row and column elements in C = [c_αβ]_4×4 and using Equation (11), the fitness value when implementing key indicator X₁ alone is E₁ = [C_1•]/[∑C_α• + ∑C_•β] = 0.6368/(5.3694 + 5.3694)= 0.1186. Similarly, the fitness values E_α for other key indicators when implemented alone can be calculated (see the seventh column of Table 7). When multiple key indicators are implemented in combination and all the key indicators are interrelated, K = 4 − 1 = 3. If there are two scenarios (0 or 1) for implementing or not implementing each of the four key indicators, a total of 16 possible combinations are formed. Using Equations (11) and (12), the overall fitness values F_d (F₁~F₁₆) for the 16 combinations are calculated, with the results shown in

Table 8. Composite fitness values of key safety performance indicators in PBC.

Serial Number	X1	X6	X12	X14	Fd	Path
1	0	0	0	0	0.0000
2	1	0	0	0	0.1186
3	0	1	0	0	0.1372	①
4	0	0	1	0	0.1247
5	0	0	0	1	0.1195
6	1	1	0	0	0.3197	②
7	1	0	1	0	0.2897
8	1	0	0	1	0.2833
9	0	1	1	0	0.2964
10	0	1	0	1	0.3098
11	0	0	1	1	0.2983
12	1	1	1	0	0.5253
13	1	1	0	1	0.5376	③
14	1	0	1	1	0.5085
15	0	1	1	1	0.5231
16	1	1	1	1	0.7972	④

.

Based on the analysis of Table 8, the interaction between X₁ and X₆ results in an allele combination of (1, 1, 0, 0). This is discussed in two scenarios: when X₁ acts on X₆, the fitness value d₁ = E₁ × c₁₂ + E₁ = 0.1186 × 0.2299 + 0.1186 = 0.1459; when X₆ acts on X₁, the fitness value d₂ = E₂ × c₂₁ + E₂ = 0.1372 × 0.2672 + 0.1372 = 0.1739. The overall fitness value F₆ = d₁ + d₂ = 0.3197. By merging key indicators X₁ and X₆ on the X-axis, and X₁₂ and X₁₄ on the Y-axis, and representing F_d on the Z-axis, an adaptive three-dimensional landscape climbing schematic is constructed to simulate the selection process of the improvement path for prefabricated building construction safety performance, as shown in Figure 2.

Analyses of Figure 2 and Table 8 indicate that the global path optimization always starts from (0, 0, 0, 0), with an initial overall fitness value F₁ = 0. First step: In Figure 2a, there are four scenarios (F₂ to F₅) for the individual implementation of key indicators X₁, X₆, X₁₂, and X₁₄. Implementing the allele combination (0, 1, 0, 0) for X₆ results in the highest overall fitness value F₃ = 0.1372. In Figure 2b, this is represented by path ①, climbing from position ((0,0), (0,0), 0.0000) to ((0,1), (0,0), 0.1372). Thus, the first step should select key indicator X₆. Therefore, (0,1,0,0) is both the endpoint of the first step and the starting point of the second step. Second step: In Figure 2a, there are six scenarios (F₆ to F₁₁) for the pairwise combination of key indicators X₁, X₆, X₁₂, and X₁₄. Implementing the allele combination (1,1,0,0) for X₁ and X₆ results in the highest overall fitness value F₆ = 0.3197. In Figure 2b, this is represented by path ②, climbing from position ((0,1), (0,0), 0.1372) to ((1,1), (0,0), 0.3197). Thus, the second step should select key indicator X₁. Therefore, (1, 1, 0, 0) is both the endpoint of the second step and the starting point of the next step. Similarly, other combination strategies for key indicators are sequentially implemented until the solution with all the key factors (1, 1, 1, 1) is found.

In summary, the basic idea of adaptive landscape climbing is to gradually adjust the improvement path until the solution with all the key indicators (1,1,1,1) is found, thus obtaining the optimal improvement path. In this case, the climbing sequence is ((0,0), (0,0), 0.0000), ((0,1), (0,0), 0.1372), ((1,1), (0,0), 0.3197), ((1,1), (0,1), 0.5376), ((1,1), (1,1), 0.7972), indicating that the optimal improvement path should be implemented in the sequence X₆ (construction and implementation of safety management systems) → X₁ (personnel safety awareness and attitude) → X₁₄ (quality and safety status of prefabricated components) → X₁₂ (construction site working environment).

5. Conclusions

This article regards the safety performance evaluation and path decision-making of prefabricated construction as a complex system and proposes a performance evaluation and improvement path method based on DEMATEL and NK. A performance evaluation index system was constructed through grounded theory, and DEMATEL was used to analyze causal relationships, identify key performance evaluation indicators, and conduct NK model simulation of key indicator fitness to explore the optimal improvement path, providing reference for safety performance management in prefabricated construction. At the same time, the practical application scenarios and shortcomings of the research results in this article were summarized.

(1)

Through survey interviews, policy review, and literature analysis, a total of 386 pieces of raw data were obtained. Using grounded theory, substantive coding and saturation testing were performed on the raw data, combining the opinions and suggestions of field experts and the experience of relevant practitioners. This ultimately formed the prefabricated building construction safety performance indicator system with 16 main categories (X₁ to X₁₆) and four core categories (personnel, management, environment, and equipment).

(2)

Based on the DEMATEL decision matrix causal relationship analysis, X₆ (construction and implementation of safety management systems) has the highest influence on other factors, while X₁₄ (quality and safety status of prefabricated components) is the most influenced by other indicators. From the perspectives of centrality and causality, X₆ (construction and implementation of safety management systems), X₁ (personnel safety awareness and attitude), X₁₄ (quality and safety status of prefabricated components), and X₁₂ (construction site working environment) are the top four performance indicators and should be focused on in the improvement path selection for prefabricated building construction safety performance.

(3)

Based on the NK model simulation analysis, key subjects were modeled for four key indicators, constructing an adaptive three-dimensional landscape climbing schematic. According to the landscape climbing process representation and the overall fitness value criteria for alleles, the optimal path for improving prefabricated building construction safety performance was determined, focusing on X₆ (construction and implementation of safety management systems) → X₁ (personnel safety awareness and attitude) → X₁₄ (quality and safety status of prefabricated components) → X₁₂ (construction site working environment).

(4)

To simplify the study, the NK model in this paper only considers two scenarios (0 and 1), lacking consideration of intermediate degrees, which affects the reasonable allocation of resources for safety performance improvement strategies to some extent. In the future, introducing intermediate degree values in the range of (0,1) or adopting a graded representation of state degrees to take reasonable resource allocation based on the optimal degree of implementation of each key indicator will be attempted, thereby obtaining the optimal performance improvement of prefabricated building construction safety performance under reasonable resource allocation.

(5)

At the same time, this study focuses on practical issues encountered during the construction process of a certain subway line in Wuhan. It can be said that the complete method framework system formed by this research provides a certain reference for other similar engineering projects to solve the same problems. However, there are certain particularities in case samples, basic data, etc. Therefore, in solving problems in other engineering projects, specific problem analysis should be carried out.