A Model Based on Variable Weight Theory and Interval Grey Clustering to Evaluate the Competency of BIM Construction Engineers

Abstract

Building information modeling (BIM) has emerged as a fundamental component of Industry 4.0 recently. BIM construction engineers (BCEs) play a pivotal role in implementing BIM, and their personal competency is crucial to the successful application and promotion of BIM technology. Existing research on evaluating BIM capabilities has mainly focused on the enterprise or project level, neglecting individual-level analysis. Therefore, this study aims to establish an individual-level competency evaluation model for BCEs. Firstly, the competency of BCEs was divided into five levels by referring to relevant standards and domestic and foreign research. Secondly, through the analysis of literature data and website data, the competency evaluation indicator system for BCEs was constructed, which includes four primary indicators and 27 secondary indicators. Thirdly, variable weight theory was used to optimize the weights determined by general methods and calculate the comprehensive weights of each indicator. Then the competency levels of BCEs were determined by the interval grey clustering method. To demonstrate the application of the proposed method, a case study from a Chinese enterprise was conducted. The main results derived from this case study are as follows: domain competencies have the greatest weight among the primary indicators; the C9-BIM model is the secondary indicator with the highest weight (${\mathsf{\omega }}_j$ = 0.0804); and the competency level of the BCE is “Level 3”. These results are consistent with the actual situation of the enterprise. The proposed model in this study provides a comprehensive tool for evaluating BCEs’ competencies from an individual perspective, and offers guideline for BCEs to enhance their competencies in pursuing sustainable professional development.

1. Introduction

With the advancement of informatization in the construction industry, many new tools and technologies have been proposed, including building information modeling (BIM), geographic information systems, mixed reality, artificial intelligence, and so on [1]. These innovative technologies can realize the digital transformation of construction projects and drive the transformation of the construction industry from being traditionally labor-intensive to being technology-intensive, knowledge-intensive, and management-intensive [2]. Meanwhile, the application of these new technologies has revolutionized construction methods, changed the working mode of construction companies, and opened a new era in the development of industries and disciplines [3].

In this range of innovative technologies, BIM stands out as a complete digital framework that integrates all building information throughout the project lifecycle, becoming an emerging technology in the architecture, engineering, construction, and operations (AECO) industry [4,5]. Beyond its fundamental attributes of visualization, coordination, simulation, optimization, and mapping, BIM manifests a host of distinct advantages, including but not limited to its efficacy in expressing project information [6], building collaborative environments [7], sustainable digital delivery [8], integrated energy analysis [9], and green building [10].

The international BIM market was valued at USD 5.4 billion in 2020 and is projected to reach USD 10.7 billion by 2026, growing at a compound annual growth rate (CAGR) of 12.5% from 2020 to 2026 [11]. In pursuit of fostering the widespread adoption and advancement of BIM technology, the Chinese government has introduced a series of policies and industry standards. These initiatives aim not only to encourage the integration of BIM into an increasing array of projects, especially large-scale projects in the infrastructure sector, but also to improve the depth of BIM implementation [12,13]. Over the past decade, BIM in China has transitioned into a stage marked by rapid evolution and profound application. The CAGR of the BIM market size in China reached 31% from 2016 to 2020 [14]. The rapid expansion of the BIM market has triggered a surge in demand for BIM engineers [15]. The report by Ministry of Human Resources and Social Security in 2020 indicated a continuous year-over-year increase in the number of BIM engineers, with the forecasted aggregate demand for them across various enterprises in China set to reach 1.3 million from 2020 to 2025 [16].

BIM engineers are a group of professionals who specialize in BIM technology. These BIM engineers can be categorized into distinct roles based on the stage of project implementation. These roles typically include BIM design engineers, BIM construction engineers (BCEs), and BIM operation and maintenance engineers, among others. BCEs are mainly engaged in the application of BIM technology during the construction stage of engineering projects. The construction stage is a critical stage in the project lifecycle, as it translates the engineering design intent into a tangible engineering entity, ultimately forming engineering value. As pointed out in other research [17], the construction stage has a significant impact on the overall quality and economic efficiency of the whole project.

BCEs emerge as indispensable contributors, playing a vital role in streamlining the construction process, optimizing construction information management, and enhancing project value. They usually use BIM technology for virtual construction, site planning, progress monitoring, cost management, etc. As such, their competencies span BIM-specific skills closely related to BIM technology, which can be obtained from academic courses. In addition, they also include a range of general professional competencies, such as effective communication, coordination with stakeholders, and the competency to work alone; these skills are often obtained from workplace training.

It is worth noting that the current competency evaluation for BCEs largely relies on self-evaluation by enterprises and lacks a standardized framework. This research gap is particularly pronounced within the Chinese context. A false understanding of BCEs’ competency levels may lead to incorrect job assignments and inappropriate performance evaluations, thereby potentially impeding their career development. Consequently, the purpose of this paper is to establish a systematic and rational competency evaluation model to evaluate the competency of BCEs, promote their occupational health, and further improve the application level of BIM.

The rest of this study is structured as follows. Section 2 conducts a literature review. Section 3 presents our research methodology. Section 4 develops an evaluation model based on variable weight theory and interval grey clustering: Firstly, the competency levels of BCEs are identified through a literature review. Secondly, indicators are selected using literature analysis and website data. Finally, the evaluation process is put forward. Section 5 conducts a case study, which demonstrates the application of the model and verifies the reliability of the model, followed by discussions in Section 6 and conclusions in Section 7.

2. Literature Review

2.1. Definition and Development of Competency

After decades of research and development, competency is considered to be increasingly important in human resource (HR) management [18]. Many scholars have pointed out that competency can be used to support the entire HR system within an organization, including recruitment, training, performance management, compensation, and benefits [19,20]. However, the concept of competency, as delineated in the relevant literature, exhibits a conspicuous diversity. It can be said that researchers have almost no consensus on the meaning of the term competency [21]. According to previous research [22,23,24], competency can be construed as a combination of implicit and explicit knowledge, behaviors, and skills which gives someone potential for task performance and can be identified, measured, and developed.

Extensive research has been conducted on individual competencies. Scholars have expanded and categorized competencies into different types. For instance, Kirovska and Qoku [25] remarked that competency can be divided into hard and soft competency, in which hard competency is related to performance and soft competency demonstrates the personal characteristics of the employee [25]. Care and Luo [26] developed the concept of transversal competencies, defining them as “the skills, values, and attitudes required for learners’ overall development and adaptability to change”. In addition, innovative competencies, digital competencies, and leadership competencies have also been further proposed [27,28]. These studies provide an overview of competency and help to identify individual competencies.

Moreover, numerous competency models have been proposed, including the hierarchical model [29], onion model [30], and ladder model [31]. These competency models are very broad, often containing many detailed competencies. However, their applicability to the emerging profession of BCEs is still limited. BCEs need a tailored competency framework that aligns with their continuous career development.

2.2. Research on Competency Elements Related to BCEs

Some scholars have conducted research on BIM competency, providing valuable insights into the competency elements of BCEs. Taiebat and Ku [32] found that in addition to proficiency with BIM software, the competency requirements for graduates in the construction industry include a grasp of BIM concepts. This is authenticated by another research study [33], which also proposed that up-to-date knowledge of BIM development, application skills and knowledge of BIM standards are the highest-rated competencies. Also, work experience, BIM-facilitated green design, and model management knowledge are considered BIM competencies that graduates should possess [34].

At the same time, some scholars have studied the classification of individual BIM competencies. Succar et al. [35] classified individual BIM competencies into three BIM competency tiers: core competencies, domain competencies, and execution competencies. In detail, the core competencies were subdivided into four competency sets: foundational traits, situational enablers, qualification licenses, and historical indicators; the domain competencies included eight competency sets: four primary sets (managerial, functional, technical, and supportive) and four secondary sets (administration, operation, implementation and research, and development). Uhm, Lee, and Jeon [15] identified 43 distinct BIM competency elements through job postings in the UK and China, further classifying them into essential, common, and job-specific competencies based on the Occupational Information Network. Their findings highlighted the importance of competencies such as cooperation, thinking creatively, interacting with computers, and specifying technical devices.

Similarly, Li et al. [36] divided BIM competency requirements into three aspects by mining BIM recruitment information: management competencies, professional and technical competencies, and personal characteristics. Notably, BIM application, construction drawing design, and information technology skills were considered key competencies for BIM recruitment. In addition, Chinese researchers emphasized that BIM engineers must continually enhance their development competencies through practical experience and ongoing learning to keep up with the development of BIM technology [37]. It is worth noting that although different studies categorized individual BIM competencies into various dimensions, they shared striking similarities in their competency items. In most models, common dimensions include those related to personal traits, those related to management and organization, those related to specific jobs, and those related to sustainability. Therefore, based on the above research, we classified the competencies of BCEs into four dimensions: general competencies, planning competencies, domain competencies, and development competencies.

2.3. Competency Evaluation Methods

The evaluation of competency is crucial for both researchers and practitioners. Over time, numerous methods have been devised to ascertain employees’ competencies, aiming for more precise and comprehensive evaluations. Approaches such as 360-degree assessments and graphic rating scales have been used in the past. However, these traditional methods focus more on short-term results and ignore organizations as a whole.

Recognizing these limitations, a range of multiple-criteria decision-making (MCDM) approaches were proposed. Among them, the analytic hierarchy process (AHP) and analytic network process (ANP) are the research methods used to evaluate personnel competency in most studies [38,39], but the results obtained through them are often subjective. The comprehensive evaluation of BCEs’ competency is a complex system that involves multiple indicators, most of which are qualitative. This makes it difficult to conduct quantitative evaluation when the information is uncertain and incomplete. Grey system theory is a method to deal with uncertainty in small data samples with imprecise information [40,41]. As an important part of grey system theory, grey clustering has unique advantages in dealing with “small data, poor information” clustering problems [42]. Traditional grey clustering is generally based on the real number domain, which is not applicable when the sample value is an interval. To solve this problem, an interval grey clustering method has been proposed, which can deal with interval data containing uncertainty or fuzziness [43]. However, the application of this method in the field of personnel competency evaluation is limited. Therefore, exploring the application of the interval grey clustering method in the field of the comprehensive evaluation of BCEs’ competency holds significant theoretical importance.

2.4. Summary

Examining prior research, several shortcomings were identified: (1) The research content is not comprehensive. Some existing research focuses on BIM competencies in the general domain, which does not put enough emphasis on the evaluation of BCEs’ competencies. (2) The limitations of competency evaluation methods still exist. The competency evaluation process frequently relies on qualitative indicators, making quantitative evaluation challenging. Prior studies have not found an appropriate method for rigorously evaluating the competency of BCEs.

Therefore, this study develops a quantitative evaluation model which provides a simple and clear set of competencies framework for BCEs while facilitating the evaluation of their competency level. The findings of this research can provide a scientific basis for the evaluating the competency of BCEs, prompting managers to take appropriate measures to enhance the competency of BCEs and optimize productivity.

3. Research Methodology

3.1. Variable Weight Theory: Calculating Indicator Weight

The scientific determination of indicator weight is directly related to the accuracy and rationality of evaluation. The more commonly used weighting methods include the expert survey method, analytic hierarchy process, entropy method, and so on. Nevertheless, these methods are more qualitative, relying heavily on expert opinions to determine the relative importance of competencies, often resulting in one-sided results due to the subjective preferences of experts.

The continuous ordered weighted average (C-OWA) operator is an effective means to alleviate the impact of subjective expert judgments [44]. The weight calculated by this method is related to the numerical values of each indicator and their corresponding indicator grade coefficients [45]. However, the weight obtained by the C-OWA operator is constant, which may lead to the phenomenon of “state imbalance” [46]. Variable weight theory can solve the impact of the deviation caused by the constant weight [47]. A series of variable weight methods such as penalty variable weight, incentive variable weight, and hybrid variable weight have been proposed [48]. However, both penalty and incentive variable weight exhibit one-sided characteristics, while hybrid variable weight has the same magnitude as the penalty and incentive methods, which is also not very consistent with actual situations. Therefore, the use of local variable weight was advocated, allowing the amplitude of the penalty to be greater than the amplitude of the incentive when there are small values of some important indicators [49].

At this stage, variable weight theory is introduced to process the constant weight obtained by the C-OWA operator, and the comprehensive weight is obtained. The comprehensive weight obtained by this method avoids the limitation of determining the weight value by the constant weight method. The steps are as follows.

3.1.1. The Calculation Method for Indicator Weights Based on the C-OWA Operator

Step 1: Acquire decision data. Experts were invited to rate the importance of each indicator. The initial decision data for an indicator is shown in $A=\left(a_1,a_2,\cdots ,a_n\right)$, where $a_n$ represents the score of the nth expert on this indicator. The rating range was set as [0, 10], and the scoring data were all multiples of 0.5. Then, the initial decision data are arranged in descending order to acquire new decision data: $B=\left(b_0,b_1,b_2,\cdots ,b_{n-1}\right),b_0>b_1>b_2>\cdots >b_{n-1}$.

Step 2: Determine the weighted vector ${\alpha }_{i+1}$ of the decision data B by using Formula (1).

$${\alpha }_{i+1}={\displaystyle \frac{C_{n-1}^i}{{{\displaystyle \sum }}_{k=0}^{n-1}{C}_{n-1}^k}}={\displaystyle \frac{C_{n-1}^i}{2^{n-1}}}$$

(1)

where $i=0,1,2,\cdots ,n-1$, ${{\displaystyle \sum }}_{k=0}^{n-1}{C}_{n-1}^k$, and $C_{n-1}^i$ is the number of combinations of i data from n − 1 data.

Step 3: Calculate the absolute weight ${\overline{\omega }}_j^{\left(0\right)}$ by weighting the decision data B with the weighted vector, as follows.

$${\overline{\omega }}_j^{\left(0\right)}={\displaystyle \sum }_{i=0}^{n-1}{\alpha }_{i+1}{b}_i$$

(2)

where $j\in \left[1,m\right]$ and m in the formula represents the number of indicators.

Step 4: Calculate the relative weight ${\omega }_j^{\left(0\right)}$ of the indicator j by normalization, as shown in Formula (3).

$${\omega }_j^{\left(0\right)}={\displaystyle \frac{{\overline{\omega }}_j^{\left(0\right)}}{{{\displaystyle \sum }}_{j=1}^m{\overline{\omega }}_j^{\left(0\right)}}}$$

(3)

3.1.2. Indicator Weight Optimization Based on Variable Weight Theory

The weights determined by the above method are constant; variable weight theory can dynamically adjust the weights according to the status change in the indicators to more accurately reflect the importance of each indicator in the evaluation process.

Step 1: According to the actual value of each competency indicator, obtain the state vector: $X=\left(x_1,x_2,\cdots ,x_j\right)$. $x_j$ is the average score of the indicator j divided by its value range.

Step 2: Determine the variable weight vector function $S_j(x)$ of the indicator j, as shown in Formula (4).

$$S_j(x)=\left\{\begin{array}{l}{\displaystyle \frac{C_2-C_1}{\lambda -\mu }}\mu ln{\displaystyle \frac{\mu }{x_j}}+C_2,x_j\in \left(0,\mu \right];\\ -{\displaystyle \frac{C_2-C_1}{\lambda -\mu }}{x}_j+{\displaystyle \frac{C_2\lambda -C_1\mu }{\lambda -\mu }},x_j\in \left(\mu ,\lambda \right];\\ C+{\displaystyle \frac{C_2-C_1}{2\left(\lambda -\mu \right)\left(\alpha -\lambda \right)}}{\left(\alpha -x_j\right)}^2,x_j\in \left(\lambda ,\alpha \right];\\ C,x_j\in \left(\alpha ,\beta \right];\\ K\left(1-\beta \right)ln{\displaystyle \frac{1-\beta }{1-x_j}}+C,x_j\in \left(\beta ,1\right);\end{array}\right.$$

(4)

α is the penalty level; β is the incentive level; $C,c_1$, and $c_2$ are the assessment strategies; K is the adjustment factor; and $0<\mu <\lambda <\alpha <\beta <1$, $0<C<1$, and $0<1-\beta <C$. In this research, the value of each parameter was obtained by referring to the literature [50] and then a reasonable vector function $S_j(x)$, as shown in Formula (5).

$$S_j(x)=\left\{\begin{array}{l}{\displaystyle \frac{C_2-C_1}{\lambda -\mu }}\mu ln{\displaystyle \frac{\mu }{x_j}}+C_2,x_j\in \left(0,\mu \right];\\ -{\displaystyle \frac{C_2-C_1}{\lambda -\mu }}{x}_j+{\displaystyle \frac{C_2\lambda -C_1\mu }{\lambda -\mu }},x_j\in \left(\mu ,\lambda \right];\\ C+{\displaystyle \frac{C_2-C_1}{2\left(\lambda -\mu \right)\left(\alpha -\lambda \right)}}{\left(\alpha -x_j\right)}^2,x_j\in \left(\lambda ,\alpha \right];\\ C,x_j\in \left(\alpha ,\beta \right];\\ K\left(1-\beta \right)ln{\displaystyle \frac{1-\beta }{1-x_j}}+C,x_j\in \left(\beta ,1\right);\end{array}\right.$$

(5)

Step 3: Calculate the comprehensive weight ${\omega }_j$ of the indicator j, which can be obtained by Formula (6).

$${\omega }_j={\displaystyle \frac{{\omega }_j^{\left(0\right)}{S}_j(x)}{{{\displaystyle \sum }}_{i=1}^m{\omega }_j^{\left(0\right)}{S}_j(x)}}$$

(6)

where ${\omega }_j$ is the comprehensive weight obtained by the optimization of variable weight theory.

3.2. Interval Grey Clustering Method: Comprehensive Evaluation

On the basis of obtaining the indicators’ weights, the interval grey clustering method is used to comprehensively evaluate the research objects. The interval grey clustering method is a clustering analysis method that represents multiple indicators of the research object as interval grey numbers (that is, the value range of each indicator is an interval). Therefore, the basic theory of interval grey numbers and the implementation steps of the interval grey clustering method are introduced below.

3.2.1. Basic Theory of Interval Grey Numbers

An interval grey number is a type of grey number that has both an upper and lower bound and is denoted as $\otimes \in \left[{\otimes }^{-},{\otimes }^{+}\right]$. Interval grey number operations have been of great interest to scholars. In the absence of the value distribution information of an interval grey number, $\widehat{\otimes }=\left({\otimes }^{-}+{\otimes }^{+}\right)/2$ is said to be the kernel of $\otimes$ and $g^0\left(\otimes \right)=\mu \left(\otimes \right)/\mu \left(\Omega \right)$ is defined as the degree of greyness of $\otimes$ [51]. $\mu \left(\otimes \right)={\otimes }^{+}-{\otimes }^{-}$ is the measurement of the range of $\otimes$, and Ω is the domain of the values. ${\widehat{\otimes }}_{({\mathrm{g}}^0)}$ is referred to as the simplified form of the interval grey number. For example, considering that $\otimes =\left[89,95\right]$ is the interval grey number defined on the domain of discourse [0, 100], then $\mu \left(\otimes \right)=95-89=6$, $\mu \left(\Omega \right)=100-0=100$, $\widehat{\otimes }=\left(89+95\right)/2=92$, $g^0\left(\otimes \right)=6/100=0.06$, and ${\widehat{\otimes }}_{({\mathrm{g}}^0)}={96}_{(0.06)}$.

According to the interval grey number ranking method [43] (Dang, Yu, Song, and Long, 2017), it is assumed that $\otimes$ is the standard interval grey number, $\gamma \left(\otimes \right)=1/\left(1+g^0\left(\otimes \right)\right)$ is the precision of $\otimes$, and $\delta \left(\otimes \right)=\gamma \left(\otimes \right)\times \widehat{\otimes }$ is the relative kernel of $\otimes$. Assuming the two standard grey numbers ${\otimes }_1$ and ${\otimes }_2$, respectively, if $\delta ({\otimes }_1)\ne \delta ({\otimes }_2)$, when $\delta \left({\otimes }_1\right)>\delta \left({\otimes }_2\right)$, then ${\otimes }_1>{\otimes }_2$; when $\delta \left({\otimes }_1\right)<\delta \left({\otimes }_2\right)$, then ${\otimes }_1<{\otimes }_2$. If $\delta \left({\otimes }_1\right)=\delta \left({\otimes }_2\right)$, when $\gamma \left({\otimes }_1\right)>\gamma \left({\otimes }_2\right)$, then ${\otimes }_1>{\otimes }_2$; when $\gamma \left({\otimes }_1\right)<\gamma \left({\otimes }_2\right)$, then ${\otimes }_1<{\otimes }_2$; and when $\gamma \left({\otimes }_1\right)=\gamma \left({\otimes }_2\right)$, then ${\otimes }_1={\otimes }_2$.

Research [52] has proposed the operation of interval grey numbers based on kernel and degree of greyness. Assume there are two interval grey numbers ${\otimes }_1\in \left[{{\otimes }_1}^{-},{{\otimes }_1}^{+}\right]$ and ${\otimes }_2\in \left[{{\otimes }_2}^{-},{{\otimes }_2}^{+}\right]$, which are simply recorded as ${\widehat{\otimes }}_{1_{(g_1^o)}}$ and ${\widehat{\otimes }}_{2_{(g_2^o)}}$, then the algorithms of the interval grey numbers are ${\widehat{\otimes }}_{1_{(g_1^o)}}+{\widehat{\otimes }}_{2_{(g_2^o)}}={({\widehat{\otimes }}_1+{\widehat{\otimes }}_2)}_{(g_1^o\vee g_2^o)}$; ${\widehat{\otimes }}_{1_{(g_1^o)}}-{\widehat{\otimes }}_{2_{(g_2^o)}}={({\widehat{\otimes }}_1-{\widehat{\otimes }}_2)}_{(g_1^o\vee g_2^o)}$; ${\widehat{\otimes }}_{1_{(g_1^o)}}\times {\widehat{\otimes }}_{2_{(g_2^o)}}={({\widehat{\otimes }}_1\times {\widehat{\otimes }}_2)}_{(g_1^o\vee g_2^o)}$; ${\widehat{\otimes }}_{1_{(g_1^o)}}/{\widehat{\otimes }}_{2_{(g_2^o)}}={({\widehat{\otimes }}_1/{\widehat{\otimes }}_2)}_{(g_1^o\vee g_2^o)}$; and $k\cdot {\widehat{\otimes }}_{1_{(g_1^o)}}={(k\cdot {\widehat{\otimes }}_1)}_{(g_1^o)}$ (supposing k is a real number).

3.2.2. Interval Grey Clustering Powered by Interval Grey Numbers

The specific steps for comprehensive evaluation using interval grey clustering are as follows:

Step 1: Construct the interval grey number whitening weight function. The grey classes are classified according to the evaluation object. Then, the interval grey number whitening weight function of indicator j on the kth grey class is denoted as $f_j^k\left(\cdot \right)$. $f_j^k\left[-,-,{\otimes }_j^k\left(3\right),{\otimes }_j^k\left(4\right)\right]$, $f_j^k\left[{\otimes }_j^k\left(1\right),{\otimes }_j^k\left(2\right),-,{\otimes }_j^k\left(4\right)\right]$, and $f_j^k\left[{\otimes }_j^k\left(1\right),{\otimes }_j^k\left(2\right),-,-\right]$ are the lower limit interval grey number whitening weight function, the moderate interval grey number whitening weight function, and the upper limit interval grey number whitening weight function, respectively. ${\otimes }_j^k\left(1\right),$ ${\otimes }_j^k\left(2\right),$ ${\otimes }_j^k\left(3\right),$ and ${\otimes }_j^k\left(4\right)$ are, respectively, the first, second, third, and fourth turning points of $f_j^k\left(\cdot \right)$, where ${\otimes }_j^k\left(l\right)\in \left[{\otimes }_j^k{\left(l\right)}^{-},{\otimes }_j^k{\left(l\right)}^{+}\right],l\in \left\{1,2,3,4\right\}$. The function image is shown in Figure 1.

Step 2: Determine the whitening weight values. The whitening weight values are calculated according to the interval grey number whitening weight function determined in step 1. Considering the interval grey number ${\otimes }_j$ of indicator j, ${\otimes }_j={\widehat{\otimes }}_{j_{(g_1^o)}}$, $g_j^o=\mu \left({\otimes }_j\right)/\mu \left({\Omega }_j\right)$, ${\otimes }_j^k(l)={\widehat{\otimes }}_j^k{(l)}_{({g^0}_j^k(l))}$, and ${g^o}_j^k(l)=\mu \left({\otimes }_j^k(l)\right)/\mu \left({\Omega }_j\right)$. The calculation formula of the whitening weight values for the indicator j on the kth grey class can be represented as follows [43].

The lower limit interval grey number whitening weight function:

$$f_j^k\left({\otimes }_j\right)=\left\{\begin{array}{l}0,{\otimes }_j^{+}\le 0\mathrm{or}{\otimes }_j^{-}\ge {\otimes }_j^k{\left(4\right)}^{+};\\ 1_{\left(g_j^0\right)},{\widehat{\otimes }}_j\in \left[0,{\widehat{\otimes }}_j^k{\left(3\right)}^{-}\right]\mathrm{and}{\otimes }_j^{-}<0;\\ 1,0\le {\otimes }_j^{-}<{\otimes }_j^{+}\le {\otimes }_j^k{\left(3\right)}^{-};\\ ({\displaystyle \frac{{\widehat{\otimes }}_j^k\left(4\right)-{\widehat{\otimes }}_j}{{\widehat{\otimes }}_j^k\left(4\right)-{\widehat{\otimes }}_j^k\left(3\right)}}{)}_{\left(g_j^0\vee {g^o}_j^k\left(3\right)\vee {g^o}_j^k\left(4\right)\right)},{\widehat{\otimes }}_j\in \left[{\widehat{\otimes }}_j^k\left(3\right),{\widehat{\otimes }}_j^k\left(4\right)\right];\\ 0_{(g_j^0\vee {g^o}_j^k\left(4\right))},{\widehat{\otimes }}_j>{\widehat{\otimes }}_j^k\left(4\right)\mathrm{and}{\otimes }_j^{-}<{\otimes }_j^k{\left(4\right)}^{+};\end{array}\right.$$

(7)

The moderate interval grey number whitening weight function:

$$f_j^k\left({\otimes }_j\right)=\left\{\begin{array}{l}0,{\otimes }_j^{+}\le {\otimes }_j^k{\left(1\right)}^{-}\mathrm{or}{\otimes }_j^{-}\ge {\otimes }_j^k{\left(4\right)}^{+};\\ 0_{\left(g_j^0\vee {g^o}_j^k\left(1\right)\right)},{\widehat{\otimes }}_j\notin \left[{\widehat{\otimes }}_j^k\left(1\right),{\widehat{\otimes }}_j^k\left(4\right)\right]\mathrm{and}{\otimes }_j^{+}>{\otimes }_j^k{\left(1\right)}^{-};\\ ({\displaystyle \frac{{\widehat{\otimes }}_j-{\widehat{\otimes }}_j^k\left(1\right)}{{\widehat{\otimes }}_j^k\left(2\right)-{\widehat{\otimes }}_j^k\left(1\right)}}{)}_{(g_j^0\vee {g^o}_j^k\left(1\right))\vee {g^o}_j^k\left(2\right))},{\widehat{\otimes }}_j\in \left[{\widehat{\otimes }}_j^k\left(1\right),{\widehat{\otimes }}_j^k\left(2\right)\right];\\ ({\displaystyle \frac{{\widehat{\otimes }}_j^k\left(4\right)-{\widehat{\otimes }}_j}{{\widehat{\otimes }}_j^k\left(4\right)-{\widehat{\otimes }}_j^k\left(2\right)}}{)}_{(g_j^0\vee {g^o}_j^k\left(2\right))\vee {g^o}_j^k\left(4\right)},{\widehat{\otimes }}_j\in \left[{\widehat{\otimes }}_j^k\left(2\right),{\widehat{\otimes }}_j^k\left(4\right)\right];\\ 0_{(g_j^0\vee {g^o}_j^k\left(4\right))},{\widehat{\otimes }}_j\notin \left[{\widehat{\otimes }}_j^k\left(1\right),{\widehat{\otimes }}_j^k\left(4\right)\right]\mathrm{and}{\otimes }_j^{-}<{\otimes }_j^k{\left(4\right)}^{+};\end{array}\right.$$

(8)

The upper limit interval grey number whitening weight function:

$$f_j^k\left({\otimes }_j\right)=\left\{\begin{array}{l}0,{\otimes }_j^{+}\le {\otimes }_j^k{\left(1\right)}^{-};\\ 0_{\left(g_j^0\vee {g^0}_j^k\left(1\right)\right)},{\widehat{\otimes }}_j<{\widehat{\otimes }}_j^k\left(1\right)\mathrm{and}{\widehat{\otimes }}_j^{+}>{\widehat{\otimes }}_j^k{\left(1\right)}^{-};\\ ({\displaystyle \frac{{\widehat{\otimes }}_j-{\widehat{\otimes }}_j^k\left(1\right)}{{\widehat{\otimes }}_j^k\left(2\right)-{\widehat{\otimes }}_j^k\left(1\right)}}{)}_{(g_j^0\vee {g^o}_j^k\left(1\right))\vee {g^o}_j^k\left(2\right))},{\widehat{\otimes }}_j\in \left[{\widehat{\otimes }}_j^k\left(1\right),{\widehat{\otimes }}_j^k\left(2\right)\right];\\ 1_{(g_j^0\vee {g^o}_j^k\left(2\right))},{\widehat{\otimes }}_j>{\widehat{\otimes }}_j^k\left(2\right)\mathrm{and}{\otimes }_j^{-}<{\otimes }_j^k{\left(2\right)}^{+};\\ 1,{\otimes }_j^{-}>{\otimes }_j^k{\left(2\right)}^{+};\end{array}\right.$$

(9)

Step 3: Calculate the comprehensive clustering coefficient. The comprehensive clustering coefficient ${\sigma }^k$ of grey class k is calculated by the following formula.

$${\sigma }^k={\displaystyle \sum }_{j=1}^m{f}_j^k\left({\otimes }_j\right)\cdot {\omega }_j$$

(10)

where $f_j^k\left({\otimes }_j\right)$ represents the whitening weight values and ${\omega }_j$ represents the comprehensive weight of indicator j.

Step 4: Determine the grey class. According to the principle of maximum affiliation, the grey class of the research object is determined by the following formula.

$${\sigma }^{k^{*}}=max\left\{{\sigma }^k\right\}$$

(11)

Then the evaluated object can be said to belong to the grey class $k^{*}$.

4. Proposed Competency Evaluation Model of BCEs

The proposed evaluation model is an approach to evaluating the competency of BCEs. Assessments using this approach can enable organizers to understand the current competency levels of BCEs. The evaluation results can promote the development of BCEs and the efficient execution of projects. The evaluation model has a framework which defines three parts: the competency level, indicator system, and evaluation process.

4.1. Division of BCE Competency Levels and the the Grey Class

4.1.1. The Competency Levels of BECs

Accurately and visually representing the competency levels of BCEs is of paramount importance. However, the lack of standardized criteria for classifying these levels poses a challenge. Existing government documents provide some initial guidance on the classification of competency levels, suggesting division into either three or five levels [53,54]. Additionally, internationally recognized models, namely BIM project planning [55] and the BIM maturity matrix [56], have been devised to assess BIM application capability at both project and organizational levels, respectively, advocating for a five-level classification system.

Consider that a five-stage division has been frequently proposed and tested in areas related to BIM capabilities. Therefore, we developed a structure of five competency levels (ranging from level 1 to level 5). At the same time, given that BCEs often possess both information technology and engineering backgrounds, the competency levels in this paper draw inspiration from evaluation standards for information personnel and project management personnel [57,58]. The classification standards for BCEs’ competency levels are presented in

Table 1. Competency level division standards for BCEs.

Levels	Standards for the Classification of Competency Level
Level 5	They have extensive knowledge, developing skills, comprehensive experience, can integrate BIM interdisciplinary knowledge and organize technical innovation activities, and have sufficient management ability.
Level 4	They have significant knowledge, high-level skills, and effective experience, with a systematic knowledge of BIM, independent and innovative thinking, and a certain level of management ability.
Level 3	They have solid knowledge and some practical applications and successful cases, and have further expanded their BIM knowledge, completed some unconventional work, and met some technical challenges.
Level 2	They have limited knowledge and work experience; their understanding of BIM is often confined to limited concepts and operations, and they can complete technically complex work under specific circumstances.
Level 1	They have basic knowledge and are able to use basic skills for simple technical operations, as well as complete the tasks they undertake under the guidance of others.

, which will be an important reference standard for evaluating the competency of BCEs.

4.1.2. The Grey Class

According to Table 1 and experts’ opinions, the grey class was also divided into five levels and the range of values was set as [0, 100]. The specific quantitative values are detailed in

Table 2. Classification of grey classes and range of values.

Level 1	Level 2	Level 3	Level 4	Level 5
(0, 30]	(30, 50]	(50, 70]	(70, 90]	(90, 100]

, in which the five levels correspond to those in Table 1.

4.2. Indicator System Establishment

4.2.1. Determine an Initial Competency Indicator List Based on Literature Data

The evaluation of BCEs’ competency is multifaceted, influenced by an array of diverse indicators. Through a systematic review and synthesis of the relevant literature, mainly including the relevant theoretical literature sourced from Web of Science and China National Knowledge Infrastructure (CNKI), as well as some BIM policies issued by the Chinese government, a total of 10 studies were identified that were highly relevant to BCEs’ competency indicators, including 6 English journal studies, 2 Chinese journal studies, and 2 published BIM-related standards. Through the careful reading of the above literature, a series of secondary indicators were identified. An initial list of secondary indicators for BCE competency evaluation was identified from the literature data. The sources of these indicators are shown in

Table 3. Initial list of secondary indicators for BCEs’ competency evaluation.

Secondary Indicators	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]
Project experience	√	√				√
BIM environment	√	√	√	√	√	√	√	√	√	√
Technical standard	√	√				√		√	√	√
Coordination	√	√	√	√		√		√	√	√
Schedule		√	√			√	√	√	√	√
Deliverable		√	√	√		√	√	√	√	√
Cost management	√	√	√				√	√	√	√
Risk analysis					√			√	√	√
BIM model	√	√	√	√	√	√	√	√	√	√
Key point analysis	√			√					√	√
Strategic planning	√		√						√
BIM theories	√			√				√	√	√
Certification	√					√	√	√	√	√
Team management	√		√	√		√	√		√	√
Simulation	√	√	√		√				√	√
Innovation			√			√		√	√	√
Training and teaching	√	√				√	√	√		√
Technical route		√					√		√	√
Interface integration	√		√	√
Space planning									√	√

Note: [1]—(Succar, Sher, and Williams, 2013) [35]; [2]—(Uhm, Lee, and Jeon, 2017) [15]; [3]—(Kassem, Abd Raoff, and Ouahrani, 2018) [24]; [4]—(Davies et al., 2017) [59]; [5]—(Barison and Santos, 2010) [60]; [6]—(Yakami, Singh, and Suwal, 2017) [33]; [7]—(Dai and Long, 2018) [61]; [8]—(Li and Li, 2019) [37]; [9]—(MIIT, 2018) [53]; [10]—(MOHRSS, 2021) [54].

.

4.2.2. Construction of Competency Evaluation Indicator System Based on Website Data

This stage aims to offer a BCE competency dataset extracted from the real-world job market by mining recruitment website data. The dataset was analyzed to validate and supplement the initial list of secondary indicators obtained from the literature data. Due to data from recruitment sites often being presented in text form, it was necessary to adopt an analysis technology suitable for unstructured data to systematically process the data. Notably, NVivo is a multifunctional platform that can collate and in-depth analyze unstructured or qualitative data [62].

“BIM engineers” and “BIM construction engineers” were used as keywords to search related recruitment advertisements on major recruitment websites (mainly including “http://www.bimw.cn/”, “http://www.buildhr.com/”, and “https://jobs.51job.com/”). The Capture plugin was used to crawl the recruitment advertisement webpages and export them as PDF files. Then, Nvivo11 software was used to browse through 40 captured PDF files, manually code them sentence-by-sentence, and select keywords and phrases to form child nodes. The prefixes of the child nodes were denoted as $Kmn$, which represents the $nth$ child node extracted from the $mth$ PDF file, as shown in

Table 4. Sample extraction of tree nodes in PDF file.

PDF File Content Excerpt	Extracted Child Node
Able to use various BIM technology software proficiently to create, apply and manage 3D digital models …… Understand the knowledge and skills of BIM-related management, technology, and regulations, with a high level of comprehensive quality, both theoretical level and fundamentals of Modeling ……	K11—BIM software; K12—3D digital models; K13—Knowledge and skills; K14—Theoretical level; K15—Fundamentals of Modeling ……
Knowledge of at least Revit software …… Relevant experience in the field with knowledge of civil engineering, MEP, and HVAC ……	K21—Revit software; K22-Relevant experience ……
……	……

. For example, “K14-Theoretical level” indicates the fourth child node extracted from the first PDF file. Finally, 357 child nodes were created.

Since many child nodes had similar or the same meanings, they needed to be merged or summarized into tree nodes. A tree node is a secondary indicator. For example, the child nodes “K11—BIM software” and “K21—Revit software” can be categorized as the tree node “BIM software”. Ultimately, the 357 child nodes were further summarized into 32 tree nodes. From reference [63], we took tree nodes that included more than 1% (>3) of the total number of child nodes to have reference value; a total of 27 tree nodes were screened out, and these tree nodes constitute the secondary indicators.

4.2.3. Establishment of Final Competency Evaluation Indicator System for BCEs

The literature data better reflects the research status of the competency of BCEs, providing a theoretical basis, while the website data reflects the actual demands of construction companies on the competency of BCEs, providing a practical basis for the construction of the index system.

A theoretical and practical approach was used to aggregate data from multiple sources. The practical and theoretical significance of the indicators was ensured through the cross-corroboration and supplementation of the website data and literature data. Based on this, the expert interview method was used to obtain the final index content. Compared with Table 3, seven secondary indicators were added, including “Professional basic”, “Education background”, “Professional ethics”, “Family library”, “Work independently”, “Safety assurance”, and “Interface integration”, and eventually, the BCE’ competency measurement index system was established.

According to the definition of the primary indicators in Table 3, 27 secondary indicators were classified. The competency evaluation indicator system was constructed as shown in

Table 5. BCEs’ competency evaluation indicator system.

Primary Indicators	Secondary Indicators	Indicator Interpretation and Explanation
General competencies A	Education background A1	Relevant educational background (civil, HVAC, computer, etc.)
	Work independently A2	Complete tasks without guidance of superior
	BIM theories A3	Theories, frontiers, and policy specifications of BIM
	Coordination A4	Communication and collaboration with project participants
	Professional ethics A5	Code of conduct that BCEs should follow at work
	Professional basic A6	Basic knowledge of construction engineering industry
Planning competencies B	Strategic planning B1	Difficulties, keys, and objectives of BIM implementation
	Technical standard B2	Integrity of BIM standards
	Team management B3	Arrange and manage team BIM positions and responsibilities
	Technical route B4	BIM technology roadmap for construction phase
	BIM environment B5	BIM software selection and environment configuration
	Key point analysis B6	Key difficulties and innovation points of BIM application
	Interface integration B7	Interface integration of various types of work
Domain competencies C	Family library C1	Ability to build and manage family libraries
	Space planning C2	Effectiveness of configuration (equipment, manpower, etc.)
	Schedule C3	Integration of BIM models and construction schedules
	Risk analysis C4	Identification and assessment of risks
	Safety assurance C5	Implement safety plan with BIM technology to ensure site safety
	Cost management C6	Application of cost calculation based on BIM
	Simulation C7	Energy consumption, acoustics, optics, and thermal simulate
	Deliverable C8	Quality of delivery of models, drawings, reports, etc.
	BIM model C9	Level of reading, building, and modifying of BIM models
Development competencies D	Integration extension D1	Degree of integration of BIM and information technology
	Project experience D2	Level of experience in using BIM to complete projects
	Training and teaching D3	Number of BIM academic exchanges and amount of technical training
	Innovation D4	Level of competency in scientific innovation
	Certification D5	Acquisition of BIM-related qualifications

.

4.3. Evaluation Process

The evaluation process can be divided into three stages.

Phase I—In this phase, the indicator system was explained to the experts. The expert team was invited to score the evaluation indicators twice according to the importance of the indicators and the actual situation of the evaluation objects.

Phase II—In the second stage, according to the results of the first scoring by experts in the first stage, the constant weight of the indicators was calculated using the general method. Then, variable weight theory is used to optimize the constant weight, and the comprehensive weights of the indicators are finally calculated by using the results of the second score according to the actual situation of the evaluation objects.

Phase III—Last, based on the comprehensive weights determined in the second phase, the interval grey clustering method is used to evaluate BCEs and determine the competency levels of BCEs.

5. Case Study

5.1. Case Background

This paper took the BCEs of Z construction company in China as its research objects. Z construction company is located in Changsha, China. It was founded in the 1960s, and has many years of experience in construction engineering, municipal engineering, bridge engineering, and tunneling engineering. Recognizing the importance of BIM technology, the company has provided BIM technology training courses since 2012 to reserve technical talents for the pilot application of BIM technology. In recent years, it has continuously promoted the development of BIM technology in terms of coverage, application depth, and standard construction. At present, the company has established a sufficiently mature and professional BIM team, which has won multiple BIM awards, and can integrate BIM technology into the whole lifecycles of projects. Although the company has initially proposed BIM application competency evaluation at the organizational level, there is no specific competency evaluation for BCEs. Therefore, it is representative and of great significance to select BCEs from Z company to conduct capability evaluation research.

5.2. Determination of Indicator Weights

5.2.1. Scoring of Indicators Based on Expert Scoring Method

In the initial phase of this study, six experts were invited to score the importance of the 27 indicators. These experts had extensive experience in project management and BIM applications. They came from related enterprises such as design institutions, civil engineering companies, civil engineering consulting companies, and research institutions, ensuring the rationality of the knowledge structure and the universality of the results. All experts had more than 6 years of work experience.

Table 6. Composition of experts.

Experts	Position	Working Years	Additional Information
Expert A	Professor	12	One of the earliest scholars to study BIM technology.
Expert B	Associate Professor	8	Organized several topics related to BIM teaching.
Expert C	Associate Professor	7	Established a mature BIM team and participated in a number of BIM competitions.
Expert D	Senior Engineer	15	Conducted project-level BIM maturity research.
Expert E	Senior Engineer	14	Participated in the formulation of BIM application standards.
Expert F	Senior Management	6	Rich experience in BIM team management.

shows the basic information of the six experts.

The rating range was set as [0, 10], and the scoring data were all multiples of 0.5. The higher the score, the higher the importance of the indicator. Subsequently, this study calculated the absolute weigh ${\overline{\omega }}_j^{\left(0\right)}$ of each indicator using the first scoring data, as outlined in Formulas (1) and (2). On this basis, the relative weight ${\omega }_j^{\left(0\right)}$ was obtained utilizing Formula (3).

Furthermore, the above-mentioned experts were also requested to perform a second round of scoring according to the evaluation indicators, considering the actual situation of the BCEs. The second round of scoring data was represented by an interval grey number of [0, 100]. The averages of the indicator scores given by the experts during the second rating were used as the indicator scores. The local variable weight vector function $S_j(x)$ was calculated based on the second round of scoring data and Formula (5). Subsequently, this study calculated the comprehensive weight ${\omega }_j$ using Formula (6). The comprehensive weights of the four primary indicators were obtained by adding the corresponding secondary indicators, respectively.

5.2.2. Weight Calculation Process

In the initial phase of this study, experts were invited to rate the importance of the 27 indicators. Taking indicator A1 as an example, ranking the score data of the expert group, we can get $B=\left(7,6.5,5,5,5,4.5\right)$. Based on Formula (1), ${\alpha }_1=(0.0313,0.1563,0.3125,0.3125,0.1563,0.0313)$. Based on Formula (2), ${\overline{\omega }}_1^{\left(0\right)}=(0.0313,0.1563,0.3125,0.3125,0.1563,0.0313)\cdot {\left(7,6.5,5,5,5,4.5\right)}^T=5.2813$. In the same way, the absolute weights of the other indicators could be calculated. Then, based on Formula (3), the relative weight ${\omega }_j^{\left(0\right)}$ was calculated.

In addition, the above experts were invited to conduct a second round of scoring according to the actual situation of the evaluation objects. In consideration of the fact that one of the experts was the leader of the BCE being evaluated in this case, in order to minimize the influence of subjectivity, he did not participate in this round of scoring. Similarly, taking indicator A1 as an example, the five experts rated the data as $\left[[64,66],[50,52],[60,63],[58,60],[65,68]\right]$. According to the operation law of interval grey numbers, $x_j={\displaystyle \raisebox{1ex}{$[(64+50+60+58+65)/5+(66+52+63+60+68)/5]/2$}\!\left/ \!\raisebox{-1ex}{$100$}\right.}=0.606$. Based on Formulas (4)–(6), the variable weight vector function $S_j(x)$ and comprehensive weight ${\omega }_j$ were calculated. The results are shown in

Table 7. Competency evaluation indicator weights of BCEs.

Primary Indicators	Primary Indicators Weights	Secondary Indicators	First Scoring	${\overline{\mathsf{\omega }}}_{\mathit{j}}^{\left(0\right)}$	${\mathsf{\omega }}_{\mathit{j}}^{\left(0\right)}$	${\mathit{S}}_{\mathit{j}}\left(\mathit{x}\right)$	${\mathsf{\omega }}_{\mathit{j}}$
A	0.1662	A1	5.5	5.2813	0.0244	0.3255	0.0284
		A2	6.9	6.9844	0.0323	0.2077	0.0239
		A3	7.4	7.4844	0.0346	0.2065	0.0255
		A4	8.9	8.9844	0.0416	0.2032	0.0301
		A5	7.3	7.5469	0.0349	0.2264	0.0282
		A6	6.7	6.6719	0.0309	0.2730	0.0301
B	0.3043	B1	8.3	8.3281	0.0385	0.2730	0.0375
		B2	9.3	9.4688	0.0438	0.2853	0.0446
		B3	8.4	8.4844	0.0393	0.2426	0.0340
		B4	7.7	7.7344	0.0358	0.2354	0.0300
		B5	8.1	8.0156	0.0371	0.4484	0.0593
		B6	8.4	8.4219	0.0390	0.5140	0.0714
		B7	8.3	8.3281	0.0385	0.2000	0.0275
C	0.3169	C1	9.2	9.2344	0.0427	0.2426	0.0370
		C2	7.4	7.4219	0.0344	0.2464	0.0302
		C3	7.5	7.5000	0.0347	0.2000	0.0248
		C4	7.3	7.2500	0.0336	0.2000	0.0239
		C5	7.2	7.0938	0.0328	0.2000	0.0234
		C6	7.3	7.2656	0.0336	0.2061	0.0247
		C7	7.6	7.5156	0.0348	0.3470	0.0430
		C8	9.1	8.9375	0.0414	0.2000	0.0295
		C9	9.4	9.4844	0.0439	0.5140	0.0804
D	0.2126	D1	9.1	9.0156	0.0417	0.3347	0.0498
		D2	8.3	8.4688	0.0392	0.2449	0.0342
		D3	8.5	8.3594	0.0387	0.2004	0.0276
		D4	9.3	9.2500	0.0428	0.4484	0.0684
		D5	7.6	7.5156	0.0348	0.2617	0.0325

.

5.3. Calculation of Competency Level

According to the division of BCEs’ competency levels in Table 1, the grey class was divided into five classes. The interval grey number whitening weight function for each grey class was determined by detailed Delphi investigations, which were as follows.$f^1\left[-,-,[34,36],[52,54]\right],$ $f^2\left[[34,36],[52,54],-,[66,68]\right],$ $f^3\left[[52,54],[66,68],-,[78,81]\right],$ $f^4\left[[66,68],[78,81],-,[92,95]\right],$ and $f^5\left[[78,81],[92,95],-,-\right]$. Similarly, we took the average of the indicator values given by the experts during the second rating as the indicator score. The whitening weight values of each indicator for the different grey classes were calculated according to Formulas (7)–(9), as shown in

Table 8. Whitening weight values for indicator system.

Secondary Indicators	Second Scoring	${\mathit{f}}_{\mathit{j}}^1$	${\mathit{f}}_{\mathit{j}}^2$	${\mathit{f}}_{\mathit{j}}^3$	${\mathit{f}}_{\mathit{j}}^4$	${\mathit{f}}_{\mathit{j}}^5$
A1	60.6(0.03)	0	0.4571(0.03)	0.5429(0.03)	0	0
A2	75.2(0.04)	0	0	0.3440(0.04)	0.6560(0.04)	0
A3	75.6(0.06)	0	0	0.3120(0.06)	0.6880(0.06)	0
A4	76.9(0.05)	0	0	0.2080(0.05)	0.7920(0.05)	0
A5	71.1(0.05)	0	0	0.6720(0.05)	0.3280(0.05)	0
A6	65.2(0.06)	0	0.1286(0.06)	0.8714(0.06)	0	0
B1	65.2(0.03)	0	0.1286(0.03)	0.8714(0.03)	0	0
B2	63.4(0.04)	0	0.2571(0.04)	0.7429(0.04)	0	0
B3	68.7(0.04)	0	0	0.8640(0.04)	0.1360(0.04)	0
B4	92.1(0.04)	0	0	0	0.1000(0.04)	0.9000(0.04)
B5	52.7(0.03)	0.0167(0.03)	0.9833(0.03)	0(0.03)	0	0
B6	48.5(0.05)	0.2500(0.05)	0.7500(0.05)	0	0	0
B7	82.4(0.04)	0	0	0	0.7929(0.04)	0.2071(0.05)
C1	68.7(0.05)	0	0	0.8640(0.05)	0.1360(0.05)	0
C2	68.2(0.06)	0	0	0.9040(0.06)	0.0960(0.06)	0
C3	82.3(0.05)	0	0	0	0.8000(0.05)	0.2000(0.05)
C4	85.2(0.03)	0	0	0	0.5929(0.03)	0.4071(0.03)
C5	80.5(0.03)	0	0	0(0.03)	0.9286(0.03)	0.0714(0.03)
C6	90.4(0.04)	0	0	0	0.2214(0.04)	0.7786(0.04)
C7	59.0(0.04)	0	0.5714(0.04)	0.4286(0.04)	0	0
C8	79.9(0.05)	0	0	0(0.05)	0.9714(0.05)	0.0286(0.05)
C9	49.3(0.06)	0.2056(0.06)	0.7944(0.06)	0	0	0
D1	59.9(0.04)	0	0.5071(0.04)	0.4929(0.04)	0	0
D2	68.4(0.05)	0	0	0.8880(0.05)	0.1120(0.05)	0
D3	78.9(0.06)	0	0	0.0480(0.06)	0.9520(0.06)	0(0.06)
D4	52.7(0.05)	0.0167(0.05)	0.9833(0.05)	0(0.05)	0	0
D5	66.4(0.06)	0	0.0429(0.06)	0.9571(0.05)	0	0

.

The comprehensive clustering coefficients were calculated based on Formula (10). Then, the following results were obtained with the interval grey number ranking method. ${\sigma }^1={0.0365}_{\left(0.06\right)},$ ${\sigma }^2=0.3275_{\left(0.06\right)},{\sigma }^3=0.3431_{\left(0.06\right)},{\sigma }^4=0.2237_{\left(0.06\right)},{\sigma }^5=0.0692_{\left(0.06\right)}$, and ${\sigma }^3>{\sigma }^2>{\sigma }^4>{\sigma }^5>{\sigma }^1$. According to Formula (11), the competency level of the BCEs was “Level 3”.

6. Results and Discussion

6.1. Main Findings of the Case Study

(1) Weight analysis of primary indicators:

According to the weights of the primary indicators in Table 7, the importance of each competency primary indicator is shown in Figure 2. As shown in Figure 3, domain competencies have the greatest weight among the primary indicators, followed by planning and development competencies, and finally general competencies. The dynamic management of the construction phase of a construction project mainly includes cost management, schedule management, safety management, etc. [64,65]. In order to ensure the smooth progress of project quality, schedule, and resource allocation, it is necessary to apply BIM technology to achieve data integration and model management of engineering projects. Therefore, the domain competencies are a key dimension. It is an important link for BIM technology to move from design to application, and it is also the key to realizing the application value of BIM technology.

(2) Weight analysis of secondary indicators:

The weight composition of the secondary indicators under each primary indicator according to Table 8 is shown in Figure 3.

Under general competencies, the indicators are sorted according to the weight, obtaining the following relation: A4 = A6 > A1 > A5 > A3 > A2. Among them, A4—Coordination and A6—Professional basic have the highest weights (${\mathsf{\omega }}_j$ = 0.0301). Engineering projects are prone to communication problems in the process of the coordination of various disciplines and handover of various departments. Each BCE needs to use BIM technology to complete communication between various departments in an orderly manner and improve construction efficiency. Some previous studies have also verified this point. Yakami, Singh, and Suwal [33] found that collaboration and coordination are considered to be two of the most important competencies required by BIM personnel and BIM teams. Rahman [66] also believed that communication and collaboration are essential elements in the process of using various BIM tools in practice. In addition, in the recruitment stage, the professional basic qualification directly reflects the extent to which a BCE has certain professional knowledge, theories, and skills. BCEs with a professional basic qualification have the basic cognition to ensure that a process is executed correctly [28].

Under planning competencies, the order of indicator weights is B6 > B5 > B2 > B1 > B3 > B4 > B7. B6—Key point analysis has the highest weight (${\mathsf{\omega }}_j$ = 0.0714). The analysis of key points and difficulties is of great significance to the application of BIM in projects. According to the characteristics of the project and the needs of the owner, BCEs need to identify, sort out, and analyze the key points and difficulties. Furthermore, corresponding countermeasures and solutions are formulated according to the major and difficult points to ensure the smooth implementation of the project through BIM technology.

Under domain competencies, the order of indicator weights is C9 > C7 > C1 > C2 > C8 > C3 > C6 > C4 > C5. C9—BIM model has the highest weight (${\mathsf{\omega }}_j$ = 0.0804). The BIM model is the foundation for information extraction, processing, and application, and is also a key criterion for the performance of BIM competency. Nguyen [67] proposed that using BIM software to operate models is a necessary competency. C7—Simulation ranks second (${\mathsf{\omega }}_j$ = 0.0430). Simulation analysis is considered to be a hot application in current BIM practice, especially energy simulation, thermal simulation, and lighting simulation. C1—Family library is the third indicator among the domain competencies (${\mathsf{\omega }}_j$ = 0.0370). A family library is the unit that makes up a project in the BIM series of software, and it also serves as a carrier of parameter information. It is a group of elements that contains a common attribute set and related graphical representations. The BIM family library can be said to be an intangible source of knowledge productivity. The quality of a family library is a manifestation of the core competitiveness of relevant industry enterprises or organizations.

Under development competencies, D4—Innovation is the most important indicator (${\mathsf{\omega }}_j$ = 0.0684). BCEs should not simply turn project drawings into BIM models but should use BIM technology for innovative applications, resulting in process improvements or process innovation, and ultimately leading to the improvement of the benefits of the entire project. They must constantly seek new methods and technologies to address any potential issues and increase their advantage over other competitors.

Each BCE can refer to the comprehensive weight of each indicator and focus on the indicator that needs to be improved. Through the improvement of the corresponding indicators, they will continuously improve their competency in the subsequent promotion and training stages, and provide themselves with tailored and comprehensive career development opportunities. Meanwhile, decision makers can improve the competencies of all BCEs by improving their competency in the corresponding key indicators.

(3) Competency level analysis:

In order to make the evaluation results reflect the true situation of the evaluation object more accurately, the comprehensive weight based on the real scoring data of the evaluation object can more accurately reflect the ability weight of a single BCE. The clustering results based on comprehensive weights show that the overall competency level of the BCEs is “Level 3”. This result is consistent with the internal evaluation of the employees’ competency within the organization. These results were fed back to corporate BIM managers for discussion, and respondents indicated that the results offered a clear and concise depiction of the research subjects’ competencies, including the level of competency, strengths, and weaknesses. The company’s positive feedback affirmed the practicality and effectiveness of the proposed evaluation model.

6.2. Comparison of Clustering Results Based on Constant Weight and Variable Weight

This paper presents a novel approach by combining variable weight theory with the interval grey clustering method. Variable weight theory is used to optimize the constant weights obtained by general weight methods, thereby improving the sensitivity of deterioration indicators [68], addressing the limitations of traditional evaluation methods such as complex weight distribution and constant weight.

To further demonstrate the superiority of this method, a comparison was made between the clustering results obtained from two methods: the constant weight method and variable weight method. The clustering results obtained with variable weight theory were explained in Section 5.3. Similarly, according to the relative weight ${\omega }_j^{\left(0\right)}$ and Formula (10), the comprehensive clustering coefficient results based on constant weights were obtained. ${\sigma }^1={0.0201}_{\left(0.06\right)},$ ${\sigma }^2={0.2166}_{\left(0.06\right)},$ ${\sigma }^3={0.3677}_{\left(0.06\right)},$ ${\sigma }^4={0.3050}_{\left(0.06\right)},$ and ${\sigma }^5={0.0905}_{\left(0.06\right)}$, as shown in Figure 4.

Compared with the comprehensive clustering coefficients obtained by the variable weight method, the comprehensive clustering coefficients calculated using the constant weight method are larger at levels 3, 4, and 5, and smaller at levels 1 and 2. Moreover, Table 7 reveals that as the indicator score improves, the corresponding reduction in comprehensive weight becomes smaller, whereas for worse indicator score, the corresponding increase in comprehensive weight becomes greater. These findings indicate that in the constant weight method, individual risk indicators are neutralized by other indicators, resulting in inaccurate clustering results [69]. Therefore, the clustering result obtained by the variable weight method is more in line with reality.

7. Conclusions

BIM has been rapidly developed in the construction industry, which has caused a second revolution in the industry. However, due to the steady growth of the trend towards project management through BIM technology, there is a shortage of BCEs in multiple industries. More high-level BCEs will be needed to meet the rapid growth in global demand for BCEs. This study established an evaluation model that analyzes the multidimensional competency of BCEs and evaluates their level of competency.

This paper provides a structured competency indicator system for BCEs. Furthermore, this paper provides a new analytical method to evaluate the competency of BCEs through the use of variable weight theory and the interval grey clustering method and applies the model in a case study. The research results indicate that the domain competencies are the most important of the four primary competency indicators. The BIM model, key point analysis, and innovation are the most important of all the secondary indicators. Managers can give priority to these indicators when formulating measures. For instance, they can enhance theoretical training on BIM technology, hire experienced BIM experts to provide targeted guidance on BIM models, key point analysis, and innovation analysis, and thereby improve the current performance of BCEs.

Educational institutions can integrate BIM technology into their existing curriculum systems to improve students’ domain competencies. Additionally, these findings can be used to help BCEs determine specific competencies that need improvement as a priority and provide a reference for evaluating their work performance.

However, the limitations of this study should also be noted, which may be taken into account in future research. To enhance the model’s reliability, we plan to increase the number of experts and conduct more case studies to further validate the model. The comparative analysis of interval grey clustering and fuzzy clustering under conditions of abundant data and scarce data remains an open and promising research direction. Additionally, the quantification of the indicator system and the robustness of the indicators also needs to be paid attention to in future research. Moreover, we plan to use adaptive weight calibration to verify the robustness of the indicator system.