Application maturity evaluation of building steel structure welding robotic technology based on combination weight and multi-level grey theory

Abstract

In China, steel structure building has become an important direction of national support and development. As a link in steel structure construction, welding plays a vital role. With the continuous development of domestic steel structures in the direction of “big, special, and new”, manual welding becomes increasingly difficult. The application of robotic technology can effectively reduce the problems of unstable quality and low efficiency caused by manual welding. However, how to evaluate the overall application effect of this technology from the perspective of steel structure construction projects is an urgent problem to be solved at present. Through an in-depth analysis of the technology of building steel structure welding robots, combined with the idea of the capability maturity model and WSR methodology, the evaluation index system of application maturity of building steel structure welding robotic technology is designed. In addition, according to the gray, fuzzy, and difficult-to-quantify characteristics of the evaluation index system, the evaluation model of the application maturity of the building steel structure welding robot technology is established by using the subjective and objective combination weighting method and the gray system theory. In this model, the mixed weighting method of AHP and entropy weight method is used to determine the index weight, and then the multi-level gray theory is used to comprehensively evaluate the maturity of the technology application. Lastly, a project is used as an example to check the science and feasibility of the model.

Keywords

Welding robot steel structure WSR maturity model multi-level grey theory

1 Introduction

Welding robot refers to the industrial robot engaged in welding. The International Organization for Standardization (ISO) defines an industrial robot as a multi-purpose, repeatable programmable automatic control operator with three or more programmable axes for use in the field of industrial automation. Welding robots originated from the United States Unimation Inc in 1962, which developed the world’s first truly practical industrial robot (robot arm) named “Unimate”. After decades of rapid development, welding robots have been widely used in the automobile industry, aerospace, shipbuilding, mechanical processing industry, electronic and electrical industry, and other related manufacturing industries in industrially developed countries [1]. However, compared with industries with a high utilization rate of welding robots such as automobiles, construction machinery, boilers, and pressure vessels, the application and development of robot welding technology in steel structure buildings is still relatively slow [2]. The welding workload in modern steel structure buildings is massive, and more than 40% of them need welding, so the importance of welding is self-evident [3]. According to statistics, more than 90% of welding work is still done manually, which is even higher in heavy industry [4]. Nowadays, with the shortage of welders, soaring costs, bad welding environment, low efficiency of manual welding, unstable quality and other problems in the field of building steel structure welding, manual welding alone has been unable to meet the basic needs. Therefore, robot automatic welding has become an important approach to solve welding problems.

In recent years, European countries have vigorously promoted the application of fully automatic welding production systems in the steel structure manufacturing and processing industry and used mature software and robotic systems to integrate automatic welding technology to create a “man-machine cooperation” working environment. In Japan, the number of steel structure buildings is the largest among the current various building structures, accounting for about 20% of the total residential building area [5]. As a country with frequent earthquakes, Japan has formulated strict a seismic design code in architectural design, and has adopted high-quality and efficient robot automatic welding and manufacturing methods; up to 2015, the number of installed steel structure welding robots in Japan has exceeded 3000, and the process of applying automatic welding robots in steel structure industry has become mature [6]. In China, welding robots are mostly used in steel structure manufacturing plants. Except for some remarkable projects, welding robots are rarely used in steel structure construction sites; typical examples include the GDC-1 rail type all position welding robot applied to the “Olympic Bird’s nest project” [7], the flexible rail type all position welding robot applied to the Shanghai center building project [8], and the mobile welding robot applied to the Beijing new airport project [9]. According to the survey, at present, the degree of welding automation in the world’s industrial developed countries has reached 80% of the welding technology, while in China, according to the estimation of welding materials consumed by manual welding and automatic welding, the nominal degree of welding automation is 30%, which is a big gap [10].

Recent years in China, the National Development and Reform Commission, the Ministry of Industry and Information Technology and the Ministry of Science and Technology have made plans and guidance for the development of robots, encouraging and supporting the technological innovation and industrial development of robots. Some Chinese local government has also issued relevant policy documents to support the development of robots. The Robot Industry Development Plan (2016–2020) clearly points out that “promote industrial robots to move towards middle and high-end, focusing on the development of arc welding robots [11].” The 2017 edition of the revised “10 New Technologies for the Construction Industry” newly added high-efficiency welding technologies for steel structures, including welding robot technology [12]. The application maturity of building steel structure welding robot technology is to describe the industrialization and application scale of the technology level, process flow, supporting resources, technology life cycle, and other aspects of this scientific and technological achievement. The maturity means that the actual application of this technology must be continuously improved over time, so as to have core competitiveness. Since the introduction of welding robots in China is relatively late, and most of them are non-core technology modifications made by domestic enterprises based on imported equipment, therefore, in addition to many bottlenecks in key technology areas to be broken, the relevant policy environment, management system, product standards, and other aspects need to be further strengthened and improved. Under the joint influence of a series of factors, how to accurately measure and describe the specific application of domestic building steel structure welding robot technology in the project, and measure its overall maturity, for subsequent technical research and improvement, until the mass application and promotion, is of great importance.

At present, in China, the application of welding robot technology for building steel structures mainly focuses on qualitative research, but lacks quantitative evaluation. Therefore, this paper put to use the WSR methodology and the idea of the capability maturity model to establish the maturity evaluation index system, use the combination of the AHP method and entropy weight method to determine the weight of indicators at all levels, and introduce multi-level gray comprehensive evaluation method, in order to more reasonably evaluate the maturity of welding robot technology application in domestic construction projects.

2 Literature review

2.1 Research status of welding robot technology for building steel structure

There are many technologies involved in welding robots for building steel structures, European and American scholars focus on the improvement and optimization of the welding process and the development of the welding robot system. In the welding process, the research on the properties and micro-structure of welded joints is a more concerning aspect abroad. For example, Friction Stir Spot Welding (FSSW) has been proven to be able to connect very advanced high-strength steel and has flexibility in controlling welding heat and welding joint micro-structure, which makes friction stir welding a potential alternative to resistance spot welding [13]. Stanciu, et al. [14] studied the influence of the key parameters of laser welding on the geometric shape and micro-structure of the weld. Another hot keyword in the welding process is laser welding, which is an efficient and precise welding method. This method uses a high-energy-density laser beam as the heat source. Kang, et al. [15] studied the laser welding quality monitoring technology and proposed the quality monitoring method and the robot-based remote laser welding system to solve the problem of limited welding speed and accuracy of traditional laser welding systems; Jasnau, et al. [16] introduced a laser arc hybrid welding process and compared with the laser or arc welding process alone, this hybrid welding process has obvious advantages. With the increasing thickness of steel members, in order to achieve high-quality welding, higher requirements are put forward for the robot system. Tavares, et al. [17] proposed a BIM-based robotic reprogramming and spatial augmented reality collaborative welding system, which has the advantage of not only ensuring maximum flexibility in the beam assembly stage but also improving overall productivity and product quality. For the problem of insufficient automation of H-column structures, Moon, et al. [18] proposed a practical steel beam welding robot system, which was specially designed for the welding of H-column structures.

Chinese scholars mainly focus on automatic welding of high-strength steel and box steel structure. The Code for Welding of Steel Structures (GB50661-2011), implemented on August 1, 2012, is an important turning point for the large-scale adoption of high-strength steel in the field of building steel structures [19]. The appearance of high-strength steel promotes the development of building steel structure welding towards automation. Zhang [20] analyzed the characteristics and difficulties of high-strength steel welding, the demand for welding materials for efficient welding of high-strength steel, and the application and development of automatic welding technology for high-strength steel. Yang [21] believes that the current welding automation technology used in high-strength steel is still in essence the general automatic welding technology to weld high-strength steel, so there are some processes that have not become part of the welding automation, which need further exploration. The advantages of box-shaped steel structures are mainly reflected in their light weight, plasticity, and good toughness, thus promoting the wide application of box-shaped steel structures in the field of bridges and steel buildings. Guo et al. [22] designed a new box-type steel structure all-position welding robot system to solve some problems in the process of box-type steel structure welding construction, mainly including the lack of stability of the joint quality, low degree of welding automation and dangerous work at height, and the welding robot system parameters selection and structural design can adapt to the ring seam all-position welding during the construction of box-type steel structure.

2.2 Evaluation method of technology application

There are many of evaluation literatures on technology applications, including application demand evaluation, application suitability evaluation, application risk evaluation, etc. The methods used can be divided into the fuzzy comprehensive evaluation method, the matter element analysis method, and the TOPSIS method. Chu et al. [23] used the factor analysis method and fuzzy comprehensive evaluation method to evaluate the application demand of Internet of Things technology in China’s agricultural informatization; Wang et al. [24] evaluated the suitability of the application of low-pressure pipeline irrigation technology in southern China by building a comprehensive evaluation model combining ahp and fuzzy evaluation method. Hu et al. [25] built a matter-element evaluation model based on COWA-G1 combination weighting to comprehensively evaluate the risk of BIM technology application in EPC projects; Wang [26] evaluated the application risk of municipal traffic engineering BIM technology by building a combination weighted matter-element model of analytic hierarchy process and entropy weight method. Mo et al. [27] used the weighted TOPSIS method to evaluate the comprehensive effectiveness of the HIR (Hot in-place recycling) technology application; Han et al. [28] used the improved entropy weight TOPSIS evaluation model to evaluate the application ability of BIM technology. The above evaluation methods are summarized as shown in Table 1.

Table 1
Main characteristics of the evaluation method

Evaluation method Basis of the method Characteristic [34]

Fuzzy comprehensive evaluation method Fuzzy mathematical method It can accurately quantify and describe the fuzzy information and make a reasonable quantitative evaluation

Matter element analysis Extension set theory Can effectively deal with the variability and incompatibility of system indicators

TOPSIS method Multiple attribute decision making method There is no strict restriction on samples, and the original data is fully used

Evaluation method	Basis of the method	Characteristic [34]
Fuzzy comprehensive evaluation method	Fuzzy mathematical method	It can accurately quantify and describe the fuzzy information and make a reasonable quantitative evaluation
Matter element analysis	Extension set theory	Can effectively deal with the variability and incompatibility of system indicators
TOPSIS method	Multiple attribute decision making method	There is no strict restriction on samples, and the original data is fully used

From the basic and single evaluation method to the comprehensive evaluation method under uncertain conditions. Expert rating based on the actual situation of technology application and knowledge structure: the analysis of green building technology promotion [29]. Ranking and evaluation of technological innovation capacity in different regions of China: an equation model integrating innovation input, output, and related factors [30]. Benefit evaluation of the application of new construction technology: the qualitative and quantitative analysis model established by using the analytic hierarchy process [31]. Multilevel, multi-dimensional, and quantifiable TDGS technology applicability evaluation: a three-level comprehensive evaluation method based on the binary comparative analysis method, TOPSIS, linear weighted sum method, and exponential evaluation baseline method [32]. The Green construction bid evaluation under multi-index and uncertain conditions: based on multi-level gray evaluation model [33].

2.3 CMM research status

The Capability Maturity Model (CMM) was proposed by the Carnegie-Mellon University Software Engineering Institute (CMU-SEI). Originally researching a maturity framework to help organizations improve their software process, SEI further developed the software process maturity framework into a software capability maturity model based on the publication of a brief description of the process maturity framework and a maturity questionnaire. By analyzing more than 200 maturity-related papers, Wendler [35] points out that applied research on maturity involves more than 20 fields and is conducted mainly from three aspects: first, research on the basic concept of maturity, second, research for the purpose, application, and advantages of maturity evaluation, and third, research on the construction of maturity models. He [36] introduced some basic concepts of the software capability maturity model, and then described the five-level structure and the content of the model, the relationship between different maturity levels, and the behavior characteristics of each maturity level, and pointed out some problems in the model. In terms of engineering projects, there are many pieces of research on maturity evaluation based on CMM theory. For example, Ma et al. [37] put forward the building fire emergency response capability maturity (FE-CMM) evaluation system on the basis of the capability maturity model, and developed a plug-in to evaluate the fire emergency response capability based on the building information model (BIM) platform to effectively realize the intelligent evaluation of the building fire emergency response capability; Park et al. [38] deeply discussed and studied the relevant evaluation of the PMIS communication management capability of construction projects based on CMM theory. Many researchers have constructed corresponding models by referring to the CMM model and project knowledge system. Based on CMM theory, the National Institute of Building Sciences (NIBS) has established an interactive BIM-CMM maturity model, which includes 11 research fields of interest, and defines the weight and maturity level of each field [39]. The American Project Management Institute (PMI) launched the Organization Project Management Maturity Model (OPM3) in 2003 and promoted it as an industry standard [40]. Another example is the knowledge management maturity model, including three management objectives, 68 knowledge management activities, and 19 key process areas [41]. These maturity-related studies have played a role in promoting the development of the industry.

2.4 Research status of multi-level grey theory

As a new method, gray system theory takes “small data” and “poor information” uncertainty system with “partly known information and partly unknown information” as the research object, mainly through mining the “partly” known information and extracting valuable information, and then achieve the correct description and effective control of the system operation behavior and its evolution law [42]. The multi-level grey comprehensive evaluation method is a comprehensive integration method based on grey system theory, covering fuzzy mathematics and qualitative to quantitative methods. In the field of architecture, there are many pieces of evaluation kinds of literature established by using the multi-level grey comprehensive evaluation method, whose research directions include risk evaluation [43], green construction evaluation [44], enterprise information evaluation [45], etc. It can be seen from the above literature that this method can have stronger flexibility by combining subjective or objective (combined) weighting methods to solve diversified evaluation problems. This paper uses the multi-level gray comprehensive evaluation method to evaluate the maturity, mainly considering the following points: first, the building steel structure welding robot has not been implemented for a long time in China, and there are few application examples, lacking sufficient data, which belongs to the uncertainty problem; second, the evaluation index system is multi-level and complex, and the indicators are mostly qualitative indicators, which are difficult to quantify; third, the information provided by the evaluator is affected by human factors, which is gray. Because AHP and fuzzy theory are difficult to solve the uncertainty problems such as “small samples” and “poor information”, the general methods also have defects in the use of various gray degree evaluation information [46]. Therefore, for the above evaluation problems, the multi-level gray comprehensive evaluation method is the most appropriate, which can make the evaluation results more objective and reasonable.

In general, the research on the welding robot technology for building steel structures is progressing steadily. In addition, the research on the capability maturity model and technology application evaluation method has also achieved good research results, effectively promoting the organization to achieve the set goals. However, due to the late start of China’s construction steel structure welding robot, the study of its application is mainly from a qualitative, single perspective, but they lack quantitative as well as holistic research. Thus, it is necessary to establish a maturity model that conforms to the current application situation of building steel structure welding robot technology in China, design the corresponding evaluation index system and select appropriate evaluation methods, and then systematically evaluate the application of building steel structure welding robot technology according to the gray nature of the research object.

3 Methods

3.1 Maturity level stage division

The application maturity level of building steel structure welding robot technology is a gradual upgrading process. Based on the basic theory and the idea of the Capability Maturity Model (CMM), and combined with the application characteristics of building steel structure welding robot technology in engineering projects, the maturity is divided into five levels: initial level, starting level, development level, maturity level, and optimization level. Among them, the application maturity of each level is the foundation of the next level, and the continuous improvement of maturity is also the embodiment of the gradual maturity and standardization of the application of welding robot technology for building steel structures.

(1) Initial level

The initial level is characterized by a limited overall application environment. At this stage, the national and local governments have not realized the importance and feasibility of the welding robot technology for building steel structures; the enterprise takes a wait-and-see attitude in the application of this technology. The level of automatic welding technology is low, and the welding forms are mainly manual welding and semi-automatic welding, with low welding quality and efficiency; the construction organization structure and management system of the cooperative welding robot have not been established, and the process management is in a disordered state; it is difficult to coordinate the economic, environmental and social benefits.

(2) Starting level

The starting level is characterized by the improvement of the overall application environment. At this stage, the state and local governments realized the importance and feasibility of welding robot technology for building steel structures, and formulated relevant policies and incentives for the application of welding robot technology; the enterprise formulates a scientific research investment plan. The welding robot system does not have the ability to feedback the external information, so it is difficult to adapt to the changes in the working environment; the enterprise starts to establish the construction organization structure and management system and defines the basic work contents in the process management; the economic, environmental and social benefits are not obvious.

(3) Development level

The development level is characterized by the continuous development of the overall application environment. At this stage, the state and local governments will implement relevant policies and incentives; the enterprise actively invests resources and funds. The welding robot system has a certain sense of the external environment and can adjust the working state according to the changes in the environment; the construction organization structure and management system are gradually taking shape, and the process management tends to be standardized and institutionalized; economic, environmental and social benefits have been improved simultaneously.

(4) Mature level

The characteristic of the mature level is that the overall environment has formed a positive state of all-around development and application of technology. At this stage, the state and local governments began to formulate improvement measures based on the feedback on the effects of relevant policies and measures; the enterprise continuously invests resources and funds. The welding robot system realizes the integration of multiple functions and highly intelligent feedback and self-regulation, and can adapt to the changes of the external environment and coordinate the completion of various tasks; the enterprise integrates the construction organization structure and management system to improve the process management efficiency and execution; the economic, environmental and social benefits are remarkable.

(5) Optimization level

The optimization level is characterized by a sound overall application environment. At this stage, the relevant national and local policies and systems have formed a systematic system; the enterprise optimizes the input of resources and funds. The welding robot technology has realized industrial development with outstanding advantages, achieving high quality, high efficiency, and high adaptability. Meanwhile, it is committed to further development and exploration in the fields of standardized design of steel components, optimization of welding material performance, and improvement of welding process and methods; the enterprise realizes the digital integrated management of welding equipment, welding operators, and welding production process through the network, and its management level is in a virtuous circle of continuous optimization and improvement; economic, environmental and social benefits continued to be optimized.

3.2 Thinking of WSR methodology

WSR is the abbreviation of “WuLi - ShiLi –RenLi Methodology”. It is an oriental methodology put forward by Chinese scholars in the 1990 s. WuLi is a Chinese word, which refers to the objective existence that people face in the process of dealing with a system project (or problem), and is the sum of the laws of material movement; similarly, ShiLi refers to the mechanism of intervention when people face the objective existence and laws in the process of dealing with a system project (or problem); in addition, RenLi refers to the relationship and change process between all people involved in the processing of a system project (or problem) [47]. As a systematic way of thinking, when analyzing and researching complex problems, WSR should not only consider the WuLi aspect of the object but also how to better apply the WuLi aspect to the ShiLi aspect. And when making management decisions, we can’t deviate from RenLi, and finally know WuLi, understand ShiLi and communicate RenLi.

Taking the welding robot for building steel structures as the research object, it can be applied maturely and needs to start from the following aspects. First of all, it is necessary to meet WuLi factors such as basic application environment and equipment technology. Secondly, it is also necessary to consider the process management of the application of this technology in the actual project, coordinate and solve possible problems, and strive to maximize the benefits of ShiLi factors. Finally, RenLi factors that attach importance to the role of people and groups in the system. Therefore, the idea of WSR theory is in line with the idea of building the maturity model of building steel structure welding robot technology. In this paper, the preliminary construction of the evaluation index system is carried out from the three levels of WuLi support, ShiLi optimization, and RenLi coordination.

3.3 Division of main factors based on WSR level

In order to objectively evaluate the application maturity of building steel structure welding robot technology, based on the above maturity level analysis and WSR methodology, the specific development status of building steel structure welding robot technology is compared with the maturity level characteristics, and the main factors are divided. The objects and contents emphasized by “WuLi” mainly refer to the objective material world, laws, regulations, etc. As for the construction steel structure welding robot, the WuLi support is reflected in environmental factors and technical factors. The objects and contents emphasized by “ShiLi” mainly refer to the organization, system management, and the principles of doing things. Therefore, the ShiLi optimization is reflected in management factors and benefit factors. The objects and contents emphasized by “RenLi” mainly refer to people, groups, and the principles of life. Therefore, the RenLi coordination is reflected in personnel and group factors. The factors included in all levels affect the maturity of the application of the construction steel structure welding robot technology, and the overall application of the construction steel structure welding robot technology is finally reflected by the comprehensive effect.

(1) Environmental factors

Environmental factors are the macro support required by welding robots in the field of steel structures. Policy support, scientific research investment, and future planning are the preconditions for the sustainable development of welding robots. Technical standards and specifications are the basis for the establishment of a construction system. The degree of automation reflects the current technical level of the enterprise.

(2) Technical factors

Technical factors refer to some technologies that must be possessed by building steel structures to realize automatic welding by robots. It is the core of the application of welding robots. The key technologies include: welding sensing technology, welding seam tracking technology, welding programming technology, etc. The standardized design of components is the premise and foundation of the popularization of welding robot technology for building steel structures. Upgrading and optimization of welding materials is an important development direction to ensure the quality of robot welding products. Secondly, quality and efficiency are the fundamental purpose of technology research and development, and are also important criteria for evaluating technology research results. The welding effect in dynamic environment reflects the adaptability of automatic welding technology.

(3) Management factors

The management factor refers to a series of coordination and management of the whole process when applying welding robots for on-site construction, which is some auxiliary work in the whole operation process. Specifically, it includes some management work in the early, middle, and late stages. For example, the preliminary preparations include the formulation of technical operation procedures, the erection of wind shelters, operation platforms, and horizontal safety nets, and the integrated transformation of robots. Management work carried out during operation: management of personnel, safety, and quality. Later related work: equipment maintenance, material stacking management, etc.

(4) Benefit factors

The benefit factors are mainly aimed at the three levels of economy, environment, and society. The economic benefit reflects the beneficial advantages of the robot compared with the employment of welders in terms of purchase cost and production efficiency. Environmental benefit refers to the degree to which the pollution generated by robots can be controlled during operation. Social benefits include improving workers’ working conditions and environment, reducing labor intensity, etc. Whether welding robots can be used maturely requires good coordination between the three.

(5) Personnel and group factors

The meaning of personnel and group factors refers to the basic role played by people when applying robot welding technology, mainly referring to the basic operating ability and cognitive level they should have.

3.4 Maturity model structure

According to the level construction and main factor division of WSR theory, combined with the level thought of maturity model (CMM), the established maturity model structure is shown in Fig. 1. The model includes two levels. The first level of model construction is the five levels of maturity, and the second level of model construction is the three levels of “WuLi”, “ShiLi” and “RenLi” of WSR theory.

Fig. 1

Model structure of application maturity of building steel structure welding robot technology.

3.5 Design of evaluation index system

The establishment of an evaluation index system of application maturity of welding robot technology for building steel structures needs to start from multi-level and multi-index. First of all, based on the above five main factors involved in the application maturity model structure of the building steel structure welding robot technology, and through reading the relevant documents in the CNKI database, a series of evaluation indicators affecting the technology application are summarized and sorted out, and the evaluation indicators are preliminarily classified to systematize the original complex indicators. Secondly, following the principles of typicality and reasonableness, the indicators initially summarized are screened, the indicators with overlapping relationships are merged, and the indicators with weak correlation are removed. Finally, the expert interview method is used to adjust and optimize the evaluation indicators to make the indicators more scientific and real. The evaluation index system of application maturity of building steel structure welding robot technology constructed by adopting the above steps can be divided into four layers: the overall evaluation objective, 3 first-level indicators, 5 second-level indicators, and 29 third-level indicators, as shown in Table 2.

Table 2
Evaluation index system of application maturity of welding robot technology for building steel structure

Overall evaluation objective U First-level indicators U_i Second-level indicators U_ij Third-level indicators U_ijk

Application maturity of welding robot technology for building steel structure U WuLi U₁ Environmental factors U₁₁ National and local policy support U₁₁₁

Industry development planning U₁₁₂

Standard Specification for welding robot technology U₁₁₃

Scientific research input level U₁₁₄

Enterprise automation level U₁₁₅

Technical factors U₁₂ Welding quality U₁₂₁

Welding efficiency U₁₂₂

Adaptability to dynamic environment U₁₂₃

Welding sensing technology U₁₂₄

Seam tracking technology U₁₂₅

Welding programming technology U₁₂₆

Welding process database U₁₂₇

Component standardization design U₁₂₈

Upgrading and optimization of welding materials U₁₂₉

ShiLi U₂ Management factors U₂₁ Formulation of technical operation procedures U₂₁₁

Preparation of welding environment U₂₁₂

Robot integration transformation U₂₁₃

Qualification of welding process U₂₁₄

Management of welding operators U₂₁₅

Security management U₂₁₆

Weld inspection and repair U₂₁₇

Stacking management of welding materials U₂₁₈

Equipment maintenance U₂₁₉

Benefit factors U₂₂ Economic benefit level U₂₂₁

Environmental benefit level U₂₂₂

Social benefit level U₂₂₃

RenLi U₃ Personnel and group factors U₃₁ Technical cognition level of the construction unit U₃₁₁

Professional level of operators U₃₁₂

Skill training for operators U₃₁₃

3.6 Establishment of maturity evaluation model

3.6.1 Using a combination weighting method to determine index weight

The analytic hierarchy process (AHP) is a multi-criteria decision-making method for quantitative analysis of qualitative problems. Its advantages mainly lie in its simplicity, flexibility, and practicality. This paper uses the AHP method to determine the subjective weight of indicators, and Saaty’s 1–9 scale method is used to compare the importance of each evaluation index, and then a judgment matrix $A = {[\begin{matrix} C_{ij} \end{matrix}]}_{n \times n}$ is constructed. The index weight at all levels is calculated by using the calculation steps of the sum method.

The subjective weighting method is subjective and easy to be affected by people’s experience and knowledge level. Therefore, in order to reduce the weight deviation caused by subjective weighting, this paper introduces the entropy weight method to determine the objective weight. Suppose there are p evaluation samples and n evaluation indicators, the evaluation matrix $Y = {[\begin{matrix} y_{ij} \end{matrix}]}_{p \times n}$ can be obtained. According to the calculation steps of the entropy weight method [48], the weights of indicators at all levels are calculated.

Subjective weight obtained by the AHP method: The first-level indicator weight vector is expressed as T =(t₁, t₂, t₃, ... , t_i), the second-level indicator weight vector is expressed as T_i = (t_i1, t_i2, t_i3, ... , t_ij) and the third-level indicator weight vector is expressed as T_ij = (t_ij1, t_ij2, t_ij3, ... , t_ijk).

Objective weight obtained by the entropy weight method: The first-level indicator weight vector is expressed as V = (v₁, v₂, v₃, ... , v_i), the second-level indicator weight vector is expressed as V_i = (v_i1, v_i2, v_i3, ... , v_ij) and the third-level indicator weight vector is expressed as V_ij = (v_ij1, v_ij2, v_ij3, ... , v_ijk).

Given the subjective weight determined by the AHP method and the objective weight determined by the entropy weight method, the combined weight value can be calculated by the following formula (taking the third-level indicator w_ijk as an example): $w_{ijk} = \frac{t_{ijk} v_{ijk}}{\sum_{k = 1}^{n} t_{ijk} v_{ijk}}$

3.6.2 Applying multi-level grey theory to evaluate results

(1) Determine the indicator scoring grade and standard

In the application maturity evaluation of building steel structure welding robot technology, the evaluation level is divided into optimization level, maturity level, development level, starting level, and initial level, i.e. I ={ I₁, I₂, I₃, I₄, I₅ }. Assign 9, 7, 5, 3, and 1 to the five evaluation grades, and assign 8, 6, 4, and 2 between the two adjacent grades to convert qualitative indicators into quantitative indicators, and invite p experts to score the third-level indicators. In order to accurately judge the level of each technology application maturity impact indicator, this paper briefly describes the characteristics of each indicator’s maturity level, providing a reference for maturity assessment. Due to the limited space, some indicators in “environmental factors” are selected as examples for an explanation, as shown in Table 3.

Table 3
Evaluation criteria for partial indicators of “environmental factors” of application maturity of building steel structure welding robot technology

Evaluating indicator

Evaluation criterion National and local policy support Industry development planning Standard Specification for welding robot technology

Optimization level Relevant policies and systems implemented have formed a systematic system to provide effective support for technology application Promote standardized management of the industry, integrate them, and form a good competitive situation Build a comprehensive set of technical standards system and optimize the layout of standards

Mature level Continuously improve and perfect according to the effect feedback of relevant policies and measures Supplement and improve the planning content and expand new market areas Track and analyze the implementation benefits of technical standards and specifications, and timely revise and update the standards and specifications system

Development level Implement relevant policies and incentives Formulate phased objectives and propose specific tasks and measures according to key implementation areas of the industry Continuously improve the technical standard and specification system

Starting level Begin to formulate relevant policies and incentives Clear development orientation and short-term planning for some fields Improve the quality of standards and define the content and scope of application of technical specifications

Initial level Relevant policies have not been established, and the application environment is limited There is no clear industry development plan in terms of technology application, which is relatively blind The overall quality of the standard is not high, and the technical application specifications are not coordinated

	Evaluating indicator
Evaluation criterion	National and local policy support	Industry development planning	Standard Specification for welding robot technology
Optimization level	Relevant policies and systems implemented have formed a systematic system to provide effective support for technology application	Promote standardized management of the industry, integrate them, and form a good competitive situation	Build a comprehensive set of technical standards system and optimize the layout of standards
Mature level	Continuously improve and perfect according to the effect feedback of relevant policies and measures	Supplement and improve the planning content and expand new market areas	Track and analyze the implementation benefits of technical standards and specifications, and timely revise and update the standards and specifications system
Development level	Implement relevant policies and incentives	Formulate phased objectives and propose specific tasks and measures according to key implementation areas of the industry	Continuously improve the technical standard and specification system
Starting level	Begin to formulate relevant policies and incentives	Clear development orientation and short-term planning for some fields	Improve the quality of standards and define the content and scope of application of technical specifications
Initial level	Relevant policies have not been established, and the application environment is limited	There is no clear industry development plan in terms of technology application, which is relatively blind	The overall quality of the standard is not high, and the technical application specifications are not coordinated

(2) Determine the evaluation sample matrix

According to the score d_ijkh of the h-th expert on the third-level index U_ijk, the evaluation sample matrix D is as follows: $D = {(d_{ijkh})}_{p \times m} = [\begin{matrix} d_{1111} & d_{1121} & d_{1131} & \dots & d_{ijk 1} \\ d_{1112} & d_{1122} & d_{1132} & \dots & d_{ijk 2} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ d_{111 h} & d_{112 h} & d_{113 h} & \dots & d_{ijkh} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ d_{111 p} & d_{112 p} & d_{113 p} & \dots & d_{ijkp} \end{matrix}]$

Where p is the number of experts, and m is the number of third-level evaluation indicators in the matrix.

(3) Determine the evaluation gray class

If the evaluation gray class is recorded as s, then s = (1, 2, 3, 4, 5), the corresponding grey number ⊗ = (9, 7, 5, 3, 1). The whitening weight function $f_{k}^{s} (x)$ is constructed to represent the whitening weight function of the third-level indicators U_ijk with respect to the s gray class, and the corresponding expression is as follows:

1) The first gray class is optimization level, s = 1, the gray number ⊗₁∈ [9, 10], and the whitening weight function is: $f_{k}^{1} (x) = {\begin{matrix} 0 x \notin [0, 10] \\ x \in [0, 9) \\ 1 x \in [9, 10] \end{matrix}$

2) The second gray class is mature level, s = 2, the gray number ⊗₂∈ [7, 10], and the whitening weight function is: $f_{k}^{2} (x) = {\begin{matrix} 0 x \notin [0, 10] \\ x \in [0, 7) \\ \frac{10 - x}{3} x \in [7, 10] \end{matrix}$

3) The third gray class is development level, s = 3, the gray number ⊗₃∈ [5, 10], and the whitening weight function is: $f_{k}^{3} (x) = {\begin{matrix} 0 x \notin [0, 10] \\ x \in [0, 5) \\ \frac{10 - x}{5} x \in [5, 10] \end{matrix}$

4) The fourth gray class is the starting level, s = 4, the gray number ⊗₄∈ [3, 10], and the whitening weight function is: $f_{k}^{4} (x) = {\begin{matrix} 0 x \notin [0, 10] \\ \in [0, 3) \\ \frac{10 - x}{7} x \in [3, 10] \end{matrix}$

5) The fifth gray class is initial level, s = 5, the gray number ⊗₅∈ [1, 10], and the whitening weight function is: $f_{k}^{5} (x) = {\begin{matrix} \notin [0, 10] \\ \in [0, 1) \\ \frac{10 - x}{9} x \in [1, 10] \end{matrix}$

(4) Grey evaluation weight vector of third-level indicators and grey evaluation weight matrix of second-level indicators

According to the score d_ijkh of the third-level indicators U_ijk in the evaluation sample matrix D, it is substituted into the whitening weight function, and the whitening weight function value of the third-level indicators U_ijk belonging to the l-th evaluation gray class is obtained as $f_{k}^{l} (d_{ijkh})$ . All p experts believe that the whitening weight function value of U_ijk belonging to the l-th evaluation gray class is $\sum_{h = 1}^{p} f_{k}^{l} (d_{ijkh})$ . By analogy, if the total whitening weight function value of the third-level indicators U_ijk belongs to the five evaluation gray classes is $\sum_{l = 1}^{5} \sum_{h = 1}^{p} f_{k}^{l} (d_{ijkh})$ , then all experts believe that the evaluation weight of U_ijk belongs to the l evaluation gray class is: $r_{ijkl} = \frac{\sum_{h = 1}^{p} f_{k}^{l} (d_{ijkh})}{\sum_{l = 1}^{5} \sum_{h = 1}^{p} f_{k}^{l} (d_{ijkh})}$

The grey evaluation weight vector of the third-level indicators U_ijk is: $r_{ijk} = (r_{ijk 1}, r_{ijk 2}, r_{ijk 3}, r_{ijk 4}, r_{ijk 5})$

Construct the grey evaluation weight matrix of the second-level indicators U_ij: $R_{ij} = [\begin{matrix} r_{ij 1} \\ r_{ij 2} \\ r_{ij 3} \\ ⋮ \\ r_{ijk} \end{matrix}] = [\begin{matrix} r_{ij 11} & r_{ij 12} & r_{ij 13} & r_{ij 14} & r_{ij 15} \\ r_{ij 21} & r_{ij 22} & r_{ij 23} & r_{ij 24} & r_{ij 25} \\ r_{ij 31} & r_{ij 32} & r_{ij 33} & r_{ij 34} & r_{ij 35} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ r_{ijk 1} & r_{ijk 2} & r_{ijk 3} & r_{ijk 4} & r_{ijk 5} \end{matrix}]$

(5) Grey evaluation weight vector of second-level indicators and grey evaluation weight matrix of first-level indicators

The grey evaluation weight vector of the second-level indicators U_ij is: $b_{ij} = W_{ij} R_{ij} = (b_{ij 1}, b_{ij 2}, b_{ij 3}, b_{ij 4}, b_{ij 5})$

Constructing the grey evaluation weight matrix of the first-level indicators U_i: $B_{i} = [\begin{matrix} b_{i 1} \\ b_{i 2} \\ b_{i 3} \\ ⋮ \\ b_{ij} \end{matrix}] = [\begin{matrix} b_{i 11} & b_{i 12} & b_{i 13} & b_{i 14} & b_{i 15} \\ b_{i 21} & b_{i 22} & r_{i 23} & r_{i 24} & r_{i 25} \\ b_{i 31} & b_{i 32} & b_{i 33} & b_{i 34} & b_{i 35} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ b_{ij 1} & b_{ij 2} & b_{ij 3} & b_{ij 4} & b_{ij 5} \end{matrix}]$

(6) The grey evaluation weight vector of the first-level indicators and the total grey evaluation weight matrix of the comprehensive evaluation target

The grey comprehensive evaluation weight vector of the first-level indicators U_i is: $e_{i} = W_{i} B_{i} = (e_{i 1}, e_{i 2}, e_{i 3}, e_{i 4}, e_{i 5})$

Construct the total grey evaluation weight matrix of evaluation objective U: $E = [\begin{matrix} e_{1} \\ e_{2} \\ e_{3} \\ ⋮ \\ e_{i} \end{matrix}] = [\begin{matrix} e_{11} & e_{12} & e_{13} & e_{14} & e_{15} \\ e_{21} & e_{22} & e_{23} & e_{24} & e_{25} \\ e_{31} & e_{32} & e_{33} & e_{34} & e_{35} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ e_{i 1} & e_{i 2} & e_{i 3} & e_{i 4} & e_{i 5} \end{matrix}]$

(7) General evaluation objective: Grey Comprehensive Evaluation

The grey comprehensive evaluation vector of the overall evaluation objective U is: $Z = WE = (z_{1}, z_{2}, z_{3}, z_{4}, z_{5})$

Comprehensive evaluation value of grey number of general objective U: $Q = {ZI}^{T}$

Wherein, I = (9, 7, 5, 3, 1), namely the threshold value corresponding to each evaluation gray class. At the same time, the maturity evaluation of indicators at all levels has been achieved, as shown in Table 4.

Table 4

Evaluation value of maturity of indicators at all levels

	First-level	Second-level	Third-level
	indicators	indicators	indicators
Evaluation weight vector	e _i	b _ij	r _ijk
Evaluation value	Q_i = e_iI^T	Q_ij = b_ijI^T	Q_ijk = r_ijkI^T

Fig. 2

Scene of welding robot operation on the project site.

4 Example analysis

4.1 Project overview

Jinan International Financial Center Lot A1 Phase I (A1-1 # Building) Project is located in the CBD area of Jinan City, Shandong Province, China. The building has 53 floors, with a total construction area of 128680 square meters, and the highest point is 260 meters. Among them, the total building area above the ground is 126267 square meters, and the underground building area is 2213 square meters. The ground includes office and commercial functional areas, and the underground is mainly a parking area. This project applies a permanent magnet track type intelligent girth welding robot independently developed by China Construction Fifth Engineering Bureau. The robot is developed based on the key and difficult points in project welding construction. The track of the permanent magnet track type intelligent girth welding robot adopts the magnetic suction form and can be matched with steel pipe columns of various sizes (500mm–1600 mm in diameter is applicable). Using the maturity evaluation model established above, the application maturity of the building steel structure welding robot technology in this project is comprehensively evaluated, and the corresponding evaluation level is obtained. Based on the analysis results, suggestions for improvement are put forward.

4.2 Project maturity evaluation

Calculate the index weight. Ten experts are invited to score the importance of a single indicator in the form of a questionnaire survey. The weight of indicators at all levels can be obtained by using the calculation steps of index weight of the combination weighting method, as shown in Table 5.

Construct the evaluation sample matrix. According to the expert’s rating of the third-level indicators U_ijk in the evaluation index system of the technical application maturity of building steel structure welding robot, the evaluation sample matrix D can be obtained as follows:

$D = [\begin{matrix} 5 6 6 4 6 5 6 5 6 6 5 3 5 5 5 6 4 4 4 7 5 4 3 6 4 4 5 6 5 \\ 7 6 7 6 7 7 6 7 6 4 7 7 6 6 5 6 7 7 6 4 7 7 7 4 7 4 7 7 6 \\ 7 7 9 7 6 7 7 4 7 7 7 3 7 3 7 5 5 7 3 5 5 5 5 7 7 3 3 3 3 \\ 9 6 9 6 8 8 8 5 7 7 7 5 9 5 8 8 5 9 3 5 6 5 6 9 8 2 3 2 2 \\ 7 7 9 7 6 7 7 4 7 7 7 3 7 3 7 5 5 7 3 5 5 5 5 7 7 3 3 3 3 \\ 5 6 5 2 2 6 6 5 5 5 5 3 3 5 7 5 3 5 5 6 5 5 5 5 4 5 3 4 5 \\ 4 5 5 6 5 6 7 5 6 6 6 6 5 5 5 6 5 8 5 6 7 5 8 5 5 7 3 3 3 \\ 9 9 5 5 5 7 7 7 5 5 7 5 3 1 3 3 1 7 5 5 5 3 5 7 5 5 1 3 3 \\ 8 9 8 7 7 7 5 5 5 5 5 5 5 5 7 5 5 7 7 7 7 7 7 5 5 5 5 5 5 \\ 8 8 8 8 5 6 6 5 5 5 5 6 6 5 5 6 6 5 6 5 6 7 7 5 5 5 6 6 6 \end{matrix}]$

(3) Calculate the grey evaluation weight vector r_ijk of the third-level indicators, construct the grey evaluation weight matrix R_ij of the second-level indicators, and calculate the evaluation value Q_ijk. $R_{11} = [\begin{matrix} 0.271 0.247 0.205 0.156 0.122 \\ 0.263 0.256 0.212 0.152 0.118 \\ 0.288 0.231 0.212 0.151 0.118 \\ 0.206 0.250 0.218 0.177 0.149 \\ 0.199 0.241 0.232 0.178 0.150 \end{matrix}]$ $R_{12} = [\begin{matrix} 0.231 0.282 0.214 0.153 0.119 \\ 0.226 0.276 0.219 0.157 0.122 \\ 0.169 0.217 0.257 0.200 0.156 \\ 0.195 0.251 0.244 0.174 0.136 \\ 0.189 0.242 0.244 0.183 0.142 \\ 0.204 0.262 0.235 0.168 0.131 \\ 0.155 0.199 0.230 0.234 0.182 \\ 0.197 0.223 0.228 0.199 0.154 \\ 0.147 0.188 0.251 0.219 0.194 \end{matrix}]$ $R_{21} = [\begin{matrix} 0.203 0.246 0.229 0.181 0.141 \\ 0.185 0.223 0.248 0.194 0.151 \\ 0.158 0.203 0.247 0.208 0.185 \\ 0.242 0.263 0.211 0.160 0.124 \\ 0.157 0.202 0.235 0.228 0.177 \\ 0.180 0.231 0.253 0.189 0.147 \\ 0.191 0.245 0.249 0.177 0.138 \\ 0.175 0.225 0.244 0.200 0.155 \\ 0.198 0.240 0.234 0.184 0.143 \end{matrix}]$ $R_{22} = [\begin{matrix} 0.208 0.238 0.237 0.178 0.139 \\ 0.194 0.234 0.238 0.188 0.146 \\ 0.146 0.188 0.238 0.234 0.194 \end{matrix}]$ $R_{31} = [\begin{matrix} 0.140 0.180 0.213 0.249 0.219 \\ 0.147 0.189 0.214 0.246 0.203 \\ 0.141 0.181 0.229 0.246 0.203 \end{matrix}]$

Evaluation value Q_ijk: Q₁₁₁ =5.783, Q₁₁₂ =5.793,

Q₁₁₃ =5.840, Q₁₁₄ =5.373, Q₁₁₅ =5.322;

Q₁₂₁ =5.701, Q₁₂₂ =5.654, Q₁₂₃ =5.081,

Q₁₂₄ =5.390, Q₁₂₅ =5.306, Q₁₂₆ =5.480,

Q₁₂₇ =4.822, Q₁₂₈ =5.225, Q₁₂₉ =4.745;

Q₂₁₁ =5.378, Q₂₁₂ =5.199, Q₂₁₃ =4.887,

Q₂₁₄ =5.678, Q₂₁₅ =4.863, Q₂₁₆ =5.216,

Q₂₁₇ =5.384, Q₂₁₈ =5.125, Q₂₁₉ =5.327;

Q₂₂₁ =5.396, Q₂₂₂ =5.284, Q₂₂₃ =4.716;

Q₃₁₁ =4.551, Q₃₁₂ =4.657, Q₃₁₃ =4.622.

(4) Calculate the gray evaluation weight vector b_ij of the second-level indicators, construct the gray evaluation weight matrix B_i of the first-level indicators, and calculate the evaluation value Q_ij. $B_{1} = [\begin{matrix} 0.238 0.247 0.216 0.165 0.134 \\ 0.186 0.234 0.237 0.191 0.153 \end{matrix}]$ $B_{2} = [\begin{matrix} 0.186 0.228 0.236 0.196 0.154 \\ 0.191 0.226 0.237 0.192 0.153 \end{matrix}]$ $B_{3} = [\begin{matrix} 0.142 0.183 0.220 0.247 0.208 \end{matrix}]$

Evaluation value Q_ij: Q₁₁ =5.580, Q₁₂ =5.223, Q₂₁ =5.192, Q₂₂ =5.215, Q₃₁ =4.608.

(5) Calculate the gray evaluation weight vector e_i of the first-level indicators, construct the total gray evaluation weight matrix E of the comprehensive objective, and calculate the evaluation value Q_i. $E = [\begin{matrix} 0.213 0.241 0.226 0.178 0.143 \\ 0.188 0.227 0.236 0.194 0.154 \\ 0.142 0.183 0.220 0.247 0.208 \end{matrix}]$

Evaluation value Q_i: Q₁ =5.411, Q₂ =5.197, Q₃ =4.608.

(6) Overall objective comprehensive evaluation results. According to the total gray evaluation weight matrix obtained, the gray comprehensive evaluation vector of the total evaluation target is calculated as: $Z = WE = (0 . 185, 0 . 222, 0 . 230, 0 . 200, 0 . 162)$

Comprehensive evaluation value of total evaluation objective: Q = ZI^T =5.131.

Table 5
Weights of indicators at all levels

First-level indicators Weight w_i Second-level indicators Weight w_ij Third-level indicators Weight w_ijk

WuLi U₁ 0.277 Environmental factors U₁₁ 0.517 National and local policy support U₁₁₁ 0.195

Industry development planning U₁₁₂ 0.192

Standard Specification for welding robot technology U₁₁₃ 0.112

Scientific research input level U₁₁₄ 0.362

Enterprise automation level U₁₁₅ 0.139

Technical factors U₁₂ 0.483 Welding quality U₁₂₁ 0.068

Welding efficiency U₁₂₂ 0.102

Adaptability to dynamic environment U₁₂₃ 0.041

Welding sensing technology U₁₂₄ 0.133

Seam tracking technology U₁₂₅ 0.131

Welding programming technology U₁₂₆ 0.133

Welding process database U₁₂₇ 0.133

Component standardization design U₁₂₈ 0.071

Upgrading and optimization of welding materials U₁₂₉ 0.188

ShiLi U₂ 0.517 Management factors U₂₁ 0.521 Formulation of technical operation procedures U₂₁₁ 0.140

Preparation of welding environment U₂₁₂ 0.092

Robot integration transformation U₂₁₃ 0.052

Qualification of welding process U₂₁₄ 0.140

Management of welding operators U₂₁₅ 0.288

Security management U₂₁₆ 0.053

Weld inspection and repair U₂₁₇ 0.098

Stacking management of welding materials U₂₁₈ 0.092

Equipment maintenance U₂₁₉ 0.045

Benefit factors U₂₂ 0.479 Economic benefit level U₂₂₁ 0.572

Environmental benefit level U₂₂₂ 0.207

Social benefit level U₂₂₃ 0.221

RenLi U₃ 0.206 Personnel and group factors U₃₁ 1 Technical cognition level of the construction unit U₃₁₁ 0.334

Professional level of operators U₃₁₂ 0.243

Skill training for operators U₃₁₃ 0.423

4.3 Result analysis

The comprehensive evaluation results show that the overall application maturity of the construction steel structure welding robot technology of the project is at the development level, indicating that the overall application level of the construction steel structure welding robot technology of the project is fine, but it is not mature enough and needs to be further improved. For the three levels of “WuLi - ShiLi - RenLi”, the maturity of the technology application is judged as development level, development level, between starting level and development level.

Among them, environmental factors scored the highest, indicating that the state, local, and enterprise pay attention to the basic environment needed to create the application of welding robot technology. The ranking of scores is followed by technical factors, benefit factors, and management factors, which shows that the enterprise attaches more importance to the relevant technology, process management system, and three aspects of benefits of welding robots. Enterprise improves welding quality, welding efficiency, and environmental adaptability through research on key technologies; through the consideration of three aspects of benefits, to ensure the significant improvement of some benefits; through the establishment of a management system, the work can be effectively connected, thus becoming more standardized. The lowest score of personnel and group factors indicates that the enterprise does not attach importance to the professional ability and related skills training that operators should have, and the basic knowledge of technology is limited.

4.4 Suggestions

Since the links are interrelated and cannot be short, there is a need to improve the weak links as well as the shortcomings. The key point to improve the application maturity of the construction steel structure welding robot technology should be the three-level index with low evaluation value.

In terms of environmental factors, the enterprise should increase investment in scientific research and improve its automation level.

In terms of technical factors, the focus of technical research is mainly on the upgrading and optimization of welding materials and the improvement of the welding process database.

In terms of management factors, we will strengthen the integrated transformation of robots and the management of welding operators and other related auxiliary work, so that all work in the process management system can cooperate with each other and improve the overall management efficiency.

In terms of benefit factors, we should not blindly pursue the maximization of economic benefits, but also coordinate the environmental and social benefits to achieving synchronous improvement.

In terms of personnel and group factors, in addition to the need to popularize the relevant knowledge of steel structure welding robots in the construction units, it is also necessary to pay attention to the professional level of operators and carry out pre-job skills training.

5 Conclusion

Through the exploratory research on the application maturity evaluation of steel structure welding robot technology, this paper designs an evaluation index system for the application maturity of steel structure welding robot technology, which is suitable for the actual situation and specific characteristics of China’s engineering projects, on the basis of learning from the capability maturity model and WSR methodology. In addition, the evaluation model of application maturity of building steel structure welding robot technology based on combination weight and multi-level gray theory is constructed. Finally, the scientific and feasibility of the model are verified through case analysis, which makes up for some deficiencies in the existing application research of building steel structure welding robot technology, and provides a more scientific method for evaluating the overall application level of building steel structure welding robot technology. The evaluation results obtained in this paper are basically consistent with the actual qualitative conclusions, and the methods adopted have also been verified in many pieces of literature in the field of architecture.

Of course, there are still some problems worthy of in-depth studies, such as how to deepen the evaluation index system and expand the scope of evaluation objects. Although the selection of evaluation indicators is based on the WSR methodology and capability maturity model, combined with a large number of literature evaluation standards and scholars’ research, it is still not comprehensive and authoritative. The application of welding robot technology for building steel structures is a dynamic development process. In the future development process, the evaluation indicator system needs to be synchronously revised and updated according to the actual situation and research progress. In addition, the research object of this paper is mainly the welding robot for domestic building steel structure projects. The evaluation model established is still limited to the evaluation of the technical application maturity of a single project. Because the technical application statuses of different projects are different, how to conduct a comprehensive evaluation of the technical application maturity of a certain region in China is our next work.

Conflicts of interest

The author declares that they have no conflicts of interest.

Footnotes

Acknowledgments

This work has been partially supported by two projects: the research and development project of the ministry of housing and urban-rural development (project number: 2020-K-129); the research project of philosophy and social sciences in Hubei province colleges and universities (project number: 21Y039).

References

Y.L.

, Lin

, Chen

S.B.

Application status and research development trend of welding robot , MW Metal Forming (08) (2010), 32–36.

Dai

W.Z.

, Yu

H.T.

, Wang

J.W.

Current status and development direction of welding robots for steel structures , MW Metal Forming (12) (2021), 7–12.

Guan

Research on the application of robot welding technology in modern architecture, International Journal of System Assurance Engineering and Management (2021), 1–10.

, Yu

, Zhong

, Lin

, Chen

Real-time seam tracking control technology during welding robot GTAW process based on passive vision sensor , Journal of Materials Processing Technology 212(08) (2012), 1654–1662.

Zhang

, Guo

J.K.

, Zhang

Q.Y.

The evaluation of Japanese housing industrialization , Construction and Architecture (03) (2018), 54–57.

H.L.

, Jiang

Comparison between China and Japan on welding robot and its development enlightenment , Construction and Architecture (09) (2019), 31–33.

Jiang

L.P.

, Xue

, Zou

, Zhang

W.Y.

Research and development on the all-position welding robot used for steel structure , Electric Welding Machine 37(08) (2007), 23–26.

Xue

, Zou

, Huang

J.Q.

, Liang

Y.J.

, Cao

J.F.

, Jiang

L.P.

Research and application on welding robot for steel structure field , Electric Welding Machine 43(05) (2013), 58–63.

Development and application of mobile welding robot for high altitude and long span steel structure, January 18). Retrieved from http://www.bipt.edu.cn/zhxw/162281.htm,

10.

Dai

W.Z.

, Jia

B.H.

, Zhang

J.P.

Welding demands for the informatization technology to high-strength steel structure , Electric Welding Machine 43(05) (2013), 48–51.

11.

Song

H.X.

Keywords for the future development of China’s robot industry— Interpretation of the robot industry development plan –, Automation Panorama (09) (2016), 30–31.

12.

J.F.

, Han

J.C.

, Li

J.L.

Overview for steel structure technology in the ten new technogies for construction industry Edition), Architecture Technology 49(03) (2018), 260–264.

13.

Miles

M.P.

, Karki

, Woodward

, Hovanski

Modeling of high speed friction stir spot welding using a lagrangian finite element approach, In: proceedings of the XII International Conference on Computational Plas- ticity: fundamentals and applications, CIMNE, (2013), pp.1238–1245.

14.

Stanciu

E.M.

, Pascu

, Roata

I.C.

Edge fillet laser welding of AISI 304 stainless steel, Solid State Phenomena 216 (2014), , 304–309.

15.

Kang

H.S.

, Suh

, Kim

T.H.

, Cho

T.D.

Quality moni- toring of laser welding, In: 2010 International Conference on Control, Automation and Systems (ICCAS 2010), IEEE, (2010), pp. 2144–2147.

16.

Jasnau

, Hoffmann

, Seyffarth

Nd: YAG-Laser-GMA-Hybrid welding in shipbuilding and steel construction, Lecture Notes in Control and Information Sciences 299 (2004), , 14–24.

17.

Tavares

, Costa

C.M.

, Rocha

, et al. Collaborative welding system using BIM for robotic reprogramming and spatial augmented reality, Automation in Construction 106 (2019), , 102825.1–102825.12.

18.

Moon

S.B.

, Hwang

S.H.

, Shon

W.H.

, Lee

H.G.

, Oh

Y.T.

Portable robotic system for steel H-beam welding, Industrial Robot: An International Journal 30 (03) (2003), 258–264.

19.

Dai

W.Z.

The demand trend of welding machine and welding materials for the development of building steel structure industry, MW Metal Forming(18) (2013), , 17–20.

20.

Zhang

F.R.

High efficiency welding technology of high-strength steel for building steel structure, MW Metal Forming(20) (2015), 19–20.

21.

Yang

Application of high efficiency welding and cutting technology of high strength steel in building steel structure, MW Metal Forming(20) (2015), , 13–14.

22.

Guo

J.C.

, Zhu

Z.M.

, Chen

M.H.

, Li

Q.Y.

Structural design and kinematics modeling of welding robot system for box-type steel structure, Transactions of the China Welding Institution 39 (08) (2018), , 32–37+130.

23.

Chu

C.X.

, Dai

X.T.

, Yang

X.D.

Assessment of and countermeasures to the needs of Internet of Things application in Chinese agricultural informationization:a case study of Southern Jiangsu area, (Social Science Edition) 13 (03) (2011), , 35–41.

24.

Wang

, Liu

J.H.

, Liu

Q.C.

, Zhou

M.Y.

Applicability Assessment for Technology of Low-pressure Pipeline Irrigation Projects in Southern China, Journal of Water Resources and Architectural Engineering 12(01) (2014), , 87–91.

25.

J.D.

, Tang

, Yang

M.J.

Risk Assessment of BIM Technology Application in EPC Project, conomy 31 (04) (2021), , 68–73.

26.

Wang

Y.T.

Risk Assessment of BIM Technology for Munici-pal Traffic Engineering Based on the Integrated Empowered Matter Element Model, M.A Thesis, Tianjin: Tianjin Uni- versity, (2018).

27.

L.W.

, He

, Sun

J.G.

, Huang

G.Y.

Evaluation of Comprehensive Utility of HIR Technology Based on Weighted TOPSIS Method, Road Machin- 1026 ery & Construction Mechanization 30(01) (2013), , 65–69.

28.

Han

H.K.

, Sun

G.Z.

Evaluation of BIM Technology Application Ability in Engineering Consulting Agency Based on Entropy Weight TOPSIS Method, Construction Economy 41(01) (2020), , 104–109.

29.

Ding

, Xia

Analysis of green building technology promotion based on practical application and evaluation–A case study of Chongqing area, Heating Ventilating & Air Conditioning 51(12) (2021), 56–62+32.

30.

Tang

F.G.

, Chen

Analysis on Regional Disparities in Technovation Capabilities: Framework, Measures and Evaluation, R&d Management(05) (2001), , 32–36+61.

31.

X.T.

, Ma

R.Q.

, Xu

, Zhao

The Benefit Evaluation Model of New Construction Technology Application Based on AHP, Construction Technology 41(16) (2012), , 52–55.

32.

S.L.

, Yu

Z.W.

, Fan

M.C.

Multi-layered and multi-dimensional suitability evaluation of tubular daylight guidance systems, Journal of Building Engineering 32(2020), 1–13.

33.

H.L.

, Li

Study on the Green Construction Bid Evaluation System— Based on Multilevel Gray Evaluation Method, Management(01) (2013), 20–23.

34.

Zhang

, He

Study on Classification and Applicability of Comprehensive Evaluation Methods, Decision 38(06) (2022), 31–36.

35.

Wendler

The maturity of maturity model research: A systematic mapping study, Information and Software Technology 54(12) (2012), 1317–1339.

36.

X.G.

Frame and Contents of SEI^′S Capability Maturity Model, Computer Applications (03) (2001), 1–5.

37.

G.F.

, Tan

, Shang

S.S.

The evaluation of building fire emergency response capability based on the CMM, International Journal of Environmental Research and Public Health 16(11) (2019), 1–15.

38.

Park

J.H.

, Shin

K.C.

, Lee

J.S.

Appraisal for communication Management Capability of PMIS in construction Projects utilizing Capability Maturity Model concept, Journal of Architectural Institute of Korea & Construction 19(07) (2003), 179–186.

39.

McCuen

T.L.

, Suermann

P.C.

, Krogulecki

M.J.

Evaluating award-winning BIM projects using the national building information model standard capability maturity model, Journal of Management in Engineering 28(02) (2012), 224–230.

40.

Kenneth

Organizational project management maturity model (Book Review), Project Management Journal 35(01) (2004), 59–60.

41.

Hsieh

P.J.

, Lin

The construction and application of knowledge navigator model (KNM ™): An evaluation of knowledge management maturity, Expert Systems with Applications 36(02) (2009), 4087–4100.

42.

Liu

S.F.

, Forrest

, Vallee

Emergence and development of grey systems theory, Kybernetes 38(7-8) (2009), 1246–1256.

43.

Zhou

X.P.

, Chen

J.M.

Research on Construction Supply Chain Risk Evaluation and Management Based on Multi-level Gray Evaluation Model, Journal of Engineering Management 30(02) (2016), 45–49.

44.

H.S.

, Han

Y.K.

Evaluation of Green Construction Scheme Based on Value Engineering Principle, Building Energy Efficiency 45(02) (2017), 117–121.

45.

Peng

W.R.

, Zhong

W.Q.

TO Study on Evaluating of Building Enterprise Informationization, Value Engineering 27(12) (2008), 121–123.

46.

, Huang

N.J.

A Comprehensive Evaluating Model Based on Multi-hierarchy Gray Theory, Journal of Sichuan University(Natural Science Edition) 42(05) (2005), 889–895.

47.

Zhang

C.J.

, Sun

D.C.

Some Concepts and Understandings about WSR, Systems Engineering 19(06) (2001), 1–8.

48.

, Li

H.L.

, Dong

S.Q.

Weapon SystemNetwork Security Assessment Based on CombinationWeighting and Fuzzy Gray Clustering, Fire Control & Command Control 45(09) (2020), 22–28.

Overall evaluation objective U	First-level indicators U_i	Second-level indicators U_ij	Third-level indicators U_ijk
Application maturity of welding robot technology for building steel structure U	WuLi U₁	Environmental factors U₁₁	National and local policy support U₁₁₁
			Industry development planning U₁₁₂
			Standard Specification for welding robot technology U₁₁₃
			Scientific research input level U₁₁₄
			Enterprise automation level U₁₁₅
		Technical factors U₁₂	Welding quality U₁₂₁
			Welding efficiency U₁₂₂
			Adaptability to dynamic environment U₁₂₃
			Welding sensing technology U₁₂₄
			Seam tracking technology U₁₂₅
			Welding programming technology U₁₂₆
			Welding process database U₁₂₇
			Component standardization design U₁₂₈
			Upgrading and optimization of welding materials U₁₂₉
	ShiLi U₂	Management factors U₂₁	Formulation of technical operation procedures U₂₁₁
			Preparation of welding environment U₂₁₂
			Robot integration transformation U₂₁₃
			Qualification of welding process U₂₁₄
			Management of welding operators U₂₁₅
			Security management U₂₁₆
			Weld inspection and repair U₂₁₇
			Stacking management of welding materials U₂₁₈
			Equipment maintenance U₂₁₉
		Benefit factors U₂₂	Economic benefit level U₂₂₁
			Environmental benefit level U₂₂₂
			Social benefit level U₂₂₃
	RenLi U₃	Personnel and group factors U₃₁	Technical cognition level of the construction unit U₃₁₁
			Professional level of operators U₃₁₂
			Skill training for operators U₃₁₃

First-level indicators	Weight w_i	Second-level indicators	Weight w_ij	Third-level indicators	Weight w_ijk
WuLi U₁	0.277	Environmental factors U₁₁	0.517	National and local policy support U₁₁₁	0.195
				Industry development planning U₁₁₂	0.192
				Standard Specification for welding robot technology U₁₁₃	0.112
				Scientific research input level U₁₁₄	0.362
				Enterprise automation level U₁₁₅	0.139
		Technical factors U₁₂	0.483	Welding quality U₁₂₁	0.068
				Welding efficiency U₁₂₂	0.102
				Adaptability to dynamic environment U₁₂₃	0.041
				Welding sensing technology U₁₂₄	0.133
				Seam tracking technology U₁₂₅	0.131
				Welding programming technology U₁₂₆	0.133
				Welding process database U₁₂₇	0.133
				Component standardization design U₁₂₈	0.071
				Upgrading and optimization of welding materials U₁₂₉	0.188
ShiLi U₂	0.517	Management factors U₂₁	0.521	Formulation of technical operation procedures U₂₁₁	0.140
				Preparation of welding environment U₂₁₂	0.092
				Robot integration transformation U₂₁₃	0.052
				Qualification of welding process U₂₁₄	0.140
				Management of welding operators U₂₁₅	0.288
				Security management U₂₁₆	0.053
				Weld inspection and repair U₂₁₇	0.098
				Stacking management of welding materials U₂₁₈	0.092
				Equipment maintenance U₂₁₉	0.045
		Benefit factors U₂₂	0.479	Economic benefit level U₂₂₁	0.572
				Environmental benefit level U₂₂₂	0.207
				Social benefit level U₂₂₃	0.221
RenLi U₃	0.206	Personnel and group factors U₃₁	1	Technical cognition level of the construction unit U₃₁₁	0.334
				Professional level of operators U₃₁₂	0.243
				Skill training for operators U₃₁₃	0.423