Quality Evaluation Approach for Prefabricated Buildings Using Ant Colony Algorithm and Simulated Annealing Algorithm to Optimize the Projection Pursuit Model

Abstract

There are problems with an inadequate quality assurance system and non-standard construction organization and administration while creating prefabricated buildings. There are currently fewer quality assessments employing prefabricated component combinations as the research focus, and the quality evaluation methodology is more subjective. We propose a method for evaluating the quality of prefabricated buildings using an ant colony algorithm and a simulated annealing algorithm to optimize the projection pursuit model: firstly, create a prefabricated building quality index system; secondly, questionnaires were distributed, tested for reliability and validity to avoid the influence of questionnaire subjectivity on the results, and structural equation modeling was used to calculate the weights of the quality influencing factors; thirdly, quantify the quality factors of prefabricated components by using the quality function development method, and construct a quality optimization model for the prefabricated component combinations; fourthly, use the ant colony algorithm to solve the quality optimization model to obtain a set of prefabricated component combinations to satisfy the quality requirements; and lastly, use a simulated annealing to optimize the projected pursuit method for evaluating the quality of prefabricated component combination solutions. The results show that (1) The use of optimization algorithms can successfully avoid the issue of a more subjective evaluation approach and increase the efficiency and accuracy of evaluation. (2) Residential Comfort (RC), Usage Durability (UD) and Structural Reliability (SR) have a substantially negative association, but Residential Comfort (RC) and Installation Stability (IS) have strong positive correlations. (3) Based on the magnitude of the vector of the ideal projection direction of the quality indicators, it was determined that the Installation Stability (IS) indicator had the greatest influence on the evaluation of the program, and the Structural Reliability (SR) indicator had the least influence on the program.

1. Introduction

1.1. Background of the Study

China’s population is aging, the construction industry has lost some of its attractiveness to young people, and labor is becoming harder to come by. A “dual-carbon” strategic objective has also been put up by China in the context of global energy conservation and emission reduction. As one of the industries with high energy use and emissions, the construction industry has to be transformed and upgraded, and prefabricated buildings have opened up new growth opportunities [1]. China is currently actively creating prefabricated buildings, and it is predicted that by 2025, prefabricated buildings will account for 30% of all new building space. But compared to cast-in-place building, prefabricated buildings’ construction sites and procedures have changed as a result of China’s late start. Prefabricated building construction involves multiple partners, which raises issues including a weak quality assurance system, a lack of standardization in construction organization and administration, and a lack of professionalism among construction employees. The quality of the prefabricated buildings will be severely hampered by this [2]. The prefabricated building industry continues to be concerned with quality. Using SEM-SDM, Li et al. assessed the safety risk of prefabricated building construction [3]. In an effort to enhance the management of quality for prefabricated buildings, Zhang et al. used ISM-BN to establish an evaluation model of the factors influencing the quality of as-assembled structures [4]. Zhang et al. used ISM-MICMAC to investigate the relationships between 23 components of prefabricated structures quality management [5]. As can be seen, quality issues continue to be a major consideration in the design of prefabricated buildings, making research into enhancing and evaluating their quality necessary.

1.2. Literature Review

1.2.1. Research on Quality Assessment of Prefabricated Buildings

When it comes to building technology and techniques, prefabricated concrete structures still differ greatly from conventional cast-in-place structures. The advantages of prefabricated buildings in terms of building functions and quality have been established, despite the fact that assembled concrete structures still have some safety and quality difficulties due to the nascent state of the technology [6]. Prefabricated components, along with the prefabricated component assembly scheme used, have a significant impact on the overall benefits of prefabricated buildings because they are the fundamental elements of prefabricated building [7]. The selection of prefabricated component combinations has a significant impact on whether a prefabricated building has a more reliable quality assurance after construction. Xia et al. examined the quality criteria during the three stages of manufacturing, shipping and storage, and lifting of the assembled structure [8]. Garay et al. used case studies of built buildings to evaluate the strength and caliber of prefabricated wood frame constructions [9]. As can be seen, investigations on the quality of prefabricated buildings seldom employ prefabricated components as the study object and instead tend to concentrate more on the prefabricated building as a whole. In this study, prefabricated component combinations are used as the research subject to analyze the quality of prefabricated buildings. This boosts the study’s methodical quality and thoroughness, broadens its reach, and makes it possible for a greater variety of potential applications for the study’s findings.

1.2.2. Ant Colony Algorithm

A variety of influencing factors will have an impact on the prefabricated building because it requires the use of many different kinds of prefabricated parts and components during the construction stage [7]. And as the collaborative design process progresses, more people will be involved in the construction phase. These influencing factors have a complicated interactions with one another and are related to and restricted by one another. As a result, the challenge of addressing prefabricated component combinations that fulfill a variety of quality criteria may be transformed into a multi-objective optimization solution problem. Intelligent algorithms, such genetic algorithms, particle swarm algorithms, and ant colony algorithms, perform well in addressing engineering optimization challenges as building scale complexity increases. Although genetic algorithms have produced some research findings in the fields of resource allocation for component production, optimal site layout, and production scheduling in the engineering field, most of their fitness functions are typically determined subjectively based on experience, which may lead to local optimization and thus deviate from the actual scenarios of the practice [10]. Particle swarm algorithms are related to genetic algorithms and are simpler than genetic algorithms, which are concise and easy to implement but can easily fall into local optima [11]. Ant colony algorithms have excellent search capabilities, and by using collective intelligence to evaluate building quality, they can identify the greatest design options and carry out the best quality assessment. Secondly, the ACO algorithm has self-organization and dispersion. The challenge in building quality evaluation may be broken down into several smaller problems, and numerous ant colonies can conduct the search simultaneously to speed up the solution process. Last but not least, the ACO algorithm has significant resilience, and in the evaluation of building quality, owing to the complexity and unpredictability of the evaluation issue, the ACO algorithm can effectively handle numerous changes and produce stable and dependable results. Afshar built a model, solved it using the ant colony method with several swarms, and linked the overall project quality level to the quality weighting of the sub-projects [12]. Reyes used the ant colony technique to solve the issue by discretizing the quality, cost, and schedule multi-objective optimization issue [13]. In conclusion, the ACO algorithm has the benefits of group intelligence, responding to nonlinear issues, having self-organization and distribution, as well as resilience in evaluating building quality, which may offer efficient solutions and optimize the process of evaluating building quality. As a result, in this paper, the prefabricated component combinations that satisfy the quality standards are solved using the ACO method.

1.2.3. Projection Pursuit Methods

After selecting the appropriate prefabricated component combination solutions, the quality optimization of those solutions must be evaluated. Currently, material element analysis, fuzzy analysis, gray correlation analysis, and hierarchical analysis are the most frequently utilized evaluation methodologies. Ranjbar et al. discovered the risk indicators of hazardous, earthquake-induced structures using the modified, hierarchical, fuzzy TOPSIS approach [14]. In order to assess the risk of assembled risk in building construction and scheduling, as well as to look at the method by which risks are transmitted, Fan et al. used hierarchical analysis [15]. The sustainability of SIP buildings in rural China was evaluated by Bai et al. based on AHP-gray correlation analysis, and they offer a guide to help builders select the optimal building structure for rural China [16]. Zhang et al. build the assessment system of lean knowledge management capabilities using the enhanced gray correlation analysis approach in order to precisely quantify the degree of lean knowledge management [17]. However, these assessment methods are more arbitrary, and different weight settings will result in various evaluation results. Additionally, the judges select the bulk of weight values based on their personal tastes. The projective pursuit (PP) approach is used in this study to evaluate the prefabricated component combinations.

As an objective assessment approach that does not need assigning weights, the projection pursuit method (PP) is commonly used in the evaluation and preference of multi-factors, etc. The research by Li et al. demonstrated the potential of the projection pursuit model as a tool for multi-factor clustering analysis and as a fresh approach to identifying agricultural surface source contamination areas [18]. For the purposes of defining agricultural surface source contamination regions in China, the study was based on the projection pursuit clustering model. Xu et al. used the sparrow search algorithm to enhance the projection pursuit model and assess the stability of the composite system of agricultural soil-water resources [19]. Tao et al. created a model to predict the filtering efficiency of cleaning tanks based on the projection pursuit approach, which served as a roadmap for cutting-edge, environmentally friendly irrigation technology [20].

1.2.4. Simulated Annealing Algorithm

In this paper, the objective function of the projection pursuit technique is improved using simulated annealing to obtain the best projection that faithfully captures the original data. The Simulated Annealing Algorithm (SA) replicates the thermodynamic process of high-temperature metal cooling in physics in order to discover the global optimal solution of the objective function at random. The local optimal solution can be probabilistically extracted from the ultimate convergence of the global optimum by starting at a certain beginning temperature, coupled with the continual drop in temperature parameters, paired with probabilistic leaps in the solution space. In order to improve the design of light-weight steel-framed structures in rural China, Zhou et al. colleagues applied the simulated annealing technique [21]. For constructed buildings, Liu et al. employed the simulated annealing approach to optimize the component assembly order [22]. In order to achieve the sustainable use of regional water resources, Wang et al. employed the simulated annealing approach to optimize the distribution of water resources in the area [23]. The simulated annealing approach, on the other hand, can leave the local optimum by obtaining the likelihood of deteriorating solutions. It has great convergence and solution efficiency. Therefore, in this paper’s simulated annealing technique, the projection pursuit model is optimized to evaluate the quality of prefabricated component combinations.

1.3. Problems and Main Contributions

In conclusion, the present study on the quality of prefabricated buildings has made some progress; however, the following problems persist: (1) When it comes to evaluating and optimizing the quality of prefabricated buildings, prefabricated component combinations are a less common research topic than full structures. (2) The method of assessing the quality of prefabricated buildings is more subjective, and the influence of the weights has a significant impact on the evaluation’s findings.

The primary contributions of this paper are (1) quantifying the prefabricated component quality index factors using the quality function development (QFD) method and creating a prefabricated component combination quality optimization model; (2) solving the prefabricated component combination quality optimization model using the ant colony algorithm to obtain the prefabricated component combination optimal Pareto solution; (3) assessing the quality factors of the prefabricated component combination optimal Pareto solution utilizing the simulated annealing optimization projection pursuit method.

2. Research Method

2.1. Evaluation Process

In order to create the prefabricated component combination in this paper, an ant colony method is used to solve a prefabricated component combination quality optimization model. The simulated annealing optimization projection pursuit approach is then utilized to assess the quality of the prefabricated component combination. The evaluation flowchart is shown in Figure 1.

2.2. Prefabricated Component Combination Solution Method Based on Ant Colony

The Ant Colony Algorithm (ACO), a heuristic algorithm, imitates ant foraging behavior. The Traveler’s Problem (TSP), which is akin to combinatorial optimization problems handled by simulating the activity of ants searching for food, is one such related optimization problem that it is particularly well suited for. Following are the procedures for using the ant colony method to solve the prefabricated component combination in this paper:

Step 1: Define the variables. Before starting the algorithm, initialize all parameters, including the ant population, component node pheromones, and heuristic function.

Step 2: Initialize the population by placing ants at random. Each ant represents a potential solution and is comparable to simulating the project once.

Step 3. Determine the likelihood that the ants will choose a particular path. Each ant chooses the next node of a construction block to be transported based on the pheromone concentration and visibility of each path, and then updates the path and distance.

Step 4. Update pheromone: After all ants have finished travelling, update the pheromone value between the nodes of the construction blocks in accordance with the ants’ paths and the paths that are shorter than the overall ideal.

Step 5. Repeat the moving and updating process: repeat Step 3 and Step 4 until the termination conditions (such as completing the greatest number of iterations or identifying the best solution) are met.

Step 6. Output the optimal solution: find the Pareto solution that satisfies the condition.

2.3. Simulated Annealing Algorithm to Optimize the Projection Pursuit Evaluation Model

In order to identify the optimum projection that accurately represents the original data, the simulated annealing algorithm is used in this research to maximize the objective function. The simulated annealing algorithm can be used to find the ideal projection pursuit parameters in the optimization of projection pursuit evaluation. The following are the steps of the simulated annealing algorithm to improve the projection pursuit evaluation:

Step 1. Define the problem: Define the decision variables and the objective function. The minimization of reconstruction error can be the objective function in a projection pursuit evaluation, and the decision variables can be different projection pursuit parameters like the number of projections, angular intervals, and so on.

Step 2. Initialization: initialize the simulated annealing algorithm’s settings, such as the starting temperature, cooling rate, stopping temperature, and other variables, in accordance with the needs of the task.

Step 3. Generate initial solution: create the initial solution—the projection pursuit parameters—at random or in accordance with prior knowledge.

Step 4. Calculate the objective function value of the initial solution: Calculate the objective function value of the initial solution and evaluate the projection pursuit using the initial solution.

Step 5. Iterative search: Iterative search is carried out in accordance with the existing temperature and cooling requirements. A fresh solution is produced with each iteration, depending on the previous one. This can be carried out by performing some sort of transformation operation on the current solution (such as perturbation, exchange, etc.).

Step 6. Determine whether to accept the new solution in accordance with the Metropolis criteria by calculating the value of the new solution’s objective function. The Metropolis criteria decide whether the new solution advances or, with a given probability, accepts the subpar solution. The objective function value is compared to a predetermined probability threshold to decide if the new solution will be accepted.

Step 7. Update the current solution: Using the Metropolis criterion, choose whether to accept the new solution. Update the existing solution to the new one if the new one is approved; otherwise, leave it as is.

Step 8. Update Temperature: according to the chosen cooling rule, update the current temperature.

Step 9. Judge stopping conditions: Depending on the circumstances, such as reaching the maximum number of iterations or reaching the stopping temperature, decide whether to end the search.

Step 10. Output result: consider the ideal parameter value for the evaluation of projection pursuit to be the optimal solution produced by the simulated annealing technique.

2.4. Quality Evaluation Model of Prefabricated Component Combination

2.4.1. Quality Evaluation Index System

The complexity of the influencing elements that determine the quality of prefabricated buildings will have an immediate impact on the researcher’s assessment of the quality of prefabricated buildings and the remedies they will propose [24]. This essay initially looks into the traits of assembly concrete construction, the building procedure, and several other topics. It then reads pertinent domestic and international literature to analyze, compares and contrasts the assembly construction process with the cast-in-place building construction process. And, lastly, through a review of the actual project site and expert interviews, further adjusts the quality parameters. After careful investigation and screening, the final quality index system provided in this work is shown in Figure 2.

This research presents 12 influencing factors and classifies them according to their category qualities into four key categories: Residential Comfort (RC), use durability (UD), Installation Stability (IS), and Structural Reliability (SR), as shown in Figure 2. Residential Comfort (RC), for example, contains tightness, waterproofness, and insulations. Each category has three sub-factors. In compared to traditional construction, the use of prefabricated components allows for the optimization of tightness, waterproofing, and insulations in terms of residential comfort indicators. Firstly, it can prevent unstable construction quality brought on by changes in the construction environment on the job site and, at the same time, ensure that the connection between the components is tight, improving the airtightness of the product as a whole, after strict inspection and testing during the production process. Secondly, as a result of special waterproofing treatments applied during the manufacturing process and the use of materials with good water-proofing properties, prefabricated components have high waterproofing performance after installation. This effectively prevents rainwater, groundwater, and other liquids from penetrating into the interior of the building. Finally, in order to increase the building’s thermal insulation performance, prefabricated components can also integrate thermal insulation materials during the fabrication process. This will limit heat conduction and dissipation. Overall, prefabricated parts can offer superior quality assurance and performance by utilizing airtightness, watertightness, and thermal insulation to the fullest extent possible through factory manufacturing and exacting quality control.

When it comes to the installation stability indicators of perpendicularity, flatness, and elevation control, prefabricated components have a great advantages. First of all, perpendicularity describes the amount to which a member deviates from the vertical. During the fabrication of prefabricated components, the perpendicularity of the members can be regulated using precise molds and precise measuring equipment. The overall structural stability and aesthetic appeal of the prefabricated building depend heavily on the regulation of verticality. If the prefabricated parts’ verticality does not satisfy the specifications, it could result in issues like tilting walls and uneven floor slabs after assembly, which could put the building’s use and structural integrity at danger. Secondly, the term, “flatness of prefabricated components”, describes the level of concavity and flatness of the component surfaces. Prefabricated components can be produced using cutting-edge machinery and technology, which can improve their construction quality and look. The prefabricated building’s look and ornamental effect are directly impacted by flatness. Prefabricated parts that are not flat enough may result in noticeable unevenness in the walls or floor, which will harm the decorative impact and may make it difficult to decorate the walls or install equipment. Finally, elevation control describes how far a component deviates from its intended height after installation. It is possible to guarantee that the elevation of each member satisfies the design requirements through accurate fabrication and stringent quality control. The flatness and levelness of the building’s overall structure are directly impacted by the good or poor regulation of elevation. The presence of uneven floor slabs in the built building and the visible sensation of steps between levels result from improper elevation control of prefabricated components, which has an impact on the building’s usability and safety. In conclusion, it is extremely important practically to assure the stability, appearance quality, and performance of the overall structure of the building to ensure that the verticality, flatness, and elevation control of prefabricated components match the requirements.

The durability of prefabricated components has the following considerations: firstly, ensuring the stability and durability of a building’s materials and structure during the production process; prefabrication ensures that they are more stable and reliable, reducing the risk of component damage, aging, and other issues. Secondly, the thermal insulation and energy-saving capabilities of prefabricated components are enhanced during manufacturing through the addition of thermal insulation materials and heat-insulating layers. These elements have the ability to significantly diminish heat conduction and dissipation, which lowers the building’s energy consumption and lowers running expenses. Finally, the precast materials used in production have excellent durability and aging resistance, and can withstand erosion, deformation, and damage from a variety of external environments, resulting in a longer building life and cheaper maintenance and reconstruction costs. In conclusion, prefabricated components offer a more dependable, affordable, and environmentally friendly building option, offering longer-lasting use value.

The structural reliability of prefabricated components is mainly reflected in the cast-in-place concrete’s strength, structural performance, and stability. Firstly, the cast-in-place concrete of prefabricated components can be precisely batched and cured in a factory setting, and the quality is more stable and dependable while the strength of the concrete is easier to control. Secondly, in order to improve structural performance, cast-in-place concrete for precast elements can be reinforced and steel bars can be organized in accordance with specific design criteria during the production process. Because of this, prefabricated components may be customized to fit the requirements of various building types, resulting in stronger, safer buildings. Last but not least, the consistency and stability of the concrete can be guaranteed by precise manufacturing and quality control of important parameters like water–cement ratios, batching proportions, and other parameters in a factory environment. Overall, the exact batching, production, and quality control procedures of cast-in-place concrete for precast components are largely responsible for its benefits in terms of strength, structural performance, and stability. Precast is able to offer a more dependable and high-quality building solution with excellent project quality and structural safety thanks to these benefits.

2.4.2. Quantification of Prefabricated Component Quality Indicators

To transform client expectations into precise design and development requirements in order to increase product quality and customer satisfaction, the Quality Function Development (QFD) technique uses a systematic methodology [25]. Building quality can be assessed using a variety of techniques, including statistical techniques, fuzzy mathematics, and hierarchical analysis. Each of these approaches has benefits and drawbacks of its own. Although statistical methods may be able to give a broad overview of the quality issue, they might not be able to identify the contributing variables [26]. While it is more dependent on data, fuzzy mathematics can handle some quality issues with hazy boundaries [27]. Hierarchical analysis can break difficult problems down into different layers, which clarifies the evaluation process, but it might also overlook certain crucial information [28]. The benefit of the Quality Function Deployment (QFD) technique, in contrast, is that it can be applied throughout the process in a systematic and targeted manner, enabling quality issues to be found and resolved at an early stage of the design. In order to measure the level of quality optimization when choosing different prefabricated component combination schemes for prefabricated buildings, this paper introduces the Quality Function Deployment (QFD) method for quantification. The QFD method’s concept is depicted in Figure 3.

The link between a product’s function and its quality attributes may be expressed using the Quality Function Deployment approach, as demonstrated in Figure 3. Owners and users of prefabricated buildings have unique criteria for the building’s safety and longevity, which QFD may break down into precise quality indicators to change client expectations. Meanwhile, prefabricated building construction requires a number of departments and links, and QFD can foster departmental coordination and cooperation as well as cross-departmental synergy. Ultimately, in order to increase the degree of quality and customer happiness, QFD can eventually gather and continually optimize the issues that arise during the construction and operation of assembly buildings. In conclusion, even if prefabricated building has some unique requirements and limits, QFD can be applied to the field everywhere.

The House of Quality is established in this paper based on the four components of the Quality Evaluation Indicator System: Residential Comfort (RC), Usage Durability (UD), Installation Stability (IS), and Structural Reliability (SR). And it links the Quality Evaluation Indicators to Engineering Measures. The degree of quality optimization of a process in comparison to traditional construction is indicated by the quality optimization contribution, Z_ij, which is rated using an expert grading technique on a scale from 1 to 5. This paper establishes the House of Quality based on the four aspects of Residential Comfort (RC), Usage Durability (UD), Installation Stability (IS), and Structural Reliability (SR) of the Quality Evaluation Indicator System, and corresponds the Quality Evaluation Indicators to the Engineering Measures. The quality optimization contribution, Z_ij, is scored using an expert scoring method on a scale of 1–5, indicating the degree of quality optimization of a process relative to conventional construction. The degree of correlation between the i-th process and the j-th indicator layer quality indicators is indicated by every value Z_ij in the quality house. The relationship matrix allows for the calculation of the proportion of each guideline layer quality indication optimization v_ih for each construction procedure.

$$v_{\mathrm{ih}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{m}}{w}_j{z}_{ij}}$$

(1)

where w_j is the weight coefficient of each indicator layer quality indicator and m denotes the number of indicator layer quality indicators contained in the quasi-side layer.

The main goal of constructing the quality house’s second layer is to establish a link between each pi construction process and type Xn. The prefabricated component receives a score of 1 if a procedure is performed to it and a score of 0 otherwise in the second layer’s quality house matrix, which is a 0–1 matrix. Through the building of the second layer of quality houses, the ideal contribution of various prefabricated components to each quality indicator S_n can be calculated, and the calculation formula is as follows:

$$S_{\mathrm{n}}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{i}}{\mathrm{g}}_{\mathrm{ni}}{v}_{\mathrm{ih}}}$$

(2)

where v_ih is the importance weight obtained from the first layer of the quality house, n is the number of components, and g_ni is the value of each item of the 0–1 matrix of the second layer of the quality house.

To build a high-quality home, the precast components may be examined to determine the quality metrics of each component. The quality optimization contribution of the prefabricated component combination solution is a superposition of the quality optimization contribution of the prefabricated components, and a higher quality optimization contribution index indicates a higher-quality combination solution.

3. Results and Discussion

3.1. Project Background

Figure 4 depicts the location of the project chosen for this research in Shenzhen, Guangdong Province. The building is a frame construction with three levels above ground. The more developed elements of the present assembly technology, such as frame columns, frame beams, laminated floor slabs, walls, and stairs, are chosen as the study object of combination optimization in this work. The following are the modeling presumptions:

(1)

Since prefabricated component combinations are the primary research object for this paper’s quality evaluation, the quality optimization contribution of the prefabricated building is calculated as the sum of the quality optimization contributions of the selected components, while the foundation, door, and window components that were not chosen are not taken into account.

(2)

The quality issues resulting from the choice of cast-in-place or prefabricated construction procedures for the components, as well as from the order in which the various components are assembled, are not taken into account in this paper.

The Quality Function Deployment (QFD) approach is used in this study to assess the level of quality optimization of prefabricated components, which first needs determination of the relative weight of each quality-influencing element.

A questionnaire was distributed to the field’s stakeholders in order to gauge the importance of the aspects. A five-point Likert scale was then used to grade the strength of the effect, with scores ranging from “1” to “5”. Online distribution was used to disseminate the study’s surveys. A total of 221 questionnaires were issued, and 197 of them were valid, giving the accuracy rate of 89.14%. Using SPSS 22.0, the questionnaire’s reliability and validity were also examined. The questionnaire’s Cronbach’s alpha coefficient was 0.779 > 0.6 and the CITC values were all higher than 0.5, indicating that the results were reliable and passed the reliability test. The scale’s KMO value was 0.754 > 0.5, and the Bartlett’s test of sphericity result is 0.000 < 0.05, making the scale valid and suited for factor analysis. The structural equation model of quality factors was established using AMOS software on the basis of this, and the data from the questionnaire survey were analyzed. The results are displayed in Figure 5 below:

The path coefficients of the standardized model are denoted by the numbers on the paths in Figure 5’s structural equation model of quality-influencing factors. As an example, the path coefficient of the quality indicator for living comfort is 0.66, similarly, the path coefficients of RC1, RC2, and RC3 for RC are 0.66, 0.90, and 0.78, respectively. By using the path coefficients of each indicator of structural equation modeling, it is possible to quantitatively analyze the factors influencing quality by comparing the strength of the relationships between various variables and representing the importance of the variables.

The following are the fitting results of the structural equation model as displayed in Figure 5: with a χ²/df = 1.6583.000, GFI = 0.953 > 0.8, AGFI = 0.927 > 0.8, RMSEA = 0.0490.08, and CFI = 0.982 > 0.9, the structural equation model fits the data well. All of the model’s fitting indices fall within acceptable bounds. As a result, this study quantifies the aspects that affect quality by computing the weighted average in the manners described below:

(1)

Let $A_i(i=1,2,3,4)$ be the contribution value of the first-level indicator to the research object, hereinafter referred to as weight 1, and let $B_i$ be the path coefficient between the research object and the first-level indicator, then the formula for calculating weight 1 is shown in Formula (3).

$$A_i=\frac{B_i}{{\displaystyle {\sum }_{i=1}^4{B}_i}}$$

(3)

(2)

Let $C_{i,j}$ be the contribution value of each secondary indicator to its first-level indicator, hereinafter referred to as weight 2, and let $b_{i,j}\left(j=1,2,\cdots ,k\right)$ be the path coefficient between the secondary indicator and the first-level indicator, then the formula for calculating weight 2 is shown in Formula (4).

$$C_{i,j}=\frac{b_{i,j}}{{\displaystyle {\sum }_{j=1}^k{b}_{i,j}}}$$

(4)

(3)

Let the contribution value of secondary indicators to the research object be A_j, hereinafter referred to as the total weight, which is calculated as shown in Formula (5).

$$A_j=A_i\times C_{i,j}$$

(5)

In summary, the results of the weights of the elements impacting quality are displayed in Figure 6 below by applying Formulas (3)–(5) to the standardized route coefficients of each indicator in the structural equation model.

The weights of the quality influencing factors are displayed in Figure 6 as a multi-layer circular pie chart that is split into two primary layers. The first-level indicators of quality impact factors and their weights are found in the inner layer, while the second-level indicators and their weights are found in the outer layer. Using durability as an example, the indicator weight for use durability is 0.2819. The indicator weights for the second-level-use durability indicators are 0.090 for UD1, 0.1004 for UD2, and 0.0915 for UD3. The other quality indicators are comparable. Using Figure 6, it is evident that the indicator of installation stability has the smallest weight of 0.0478, indicating that it has a lesser degree of influence on the quality factors, and the indicator of residential comfort has the largest weight of 0.3510, indicating that it has a greater degree of influence on the quality factors. The laminated floor slabs of the building’s first floor are used as an example in this paper to demonstrate how the quality house is established once the weights of the quality criteria have been determined. The results are displayed in

Table 1. Quality house scores for the first layer of laminated floor slabs.

Construction Process	Residence Comfort			Use Durability			Installation Stability			Structural Reliability
	RC1	RC2	RC3	UD1	UD2	UD3	IS1	IS2	IS3	SR1	SR2	SR3
	9.9%	13.5%	11.7%	9.0%	10.0%	9.2%	1.7%	1.7%	1.4%	11.0%	10.7%	10.2%
1	5	4	3	5	2			5		3		3
2							4		5
3								3
4										4	3
5								5		5	5
Degree of importance	1.389			0.65			0.359			2.482

1 Cast-in-place top slab support, stacking plywood support installation. 2 Laminated panel lifting. 3 Top plate installation of the upper layer of the structure support pre-buried parts. 4 Top plate reinforcement tying. 5 Pouring of top slab concrete.

below.

The first layer of the laminated floor slab quality house is represented by the scoring table in Table 1. On the left side of the table is the construction process for the laminated floor slabs; on the upper side are the quality indicators and their weights; on the lower side is the contribution to the optimization of the quality of the components obtained via aggregation; and on the table is the expert scoring for the contribution to the optimization of the quality. Using the residential comfort index as an example, the RC1 index score of stacked floor process 1 is 5, the RC2 index score is 4, and the RC3 index score is 3. And the other processes are not scored, indicating that the other processes cannot reflect the building’s residential comfort. The final summary was obtained as the optimization contribution to the quality index of the residential comfort of the stacked floor (1.389), and the other quality indexes are similar. With the first layer being constructed between component processes and quality indicators, and the second layer of quality established on the basis of learning the significance of process quality indicators. The second layer of quality for laminated floor slabs was established as shown in

Table 2. Quality house scores for the second layer of laminated floor slabs.

Type of Component	……	1	2	3	4	5	……	Degree of Importance
								RC	UD	IS	SR
Columns
Beam
Slab	0	1	1	1	1	1	0	1.389	0.65	0.359	2.482
Wall
Stairs

.

The scoring table for the second layer of the mass house with laminated floor slabs is shown in Table 2. On the left side of the table are the component types, on the top are the construction methods used for each component, and on the right side is a summary of the optimized contribution of the components. The application of the construction processes for the members is shown in the table. Consider the building of stacked floor slabs as an example. Only 1–5 construction procedures are required, hence the score is 1, while the remaining processes receive a score of 0. The summary of the quality optimization of the stacked floor slabs eventually results in the degree of RC being 1.389, the UD being 0.65, the IS being 0.359, and the SR being 2.482, with the other components being the same. The columns, beams, walls, slabs, and stairs of each story of the structure are sequentially numbered in this article for the purpose of simplifying calculations. The quality factors of a few construction components are measured in this article, and the quantification findings are displayed in Figure 7.

Figure 7 depicts a line graph of the prefabricated component quality’s optimal contribution. The horizontal coordinates represent the columns, beams, walls, slabs, and staircase components of various floors in turn. Vertical coordinates represent the magnitude of the weights, and the line with different colors represents the optimized contribution of the various quality indices. From Figure 7, it can be seen that there are differences in the optimization contribution of each member under different quality indicators, prefabricated columns have better durability in use, and prefabricated slabs and prefabricated walls have obvious advantages in terms of structural reliability. Finding an optimal method to make each quality index optimal at the same time is unachievable since the quality factors of the components compete with and constrain one another.

However, the structure must be viewed as a whole, and all indicators of the influence of quality must be taken into account simultaneously, necessitating a thoughtful selection of prefabricated component combinations. With regard to the four quality-influencing indices of resident comfort (RC), Usage Durability (UD), Installation Stability (IS), and Structural Reliability (SR), this study proposes a quality optimization model for prefabricated component combinations. This is the quality optimization model:

Objective function:

$$\left\{\begin{array}{l}\min RC=-{\displaystyle {\sum }_{i=1}^{n}R{C}_{i1}{X}_i + }R{C}_{i2}\left(1-X_i\right)\\ \min UD=-{\displaystyle {\sum }_{i=1}^{n}U{D}_{i1}{X}_i + }U{D}_{i2}\left(1-X_i\right)\\ \min IS=-{\displaystyle {\sum }_{i=1}^{n}I{S}_{i1}{X}_i + }I{S}_{i2}\left(1-X_i\right)\\ \min SR=-{\displaystyle {\sum }_{i=1}^{n}S{R}_{i1}{X}_i + }S{R}_{i2}\left(1-X_i\right)\end{array}\right.$$

(6)

Constraints:

$$\begin{array}{c}f\left(x\right)=\left\{\begin{array}{l}{X}_i=1,\mathrm{The} \mathrm{i}-\mathrm{th} \mathrm{component} \mathrm{selects} \mathrm{the} \mathrm{cast}-\mathrm{in}-\mathrm{place} \mathrm{construction} \mathrm{process}\\ X_i=0,\mathrm{The} \mathrm{i}-\mathrm{th} \mathrm{component} \mathrm{is} \mathrm{selected} \mathrm{for} \mathrm{the} \mathrm{prefabricated} \mathrm{construction} \mathrm{process}\end{array}\right.\\ R{C}^{*}\le RC,U{D}^{*}\le UD,I{S}^{*}\le IS,S{R}^{*}\le SR\end{array}$$

(7)

where RC*, US*, IS*, SR* represent the minimum values of the quality indicators Residential Comfort (RC), Usage Durability (UD), Installation Stability (IS), and Structural Reliability (SR), i.e., the most basic requirements for building quality.

3.2. Results Analysis

In this study, an ant colony is used to solve the prefabricated component combination quality model. We consider the relative weights of the various indicators in light of the case’s real circumstances, and we establish the minimum value of the quality indicator factors accordingly: RC* = 6.02, US* = 5.69, IS* = 1.39, and SR* = 8.82. The following values are used to set the ACO algorithm’s parameters: the number of loops (n) is set to 200, the number of ants (m) is 35, the importance of the pheromone (α) is 1.1, the importance of the heuristic factor (β) is 0.6, the strength of the pheromone (Q) is 15, and the volatility of the pheromone (p) is 0.15. The Pareto solution set diagram of the given prefabricated component is created using Matlab R2019b (64bit) programming and is displayed in Figure 8 below.

Each scatter in Figure 8 is an optimal solution in the Pareto solution set, which also represents the prefabricated component combinations that satisfy the constraints. The indicator values of the quality metrics of the prefabricated component combinations, RC, UD, and IS, can be determined by the position of the axes, whereas the magnitude of the indicator values of the SR is mapped by the position of the axes. The figure illustrates how the outcome of a multi-objective optimization solution is typically a group of optimal solutions rather than just one. There are obvious differences between the benefits of prefabricated component combinations in terms of various quality indicators, but there is also a certain correlation between them. In order to explore them, this paper draws a parallel coordinate diagram of quality indicators, as shown in Figure 9.

The parallel coordinate graph of the quality indicators of the prefabricated component combination is shown in Figure 9. The horizontal coordinate axis represents the quality indicators RC, UD, IS, and SR, while the vertical coordinate axis displays the interval value of the quality indicators. For instance, the RC value of the optimal solution indicator is primarily concentrated in the range of 6.03 to 7.17, and the other indicators are similar. According to the size of the RC value, the color of each curve, which represents a prefabricated component combination solution, fades from red to blue. For instance, when the RC value of the prefabricated component combination is 7.167, the values of UD, IS, and SR are 5.804, 1.598, and 9.14, respectively. The figure shows that there is a significant variation in the curve of the parallel axes of the Pareto solution set, which suggests that the prefabricated component combinations’ quality indicators are incongruous with one another and constrain one another. The curve’s trend indicates that if the value of the quality index RC of the Pareto solution set’s optimal solution is higher, the value of the quality index IS will also be higher, but the values of the quality indices, UD and SR, will be relatively lower, and vice versa. This demonstrates that there is a generally negative association between the Pareto solution set’s quality indicators. RC and UD, SR, and a generally positive correlation between RC and IS. There is some positive correlation between quality indicators RC and IS, since residential comfort is mostly dependent on the structural reliability of the building and installation stability can also influence the design and realization of residential comfort. The fact that structural reliability and durability of use are largely concerned with the stability and durability of the building may explain some of the negative link between RC and UD and SR. Use of stronger and more resilient materials can be required, increasing the building’s weight and cost. However, this design choice could have a negative impact on the residential comfort.

This work enhances the projection pursuit approach for evaluating the prefabricated component combination solutions in order to identify the prefabricated component combination solutions with the best quality. A set of prefabricated component combination solutions corresponds to each optimal solution in the Pareto solution set. The projected eigenvalues in the prefabricated component combination solution are calculated based on the initial algorithmic parameters, which are set as follows: the initial temperature T₀ = 1000, the termination temperature T_end = 0.0001, and the number of iterations n = 100. The projected eigenvalues in the solution are calculated using the optimal projection direction. MATLAB R2019b (64bit) software is used to run the application. The results of the top five predicted eigenvalue rankings in the solution outcomes are shown in Figure 10 below.

In Figure 10, the vertical coordinates indicate the evaluated values of the quality indicators; the horizontal coordinates are the top five evaluation schemes ranked by projected eigenvalues, and the PE value is the projected eigenvalue of the scheme. The predicted eigenvalue of scheme 1 in Figure 10 is 2.05, and the estimated values for the quality indicators of Residential Comfort (RC), Use Durability (UD), Installation Stability (IS), and Structural Reliability (SR), respectively, are 6.93, 6.66, 1.63, and 8.83. The other schemes are comparable. After solving the model, the optimal projection direction a* = (0.6863,0.7624,0.9913,0.0436), the vector of projection direction of quality indicator IS is the largest, and the vector of projection direction of quality indicator SR is the smallest. The optimal projection direction vector’s size indicates the evaluation indicator’s level of effect on the overall evaluation. A larger optimal projection direction vector suggests a greater level of influence. Therefore, it is clear that the SR indicator has the least impact on the program and that the IS indicator has the most impact on how the program is evaluated. This is primarily due to the fact that installation stability is essential to the overall functionality and quality of a building. Installation stability is the stability of a building’s whole structure and construction, and the degree of installation stability directly affects a building’s safety and load-bearing capacity. In other words, installation stability is what allows a building to be comfortable for its occupants, durable during usage, and structurally reliable. While each scheme has its own advantages and a quality index value that is near to one another, scheme 1 has the biggest characteristic projection value, 2.05, as can be seen in the image. The projection value of the sample in the best projection direction is indicated by the feature projection value in the projection tracing model. This value is used to evaluate the sample’s position or significance in the projected space, and the higher the value, the better the sample. Therefore, when utilizing the simulated analytic-optimization-projection-tracing dynamic model to evaluate quality, option 1 is the best choice. The prefabricated components combination option 1 for built buildings provides the greatest quality benefit.

4. Conclusions and Recommendations

This study has assessed the quality of prefabricated buildings with prefabricated component combinations as the research object in order to rationally and scientifically select the prefabricated component combinations that satisfy the quality requirements. The ant colony algorithm is used to solve the issue after establishing a quality optimization model based on the four types of influencing factors: Residential Comfort, Use Durability, Installation Stability, and Structural Reliability. In the collection of Pareto solutions that meet the requirements, each ideal solution corresponds to a prefabricated component combination solution. The projected pursuit model has been optimized using the simulated annealing process in order to assess the prefabricated component combinations. And the optimal prefabricated component combination has been found using the projected eigenvalues. The following are the paper’s conclusions:

(1)

When utilized to resolve the combinatorial optimization problem, the ant colony algorithm has a good solving impact and the capacity to explore the global optimal solution. By using the simulated annealing algorithm to optimize the projection pursuit method for evaluating the quality of prefabricated components of prefabricated buildings, the issue of more subjective evaluation methods can be effectively avoided, and the evaluation results can be made more scientific and reasonable.

(2)

Residential Comfort (RC) and Installation Stability (IS) have a somewhat positive correlation, whereas Residential Comfort (RC) and Usage Durability (UD) and Structural Reliability (SR) have a moderately negative correlation.

(3)

It is determined that the Installation Stability (IS) index has the most influence on the evaluation of the program, and the Structural Reliability (SR) index has the least influence on the program, based on the magnitude of the optimal projection direction vector.

The following recommendations are given in order to raise the caliber of prefabricated buildings as a result of the research for this paper:

(1)

We should consider the prefabricated building’s assembly stability and apply a consistent design and production technique in order to maximize accuracy and stability of assembly. Establish a quality management system and conduct quality inspections to guarantee that the quality of each assembly component meets the standards. In order to ensure that each component is linked and installed in the right place, the assembly process is also carefully watched.

(2)

Throughout construction, high-quality prefabricated building materials should be selected to ensure their durability and service life. Likewise, pay attention to the construction process to provide a strong and reliable connection between the pieces and avoid aging and material shedding. Routine inspection and maintenance should be carried out to keep machinery and parts from malfunctioning and to guarantee that the facility can be operated regularly.

(3)

When it comes to residential comfort, consider the design of the house type, rationally arrange the space layout, and provide a comfortable living environment. Consideration should be given to the home’s soundproofing, ventilation, and heat retention concurrently.

(4)

Strict control should be exerted, during manufacture, over the materials chosen and the processing procedures employed in order to ensure the strength and stability of the components. Reasonable structural connection procedures should be employed during construction to guarantee coordination and complementarity between components. Regular structural safety checks should be carried out to identify and address any potential structural problems and ensure the building’s safety.