A DPSIR Framework to Evaluate and Predict the Development of Prefabricated Buildings: A Case Study

Abstract

Prefabricated building construction is an important method of enhancing construction productivity and promoting sustainable development in the construction industry. Evaluating and predicting the development performance of prefabricated buildings will contribute to identifying and implementing the most effective responses to promote prefabricated building technologies. Based on the Drives–Pressures–States–Impacts–Responses (DPSIR) framework, 14 evaluation indexes are determined to evaluate the development level of prefabricated buildings. The entropy weight method was used to determine the weight of the evaluation index, and the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method with improved grey correlation was applied to comprehensively evaluate the trend of the index. The grey model (GM(1,1)) was developed to predict the development trend of prefabricated buildings. The development of prefabricated buildings in Shandong province, China, is employed as a case to apply the developed method and investigate development experiences. The results demonstrate that the case has achieved significant progress and has great potential in promoting the use of prefabricated buildings. The development recommendations include developing a policy and regulation system, strengthening a prefabricated building talent pool, and enhancing the investment in technological innovation. This study innovatively formulated the evaluation and prediction system based on the DPSIR, TOPSIS and GM(1,1) models, which could be used for evaluating development performance between social and environmental factors among various cause-effect relationships.

1. Introduction

Sustainable development is highly required in the building construction industry worldwide. That is because buildings have a significant impact on the environment due to higher material consumption, energy use, greenhouse gas emissions, waste generation, and lower construction productivity and technological advancement. For example, labor productivity growth in the construction industry lags behind manufacturing and the overall economy globally [1]. The building construction industry has been transformed by numerous studies and practices that have advanced construction technologies and methods in order to promote sustainable development. Prefabricated construction is an innovative and sustainable practice in the building industry aimed at promoting sustainable development [2].

A prefabricated building, also known as an integrated house, is constructed off-site in a manufacturing plant and then transported to the building site in sections. The building pieces are prefabricated before being transported to the site for prefabricated. During the 19th century in Europe, a cluster of modernist architects from France opted for prefabricated buildings as a new alternative to the conventional architectural model. In the wave of industrialization, prefabricated buildings gradually became the main way of its development and gradually matured under the witness of time. The reason why prefabricated buildings have been able to stay and develop to this day is due to their unique advantages of their own. Compared with traditional construction, the prefabricated building is more scientific, rigorous, site-specific, and can be optimized and improved according to the special geographic environment of different regions; because it is not poured at the construction site and other construction, the prefabricated building is much less polluting to the surrounding environment compared to traditional construction. Therefore, construction companies in developed Western countries, such as Sekisui Construction Company in Japan and Pulte Group in the United States, started the research of prefabricated buildings in the 1950s, and the scale of the prefabricated construction industry in Western countries has now reached a very high level.

According to the statistics of the Ministry of Housing and Urban-Rural Development, in 2015, the national new prefabricated construction area was 0.73 billion square meters, accounting for 4.7% of the new construction area of the year. Starting in 2016, China’s industrialization of construction stepped into a period of rapid development, and the national new prefabricated construction area for the year was 114 million square meters, a year-on-year increase of 56%. In 2017, China’s new prefabricated construction area accounted for 8.4% of the new construction area of the year. The proportion of newly constructed housing areas in China has reached 8.4%. Previous studies have investigated the evaluation of prefabricated buildings. However, there are still some research gaps that require further study. Firstly, some studies have analyzed the impacts of prefabricated buildings from a single perspective (e.g., sustainability, social, economic, etc.), which have shown the feasibility of prefabricated buildings. However, there is a lack of in-depth research regarding the comprehensive analysis of prefabricated buildings. Secondly, in the existing process of constructing the comprehensive evaluation and index system of prefabricated buildings, the applicability of the evaluation indexes is insufficient, and in the process of calculating the weights of the comprehensive evaluation, there is insufficient consideration of the connection between the results of the evaluation indexes and the ideal solution. Therefore, it is necessary to consider the applicability of the selected indicators and scientifically analyze the intrinsic connection between the evaluation results. Finally, although existing studies have found many evaluation indicators for prefabricated buildings, there is a certain subjectivity in the selection of these indicators. Therefore, in the process of indicator selection, the influence of subjective factors should be avoided as much as possible to prevent the impact on the research. In order to promote the development of prefabricated buildings, the evaluation of the development of prefabricated buildings is crucial. This evaluation could provide valuable insights to enhance the development of prefabricated buildings and make them more reliable. Moreover, the question regarding the future of prefabricated buildings is expected to be answered by aiming to demonstrate the development directions and strategies for prefabricated buildings. Therefore, this research will formulate a DPSIR framework including the factors of the drivers (D), pressures (P), states (S), impacts (I), and responses (R) to evaluate and predict the development of prefabricated buildings. The framework is used to develop evaluation and prediction methods. A case is used to implement the new methods and provide recommendations for promoting prefabricated buildings.

2. Literature Review

2.1. Evaluation of the Development of Prefabricated Buildings

Many countries are applying and promoting prefabricated buildings, and the requirements and proportion of prefabricated buildings vary from country to country. Japan is the earliest country to build residential components in factories, and its building ratio is 90% [3]. The United States has put forward the requirements of personalization and comfort for its prefabricated buildings, and its building ratio is 90% [4]. France has pioneered industrialized buildings, and its building ratio is 85% [5]. In these typical countries, the United States’ prefabricated building development scale is more rapid. The United States, since the outbreak of the energy crisis, began the road of industrialized construction of prefabricated buildings because of its energy savings, cost reduction, and other advantages, and the United States of industrialized construction complements each other, promoting the United States construction industry’s vigorous development. According to statistics, in 2010, the U.S. prefabricated building market size was about 22 billion U.S. dollars, followed by a rising year by year, a growth rate of 13% or so, and as of 2020, the market size is about 53 billion U.S. dollars.

In order to promote the development of prefabricated buildings from qualitative research to quantitative research, it is necessary to evaluate the development level of prefabricated buildings. Many studies have done a lot of research on evaluation indexes, evaluation methods and models, which have been supplemented and improved. Song et al. proposed a structural equation modeling and intuitionistic fuzzy analytic hierarchy process based on the evaluation system of prefabricated building construction suppliers to evaluate prefabricated building construction suppliers [6]. Han et al. constructed a system dynamics model of prefabricated building policies and performed scenario simulation to reveal the influence of different types of policies on the mechanism of different types of policies on the development system of prefabricated buildings [7]. Zhou et al. established an external benefit evaluation index system from economic, environmental, and social dimensions. They also designed a quantitative evaluation model for prefabricated buildings and studied the feasibility of the model empirically [8]. Park et al. established a system dynamics model to simulate the realistic development of the construction industry in Singapore and analyzed the need for introducing policies qualitatively and quantitatively [9].

2.2. DPSIR Model

The DPSIR model is a commonly used evaluation indicator system in environmental systems. This model was created to measure indicators of the environment and sustainable development. It analyzes the interaction between human and environmental systems from a system analysis perspective [10]. The DPSIR model categorizes evaluation indicators that describe a natural system into five types: drivers, pressures, states, impacts, and responses. Each type contains multiple indicators [11].

The DPSIR model consists of four significant elements: economic, social, resource, and environmental. Among them, “drivers” refer to the potential causes of changes in the subject of study, mainly referring to socio-economic activities [12] and industrial development trends; “pressures” refer to the impact of human activities on the resources and environment in their immediate vicinity and the natural resources and environment, which are the direct pressure factor of the research subject [13], mainly in terms of the intensity of resource and energy consumption; “states” refer to the condition of the research subject under the above-mentioned pressure; “impacts” refer to the influence of the state of the system on the quality of the research subject and socio-economic development [14]. The “responses” process indicates the countermeasures and active policies that humans have adopted in the process of promoting sustainable development [15]. Figure 1 shows the relationship among the five types of indicators.

Scholars conducted studies and made improvements to the Pressures–States–Responses (PSR) model, resulting in the creation of the DPSIR model. This new model has clearer logical relationships and accurately reflects the interrelationships among the economy, society, and environment in a systematic way. For example, Zhou et al. used the DPISR causal effects framework to investigate the interaction between environmental issues and human activities and used it to assess low-carbon cities [16]. Pagan et al. used meta-analysis and the DPSIR framework to develop a four-stage sustainability tool to study river basins and ecosystems [17]. Quevedo et al. used the DPSIR framework to analyze data from interviews to qualitatively assess blue carbon ecosystems [18]. Zhao et al. used the DPSIR model to construct an evaluation index system suitable for the green development of the Yellow River Basin as a strategic task to promote high-quality green development in the Yellow River Basin [19]. Song et al. used the DPSIR model to construct a low-carbon city evaluation index system and index assessment of low-carbon cities through this system [20]. Shao et al. developed an innovative quantitative modeling method, which includes the DPSIR model, and applied it to assess the urban ecological security in Tianjin [21].

2.3. The Prediction Method of the GM(1,1) Model

The grey forecasting method is used to predict systems with unknown uncertainties [22]. It is focused on predicting a certain range of grey processes related to time series. Social, environmental, and economic characteristics can be combined to identify the numerical relationships among the various influencing factors and thus forecast future trends using the grey system theory. The GM(1,1) model is the most widely used of the grey forecasting models, and the basic principle of this model is to eliminate the randomness and volatility among the underlying data. In making the base forecast of a certain time series, a set of new data series with a clear trend is generated by accumulating data at one time, and a grey model is established according to the growth trend of the generated new data series so as to arrive at the forecast results.

The GM(1,1) model enables accurate forecasting even with limited sample data. Zhang et al. developed a non-isometric GM(1,1) model to monitor the settlement of buildings [23]. Wang Based on the total population of Jilin Province Statistical Bulletin, the GM(1,1) model was combined to predict the population of Jilin Province in the next ten years [24]. Zhao et al. analyzed the energy consumption and structure of Hebei Province and established a GM(1,1) prediction model to predict the energy consumption and structure of Hebei Province from 2014 to 2021 [25]. Li et al. used the GM(1,1) model to forecast the energy demand in Shandong province from 2005–2015 and compared the results with the actual results, obtaining data with very high accuracy [26].

In summary, although the DPSIR model is often applied in the ecological environment system, it is less applied in the research field of prefabricated building development level. Therefore, this paper constructs the evaluation index system of the development level of the prefabricated buildings in a case based on the DPSIR model. Due to the need for objectivity in the selected evaluation indexes, the grey correlation is further improved by the Technique Order Preference Similarity to an ideal Solution method (TOPSIS). TOPSIS is a commonly used comprehensive evaluation method and can make full use of the information from the original data to accurately reflect the gaps between the evaluation schemes [27]. Because the GM(1,1) model can be applied to long-term prediction, this paper applies the GM(1,1) grey prediction model to scientifically predict the level of prefabricated building development. It provides a certain reference basis for the research related to the construction industry.

3. Research Design and Methodology

In this study, a research methodology was designed to examine the level of development in the field of prefabricated buildings. Figure 2 explains the logical framework of the method, which consists of four steps. The first step is to construct an evaluation index system from the DPSIR model. The second step is the evaluation index data processing. The data were collected and standardized by consulting statistical yearbooks and reports on the development of prefabricated buildings. The third step is to calculate the comprehensive score. This step is divided into two parts. First, the thesis uses the entropy method of the objective assignment method to assign weights to the evaluation indexes of the prefabricated buildings to avoid errors from the subjective assignment method. Second, the TOPSIS method is applied to calculate the comprehensive score C, which is used to determine the level of development of prefabricated buildings. The fourth step is the development level prediction. The GM(1,1) prediction model is used to predict the development level of prefabricated buildings.

3.1. Construction of Evaluation Index System Based on DPSIR Model

The study combines the relevant literature on sustainable development in the construction industry, the industrialization of construction, and the development of prefabricated buildings. The literature was mainly sourced from the Web of Science, and the keywords searched were prefabricated buildings, development level, and construction industrialization. Three principles were followed in the process of indicator selection. First, the evaluation indexes should reasonably reflect the current stage of development of prefabricated buildings and meet the development requirements of prefabricated buildings [28]. Second, the selection of evaluation indicators for prefabricated buildings should be done from a holistic perspective. That is, the evaluation indicators should reflect the development status of prefabricated buildings in the industry from different aspects, and the correlation between each indicator and the influence of the indicator on the overall evaluation results should be considered when selecting each indicator. Third, the research should be based on the original evaluation indexes of prefabricated buildings combined with independent innovation to predict the development of prefabricated buildings accurately [29]. Finally, 14 indicators from the five dimensions of DPSIR were identified.

Table 1. Evaluation indicators of the development level of prefabricated buildings.

Serial Number	Factor Name	Characteristic	Indicator Source
1	GDP per capita (D1)	+	[30]
2	Population density (D2)	−	[31]
3	Total construction industry output (D3)	+	[32]
4	Labor productivity (P1)	+	[33]
5	Building construction area (P2)	+	[34]
6	Residential area per capita (P3)	+	[35]
7	Energy consumption in the construction industry (P4)	−	[36]
8	Newly started prefabricated area (S1)	+	[37]
9	Ratio of prefabricated buildings to the new construction area (S2)	+	[38]
10	Value added of the construction industry as a proportion of GDP (I1)	+	[39]
11	Disposable income per inhabitant (I2)	+	[40]
12	Number of employees at the end of the year (I3)	+	[41]
13	Number of industrial bases (R1)	+	[42]
14	Number of companies (R2)	+	[43]

shows the reference summary of indicators.

3.2. Determination of Index Weights

The data collected on the evaluation indicators for the development of prefabricated buildings varies in terms of units and magnitudes. Hence, not processing them will make carrying out the subsequent analysis impossible, so the thesis standardizes these data using the polar difference method. For the selected evaluation indexes of prefabricated buildings, assigning different weights will have a greater impact on the final results. Thus, choosing the appropriate weighting method in the process of determining the weights is particularly important. In the study, the entropy weight method of the objective assignment method was used to assign weights to the evaluation indexes of the prediction of the development of the prefabricated building to avoid errors from the subjective assignment method [44]. The main steps are as follows.

(1)

Determine the value of X_ij′ after normalization of the original data X_ij.

If a large value of the evaluation indicator represents a high level of development of prefabricated buildings, then the indicator is a positive indicator, which is normalized by the following formula:

$${r^{\prime }}_{xi}=\frac{r_{xi}-\mathit{min}\left(r_i\right)}{\mathit{max}\left(r_i\right)-\mathit{min}\left(r_i\right)}$$

(1)

If a small value of the evaluation indicator represents a high level of development of prefabricated buildings, then the indicator is negative, and its standardization formula is as follows:

$${r^{\prime }}_{xi}=\frac{\mathit{max}\left(r_i\right)-r_{xi}}{\mathit{max}(r_i)-\mathit{min}(r_i)}$$

(2)

where X = (X_ij)_m*n (i = 1, 2, …, m, j = 1, 2, …, n), assuming that there are m objects to be evaluated and n evaluation indicators for each object. max(r_i) denotes the maximum value in the group, min(r_i) denotes the minimum value in the group, and r′_xi denotes the normalized data.

(2)

Calculate the weight of the jth indicator in year i:

$$Pij=X^{\prime }ij/{\sum }_{j=1}^m{X}^{\prime }ij$$

(3)

(3)

Calculate the entropy value of the jth indicator e_j:

$$ej=-k{\sum }_{i=1}^{m}Pij\times \mathit{ln}(Pij)$$

(4)

(4)

Calculate the entropy weight of the jth indicator:

$$\beta j=1-ej/\sum _{j=1}^{m}1-ej$$

(5)

3.3. Calculation of Comprehensive Evaluation Index

The main steps of the TOPSIS evaluation method based on improved grey correlation are as follows.

(1)

Calculate the weighted judgment matrix:

$$R=\left[\begin{array}{ccc}{X^{\prime }}_{11}\ast W_1& \cdots & {X^{\prime }}_{1n}\ast W_n\\ ⋮& \ddots & ⋮\\ {X^{\prime }}_{m1}\ast W_1& \cdots & {X^{\prime }}_{mn}\ast W_n\end{array}\right]$$

(6)

(2)

Based on the weighting matrix with the optimal and worst solution, calculate the grey correlation coefficient:

$${\xi }_j^{+}=\frac{\begin{array}{c}min\\ j\end{array}\begin{array}{c}min\\ i\end{array}\left|r_j^{+}-r_{ij}\right|+\rho \begin{array}{c}max\\ j\end{array}\begin{array}{c}max\\ i\end{array}\left|r_j^{+}-r_{ij}\right|}{\left|r_j^{+}-r_{ij}\right|+\rho \begin{array}{c}max\\ j\end{array}\begin{array}{c}max\\ i\end{array}\left|r_j^{+}-r_{ij}\right|}$$

(7)

$${\xi }_j^{-}=\frac{\begin{array}{c}min\\ j\end{array}\begin{array}{c}min\\ i\end{array}\left|r_j^{-}-r_{ij}\right|+\rho \begin{array}{c}max\\ j\end{array}\begin{array}{c}max\\ i\end{array}\left|r_j^{-}-r_{ij}\right|}{\left|r_j^{-}-r_{ij}\right|+\rho \begin{array}{c}max\\ j\end{array}\begin{array}{c}max\\ i\end{array}\left|r_j^{-}-r_{ij}\right|}$$

(8)

where the optimal solution vector is $r^{+}=\left\{r_1^{+},r_2^{+},\dots ,r_n^{+}\right\}$, and the worst solution vector is $r^{-}=\left\{r_1^{-},r_2^{-},\dots ,r_n^{-}\right\}$. ${\xi }_j^{+}\left(i\right)$ is the correlation coefficient of the jth indicator to the jth best indicator of the optimal solution series in year i and ${\xi }_j^{-}\left(i\right)$ is the correlation coefficient of the jth indicator to the jth worst indicator of the worst solution series in year i. $\begin{array}{c}min\\ j\end{array}\begin{array}{c}min\\ i\end{array}\left|r_j^{+}-r_{ij}\right|$ and $\begin{array}{c}max\\ j\end{array}\begin{array}{c}max\\ i\end{array}\left|r_j^{+}-r_{ij}\right|$ represent the two-level minimum and the maximum difference, respectively. ρ is the correlation coefficient, which generally takes the value of 0.5.

(3)

Calculate the combined distance:

$$\left\{\begin{array}{c}{Y}_i^{+}=\alpha D_i^{+}+\beta B_i^{-}\\ Y_i^{-}=\alpha D_i^{-}+\beta B_i^{+}\end{array}\right.,$$

(9)

where $\alpha +\beta =1$ and $\alpha ,\beta \in \left[\mathrm{0,1}\right]$ taking $\alpha =\beta =0.5$. d_i is the grey correlation. b_i is the Euclidean distance. $D_i^{+}$, $D_i^{-}$, $B_i^{+}$, and $B_i^{-}$ are dimensionless processed data, respectively.

(4)

Calculate the composite score of prefabricated buildings:

$$C_i=\frac{Y_i^{+}}{Y_i^{+}+Y_i^{-}},$$

(10)

where C_i is the comprehensive evaluation index of prefabricated buildings in year i, i = 2015, 2016, …, 2020.

Based on Zhang [45], Luo [46], and other scholars in prefabricated buildings, the study divided the development level of prefabricated buildings into five levels, from high to low. The CI value is between 0 and 12.0, and the closer to 12.0, the higher the degree of the development level of prefabricated buildings and vice versa, as shown in

Table 2. Shandong province prefabricated development degree table.

Level	Composite Index Values	Level of Development
I	0–0.3	Low level of development
II	0.3–0.6	Lower level of development
III	0.6–1.0	Medium level of development
IV	1.0–6.0	Higher degree of development
V	6.0–12.0	High degree of development

.

3.4. GM(1,1) Prediction Model

The main process is as follows.

(1)

Let the original non-negative data series be the following:

$$X^{\left(1\right)}=\left\{x^{\left(0\right)}\left(1\right),x^{\left(0\right)}\left(2\right),\dots ,x^{\left(0\right)}\left(n\right)\right\}$$

(11)

where $X^{\left(0\right)}\left(t\right)\ge 0,t=1,2,3,\dots ,n$.

(2)

Establish the GM(1,1) whitening differential equation for $X^{\left(1\right)}$ as follows:

$$\frac{d{x}^{\left(1\right)}}{dt}+\alpha x^{\left(1\right)}=\beta$$

(12)

where $\alpha$ is the development coefficient, and $\beta$ denotes the amount of grey action. Both are coefficients to be solved. $\alpha$ has a valid interval of (−2,2), and the matrix $\widehat{\alpha }={\left[\alpha ,\beta \right]}^T$ composed of $\alpha$ and $\beta$. After solving $\alpha$, $\beta$, the predicted value of $X^{\left(0\right)}$ can be found.

Use the least squares to find the grey parameter $\widehat{\alpha }$:

$$\widehat{\alpha }={\left[\alpha ,\beta \right]}^T={\left(B^{T}B\right)}^{-1}{B}^{T}Yn$$

(13)

Substitute $\widehat{a}$ into the differential equation $\frac{d{x}^{\left(1\right)}}{dt}+\alpha x^{\left(1\right)}=\beta$ and solve; cumulatively reduce the above results to yield the predicted value of the following:

$${\widehat{x}}^{\left(0\right)}\left(t+1\right)={\widehat{x}}^{\left(1\right)}\left(t+1\right)-{\widehat{x}}^{\left(1\right)}\left(t\right)=\left(1-e^{\widehat{\alpha }}\right)\left[x^{\left(1\right)}\left(1\right)-\frac{\beta }{\mathsf{\alpha }}\right]e^{-\widehat{\alpha }t}$$

(14)

(3)

Model testing

Model testing is carried out through post hoc tests, and the accuracy of the model is determined by the C-value and P-value together.

Table 3. Grey prediction model accuracy test criteria.

Model Accuracy Level Determination	The Posterior Test Difference Ratio C	Small Error Probability P
Level 1 (good)	C ≤ 0.35	P ≥ 0.95
Level 2 (pass)	0.35 < C ≤ 0.5	0.8 ≤ P < 0.95
Level 3 (barely pass)	0.5 < C ≤ 0.65	0.7 ≤ P < 0.8
Level 4 (unqualified)	C > 0.65	P < 0.7

shows the detailed accuracy criteria.

$$C=\frac{S_2}{S_1},P=\left\{\epsilon \left(k\right)-\overline{\epsilon }<0.6745S_1\right\},\overline{\epsilon }=\frac{1}{n}\epsilon (k).$$

(15)

where S₁ and S₂ are the standard deviation of the original series and the standard deviation of the residuals, respectively.

4. Case Study

4.1. Case Background and Data Collection

Shandong Province, located in East China, is one of the provinces in China where the development of prefabricated buildings started earlier. The province has made great achievements by actively exploring the road of vigorously developing prefabricated buildings, so as the object of this case study, it can fully demonstrate the development of prefabricated buildings, and based on the results of the study, it can provide development suggestions for the prefabricated building industry. During the “13th Five-Year Plan” period, the province started to construct 112 million m² of prefabricated buildings, ranking fifth in the country. In addition, seven pilot provinces were approved for national steel structure prefabricated housing construction, with the total number of pilot demonstrations ranking first in the country. In 2020, more than 40 million m² of new prefabricated buildings have been built in the province, accounting for nearly 25% of new buildings in cities and towns.

Through field research and reviewing the Statistical Yearbook of Shandong Province 2015–2020, the Prefabricated Building Development Report of Shandong Province and authoritative data websites. We then learned that the cost of scientific research investment in prefabricated buildings in 16 cities accounted for the total operating income in 2020, of which Zibo accounted for the largest share at 13.51% and Heze only 0.85%. This result indicates a large gap in regional scientific research investment. Second, the provincial industrial bases were examined and divided into three categories: component production, integrated application, and scientific research and development (R&D). Industrial bases are prefabricated building-related enterprises with clear development goals, a good industrial base, advanced and mature technology, strong R&D, and innovation capability. They are also able to play a demonstration leading and driving role, mainly including design, construction, parts production, and science and technology R&D. At present, the main focus is on parts production, and the number is unevenly distributed. Jinan has the most industrial bases (31), whereas Liaocheng has the least, with only one. Figure 3 depicts the specific distribution.

4.2. Analysis of Comprehensive Evaluation Results

First, according to the data collected from 2015 to 2020, the entropy weight method (Formulas (1)–(5)) is used to assign entropy weights to the evaluation indicators screened in Table 1. The entropy weights of the evaluation indexes were obtained, as shown in

Table 4. Objective weight values of evaluation indicators for the development level of prefabricated buildings in Shandong province.

Guideline Layer	Objective Weights	Indicator Layer	Objective Weights
Drive force indicator (D)	0.1999	GDP per capita (D1)	0.0658
		Population density (D2)	0.0594
		Total construction industry output (D3)	0.0747
Pressure indicator (P)	0.2540	Labor productivity (P1)	0.0790
		Building construction area (P2)	0.0672
		Residential area per capita (P3)	0.0505
		Energy consumption in the construction industry (P4)	0.0573
Status indicator (S)	0.1851	Newly started prefabricated area (S1)	0.1182
		Ratio of prefabricated buildings to new construction area (S2)	0.0669
Impact indicator (I)	0.2268	Value added of the construction industry as a proportion of GDP (I1)	0.1030
		Disposable income per inhabitant (I2)	0.0659
		Number of employees at the end of the year (I3)	0.0579
Response indicator (R)	0.1432	Number of industrial bases (R1)	0.0593
		Number of companies (R2)	0.0839

.

Second, based on Table 2 and the data of 2015–2020 prefabricated building indicators in Shandong province, the TOPSIS method with improved grey correlation was used to calculate the composite score and obtain the composite score C value (Formulas (6)–(10)).

Table 5. Comprehensive score of evaluation indicators of the development level of prefabricated buildings in Shandong province from 2015 to 2020.

Year	2015	2016	2017	2018	2019	2020
Overall rating C	0.0418	0.2096	0.3969	0.5237	0.7317	0.7745

shows the results.

Then, the comprehensive score of prefabricated buildings in Shandong province from 2015 to 2020 was graded, as shown in

Table 6. Shandong province prefabricated building development level division.

Year	2015	2016	2017	2018	2019	2020
Overall rating	0.0418	0.2096	0.3969	0.5237	0.7317	0.7745
Development level	I	I	II	II	III	III

.

As can be seen from Table 4, Table 5 and Table 6, the comprehensive development index of prefabricated buildings in Shandong province has been improving, from 0.0418 in 2015 to 0.7745 in 2020, and the development grade has risen from I to III, reflecting that the development of prefabricated buildings in Shandong province tends to be on an upward trend in general. This shows that Shandong province has actively responded to the requirements of the national policy of vigorously developing prefabricated buildings, which has led to the good development of prefabricated buildings in Shandong province through the efforts of the government, enterprises and people. By comparing the pressures indicators and impacts indicators, it is found that the development trend of prefabricated buildings in Shandong province is similar to these two indicators, both of which are in the trend of growth. The reason for this phenomenon is that in the evaluation index system of the development level of prefabricated buildings in Shandong province, the weights of the pressures and impacts indicators account for a relatively large proportion, reaching 0.2540 and 0.2268, respectively. In the pressure indicators, the labor productivity (P₁), the building construction area (P₂), and the consumption of energy in the construction industry (P₄). Among the impact indicators, the added value of the construction industry accounts for the proportion of GDP (I₁) and the per capita disposable income of residents (I₂). These indicators have a greater degree of influence on the development of prefabricated buildings in Shandong province. Labor productivity refers to the efficiency of prefabricated building products produced by laborers during the working period, and its size represents the maturity of prefabricated buildings in Shandong province in terms of technology. The larger the labor productivity, the better the development of prefabricated buildings in Shandong province; the larger the area of prefabricated building construction, the greater the support for prefabricated buildings in Shandong province, which indicates that prefabricated buildings can be well developed in Shandong province; construction industry The larger the proportion of added value in GDP is, the larger the output value of prefabricated buildings in Shandong province is, which in turn reflects the good development of prefabricated buildings in Shandong province. Therefore, these indicators can reflect the development of prefabricated buildings in Shandong province, so in the future development process, construction enterprises should actively correspond to the construction industry development goals issued by the government, improve the quality of enterprise housing construction area, and reduce the consumption of energy in the construction industry. National and local governments should introduce appropriate policies to improve labor productivity and enhance the regional economy so that the per capita disposable income increases, thus improving the happiness index of the residents.

4.3. Indicator Classification Evaluation Results

Table 7. Comprehensive weighting of the development level of prefabricated buildings in Shandong province.

Year	2015	2016	2017	2018	2019	2020
D	0.0593	0.0626	0.0843	0.1107	0.1409	0.1406
P	0.0655	0.1196	0.1926	0.2006	0.1763	0.1086
S	0.0000	0.0183	0.0389	0.0766	0.1263	0.1852
I	0.0098	0.0431	0.0995	0.1344	0.1662	0.1851
R	0.0000	0.0231	0.0579	0.0819	0.1001	0.1431
Combined weights	0.1346	0.2667	0.4733	0.6043	0.7098	0.7626

displays the weights of integrated weight indicators for each guideline level pertaining to prefabricated buildings in Shandong province between 2015 and 2020. The overall trend of the drive indicators is rising, and a relatively large increase was observed during 2016–2019. The change in pressure indicators is relatively large, showing a rapid upward trend during 2015–2018 but declining significantly after 2018. The state indicators and impact indicators show an overall upward trend, and the response indicators have a decreasing trend after 2019. This result indicates that the development of prefabricated buildings in Shandong province has flourished with policy support and achieved good results. Among them, the construction area of prefabricated buildings continues to increase, the proportion of the added value of the construction industry to GDP keeps rising, and the number of industrial bases and enterprises expands year by year. However, with continuous development, the energy consumption and the remaining capacity of the construction industry remain high.

4.4. Development Forecast of the Prefabricated Building in Shandong Province

The comprehensive score of the evaluation index of the development level of prefabricated buildings in Shandong province from 2015 to 2020 was selected as the initial value to prevent excessive errors and improve the accuracy of data prediction results. Moreover, the GM(1,1) prediction model was applied to predict the development of prefabricated buildings from 2025 to 2030 according to Equations (11)–(15). According to the above modeling steps, the program modeling calculation was carried out by MATLAB R2016a software, and the accuracy of the GM(1,1) model was tested by the posterior difference test method. The results are compared in Table 3. The prediction results show $\alpha$ = −0.2598, $\beta$ = 0.2501, and the prediction model is x⁽¹⁾(t + 1) = 1.004 4e^{0.259 8t} − 0.9627.

The accuracy test results show the posterior difference test GM(1,1) model C = 0.2162, P = 1. According to the accuracy test criteria of the grey prediction model in Table 3, the model design is satisfied. That is, the model can accurately predict the development status of prefabricated buildings in Shandong province.

Table 8. Predicted development level of prefabricated buildings in Shandong province in 2025–2030.

Year	2025	2026	2027	2028	2029	2030
Overall rating	3.0872	4.0031	5.1906	6.7303	8.7268	11.3156
Development level	IV	IV	IV	V	V	V

shows the comprehensive rating of the development level of prefabricated buildings in Shandong province from 2025 to 2030 according to the above model. The forecast results show that the development of prefabricated buildings in Shandong province from 2025 to 2030 shows a significant upward trend. The comprehensive development index is expected to reach 3.0872, 4.0031, 5.1906, 6.7303, 8.7268, and 11.3156, which is in line with the development center of the construction industry during the “14th Five-Year Plan” period, including the future development plans and goals of Shandong province.

5. Discussion and Recommendations

The promotion of prefabricated buildings is particularly important to the development of the construction industry and the national economy [47]. The results of the research on prefabricated buildings in Shandong province show that the good development of its prefabricated buildings has benefited from responding to the government’s call for strong policy support. However, as a dynamic and complex grey system, prefabricated building is affected by various factors, such as the environment and socio-economic conditions in the development process. It needs to be continuously optimized to ensure its stable development. Therefore, through the study of case experiences, the following suggestions to promote the development of prefabricated buildings are put forward so that the prefabricated buildings can develop well and sustainably.

5.1. Developing a Policy and Regulation System

A policy and regulation system plays a crucial role in the development of prefabricated buildings and is an important support for the steady development of prefabricated buildings. In response to the national call, Shandong province has issued a series of policy systems. For example, in 2013, the Ministry of Housing and Construction issued the 12th Five-Year Plan for the Development of Green Buildings and Green Ecological Areas, proposing to accelerate the formation of an industrialized building system throughout the country. In 2016, a number of policies were published to promote the development of prefabricated buildings, such as the Suggestions on Accelerating the Development of Prefabricated Buildings and the Development Plan for Prefabricated Buildings in Shandong Province (2018–2025) and a series of design standards and construction specifications. These policies and regulations have greatly promoted and facilitated the application of prefabricated buildings.

(1) Strengthening policy guidance and support. Shandong province can advance policy guidance and support by formulating more specific policies for the promotion of prefabricated buildings, with clear objectives and measures, in order to increase the awareness and enthusiasm of construction enterprises and developers for prefabricated buildings.

(2) Financial subsidies. For enterprises and projects adopting prefabricated building technology, Shandong province can implement financial subsidies for prefabricated buildings and give certain financial subsidies to encourage their enthusiasm. For example, when the prefabrication rate reaches a certain standard, it can be given preferential treatment in land transfer, etc.

(3) Tax incentives. As prefabricated buildings have a large upfront investment, Shandong province can give certain tax incentives to prefabricated buildings and set up different levels of incentives according to the degree of prefabrication of prefabricated buildings. For example, VAT reduction and income tax concessions could encourage enterprises and developers to adopt prefabricated building technology.

5.2. Strengthening a Prefabricated Building Talent Pool

Prefabricated building is different from the traditional construction method, which requires higher professional skills of the construction personnel. In the whole process of prefabricated building construction, it not only requires project management and construction professionals to have a systematic and comprehensive understanding of the process of the whole construction project but also requires them to skillfully apply new technologies such as BIM. Therefore, it is to strengthen a prefabricated building pool to enhance the development performance.

(1) Establishment of professional training programs. The government can organize the industry stakeholders such as universities, training institutes, and construction companies to set up the Construction Industry Modernization Education Alliance and the Provincial Prefabricated Building Expert Committee and develop a special training program for prefabricated buildings to train professionals in design, production, construction, and other areas.

(2) Strengthening industrial linkage. The government can encourage the linkage and development of the construction industry and linked industries to establish industrial chains and clusters and attract skillful talents to work in prefabricated building-related jobs.

(3) Strengthening industry exchanges. Shandong province can strengthen industry exchanges within the construction industry, encourage technical exchanges and cooperation between enterprises, improve the overall technical level of the industry, and strengthen the talent pool.

5.3. Enhancing the Investment in Technological Innovation

Science and technology play important roles in promoting the development of prefabricated buildings. Enhancing the investment in scientific and technological innovation consists of the improvement process of prefabricated building design, production, and construction. Particularly, the government and enterprises could financially support the innovations through the below two pathways.

(1) Investment in the innovations of prefabricated buildings. For enterprises, the investment in innovations can improve their technical level and competitiveness in the construction industry, thus bringing more benefits. The government should set up special funds for the research and development of new technologies for prefabricated buildings every year and make enterprises willing to spend more energy and resources on the innovation of prefabricated buildings through reasonable guidance. In addition, the government should also increase the reward for innovation achievements to promote the innovation of new technologies and promote the high-quality development of prefabricated buildings in Shandong Province.

(2) Promoting the application of digital and intelligent construction technologies. Digital technologies, including BIM technology and 3D printing technology, are used to realize digital management and full life-cycle management of prefabricated buildings. For example, Vanke Golden Area International Center adopts BIM technology for design, production, and construction management, realizing digital management and collaborative work of construction information. Intelligent manufacturing technologies include automation, robotization and other technologies used to improve manufacturing efficiency and quality control of prefabricated buildings. For example, Shandong Defeng Heavy Industry Co., Ltd. has adopted automated production lines and robotization technologies for the manufacturing and processing of prefabricated building components, improving production efficiency and product quality.

6. Conclusions

In this study, we constructed an evaluation index system for the development of prefabricated buildings based on the DPSIR model. The TOPSIS method with the improved grey correlation was developed to obtain comprehensive weight values for evaluating the development performance of prefabricated buildings. A prediction model based on the GM(1,1) model for the development index of prefabricated buildings was formulated to estimate the future development trend. The development of prefabricated buildings in Shandong province was employed as the case to investigate the evaluation and prediction system and methods.

The DPSIR evaluation system was developed in this study. The highest weight index is the Pressure index, which consists of labor productivity, building construction area, and residential area per capita. The second-highest weight index is the Impactors, which consists of the indicators of the value added of the construction industry as a proportion of GDP, disposable income per inhabitant, and the number of employees at the end of the year. The third-highest weight index is the Drivers index, including the indicators of GDP per capita, population density, and total construction industry output. Following it, the Statuses index comprises the indicators of newly started prefabricated areas and the ratio of prefabricated buildings to new construction areas. The index with the least weight is the responses index, consisting of the number of industrial bases and the number of companies. In the case study of the Shandong province, the indicators of the drivers, states, and impacts show an overall rising trend, and the weight of indicators of the pressures and impacts is relatively large, reaching 0.2540 and 0.2268, respectively. This indicates that Shandong province has achieved the vigorous development of prefabricated buildings. Among them, the construction area of prefabricated buildings continues to increase, the proportion of the added value of the construction industry to GDP keeps rising, and the number of industrial bases and enterprises expands year by year. Moreover, the overall development of prefabricated buildings in Shandong province from 2015 to 2020 is on an upward trend. Moreover, the development level has risen from I to III, with an upright development status. The recommendations are provided for promoting the development of prefabricated buildings, consisting of developing a policy and regulation system, strengthening a prefabricated building talent pool, and promoting investment in technological innovation.

The article enriches the theoretical achievements in the field of prefabricated building development. This paper introduces the DPSIR model to establish the evaluation system for the development level of prefabricated buildings. The article combined the entropy weight method with the TOPSIS method to comprehensively determine the comprehensive weights of the evaluation indexes of the development level of prefabricated buildings, which are in line with the DPSIR model, showing the relationship between social development and environmental resources. Furthermore, this paper predicts the development of prefabricated buildings through the GM(1,1) model and identifies reasonable suggestions to promote the development of prefabricated buildings in the future. However, the research still has some limitations. In determining the development evaluation indexes, the applicability of the reference standards of the evaluation indexes may be inadequate. The selected index may not completely cover all the factors of the development performance. In calculating the comprehensive evaluation index, the weights should be considered, combining subjective and objective. Future research is expected to select additional representative evaluation indexes and methods to study the development of prefabricated buildings. For example, the evaluation system can be established by qualitative methods such as questionnaires and interviews.