## 4 Investigation and Analysis  
### Analysis of Influencing Factors Based on BPNN-DEMATEL Model  
In order to better analyze the factors affecting the promotion of prefabricated housing in Hainan Province, 25 experts with at least 2 years of experience in prefabricated housing management and research were invited to score the mutual influence between the primary and secondary factors in this survey. They were government-related personnel (6 people), enterprise practitioners (12 people), some university experts (4 people) and prefabricated housing users (3 people) who have been engaged in prefabricated housing for many years in Hainan Province, and their academic qualifications were all above junior college. Likert 5-level scale assignment (0 = \"very unimportant\", 1 = \"unimportant\", 2 = \"no impact\", 3 = \"important\", 4 = \"very important\") was used to score each primary indicator factor and secondary indicator factor. This survey lasted nearly 2 months. After sorting out the questionnaires, 19 valid questionnaires were finally obtained, and the questionnaire recovery rate reached 76%. The statistical results of the working years and unit distribution of the 19 experts in the field are shown in Table 4. SPSS 26 software was used for a consistency test, and the Cronbach reliability coefficient was 0.913 > 0.8; the single measurement in the intraclass correlation coefficient was 0.919 > 0.75; and the average measurement was 0.908 > 0.75, and both were significant levels, indicating that the survey data can provide data support for the model construction and empirical analysis of this article. In this paper, the scoring results of the 19 experts on the secondary index factors were recorded as \(\mathbf{M}_{19\times 20}\), and the scoring results on the primary index factors were recorded as \(\mathbf{N}_{19\times 20}\). The original scoring results were standardized by Formula (1) to obtain the matrix \(\overline{\mathbf{M}}_{19\times 20}\) and the matrix \(\overline{\mathbf{N}}_{19\times 20}\). \(\overline{\mathbf{M}}\) was used as the input layer of the BPNN model, and \(\overline{\mathbf{N}}\) was used as the output layer. The code was written with the help of Matlab2021b software. Through multiple tests and comparisons within the range of the number of hidden layer nodes, it was found that the training effect is best when the number of hidden layer nodes is 13, so the number of hidden layer nodes was determined to be 13. Matlab software was used to write the BPNN-DEMATEL model code, and the tansig function was selected as the transfer function between the BPNN input layer and the hidden layer, and the purelin function was selected as the transfer function between the hidden layer and the output  
Figure 2: The relationship between the key factors affecting the promotion of prefabricated housing. layer. The initial learning rate was set to 0.05, the maximum number of training times was 1000 times, and the training accuracy was required to be 0.001. The code was run to train the BPNN until the network structure was stable. On this basis, we obtained the weight matrices \(\mathbf{U}\) and \(\mathbf{V}\) between the input layer and the hidden layer, and between the hidden layer and the output layer. We used Formula (5) to find the overall weight matrix \(\mathbf{B}\), and Formula (6) to find the overall weight vector \(\mathbf{B}^{\prime}\):  
Using Formula (7), we could obtain the direct correlation matrix \(T\) between the influencing factors of the promotion of prefabricated housing in Hainan Province. (See Table 5.)  
Equation (8) was used to normalize \(T=[t_{ij}]20_{\times 20}\) to obtain the normalized matrix \(\mathbf{G}=[g_{ij}]20_{\times 20}\). According to Formula (9), the comprehensive correlation matrix \(Y=[y_{\bar{y}}]20_{\times 20}\) of the evaluation index was established.