# Dynamic Quality Monitoring System to Assess the Quality of Asphal Concrete Payement
## 3 Coupling Model Based on Multidimensional Data Source and Asphalt Pavement Construction Quality
### Selection of the Evaluation Method for Asphalt Pavement Construction Quality
#### 3.2.2 Determination of Weight of Asphalt Pavement Construction Quality Evaluation Index  
This study uses the method of combining subjective and objective perspectives to calculate the comprehensive weight of the index.  
(1) Subjective weighting method based on AHP  
According to the evaluation index system shown in Figure 5, the method is divided into three levels, namely: Target level, criterion level and scheme level. Combined with expert opinions, the judgement matrix \(A\) is established by using the 1-9 scale method. The  
Figure 5: Digital construction quality evaluation index system of asphalt pavement.  
feature vector \(W\) corresponding to the maximum eigenvalue \(\lambda_{max}\) of the judgment matrix is calculated and normalized as the objective weight vector \(w^{\prime}=\left(w_{1}^{\prime},w_{2}^{\prime},\ldots,w_{n}^{\prime}\right)^{T}\) of the index [46; 47; 48].  
\[A=\left(a_{ij}\right)_{n\times n}=\left[\begin{array}{cccc}a_{11}&a_{11}& \ldots&a_{11}\\ a_{21}&a_{21}&\ldots&a_{21}\\ \ldots&\ldots&\ldots&\ldots\\ a_{n1}&a_{n2}&\ldots&a_{mn}\end{array}\right] \tag{5}\]  
where \(a_{ij}\) is the importance of index \(i\) over index \(j\), and \(a_{ij}=\frac{1}{a_{i}}\).  
In order to verify the rationality of the judgement matrix, it is essential to calculate the consistency index \(CI\) and consistency ratio \(CR\) according to Formulas (6) and (7). The consistency of the judgment matrix requires \(CR<0.1\), and the weight is valid.  
\[CI=\frac{\lambda_{\text{max}}-n}{n-1} \tag{6}\]  
\[CR=\frac{CI}{RI} \tag{7}\]  
(2) Objective weighting method based on EW  
The entropy weight method uses entropy to reflect the uncertainty of information [49; 50; 51]. The information content of the index is inversely proportional to the entropy. There are \(m\) samples and \(N\) evaluation indexes. The initial decision matrix is \(X=\left(x_{ij}\right)_{m\times n}\). After standardization, the decision matrix \(R=\left(r_{ij}\right)_{m\times n}\) is obtained.  
\[X=\left[\begin{array}{cccc}x_{11}&x_{12}&\ldots&x_{1n}\\ x_{21}&x_{22}&\ldots&x_{2n}\\ \ldots&\ldots&\ldots&\ldots\\ x_{m1}&x_{m2}&\ldots&x_{mn}\end{array}\right] \tag{8}\]  
\[R=\left[\begin{array}{cccc}r_{11}&r_{12}&\ldots&r_{1n}\\ r_{21}&r_{22}&\ldots&r_{2n}\\ \ldots&\ldots&\ldots&\ldots\\ r_{m1}&r_{m2}&\ldots&r_{mm}\end{array}\right] \tag{9}\]  
According to Formula (10), the entropy of item j is calculated:  
\[E_{j}=-\frac{1}{\ln(n)}\sum\limits_{i=1}^{m}r_{ij}\ln r_{ij} \tag{10}\]  
According to Formula (11), the objective weight of indexes are calculated:  
\[\omega^{\prime\prime}=\frac{1-E_{j}}{k-\sum\limits_{k=1}^{n}E_{k}} \tag{11}\]  
(3) Subjective and objective coupling weight  
The combination weight of the index is determined by coupling AHP with the EW method, which cannot only take account of the experience of experts, but also must effectively avoid subjectivity of weight. This is to reasonably evaluate the pavement quality and thereby more accurately reflect the actual situation of the pavement [52]. Therefore, the combination weight \(w_{i}\) of subjective and objective factors is calculated according to Formula (12).  
\[\omega_{i}=\frac{\sqrt{\omega_{i}^{\prime}\omega_{i}^{\prime\prime}}}{\sum \limits_{i=1}^{n}\sqrt{\omega_{i}^{\prime}\omega_{i}^{\prime\prime}}}(0\leq \omega_{i}\leq 1,\sum\limits_{i=1}^{n}\omega_{i}=1) \tag{12}\]  
where \(w_{i}^{\prime}\) and \(w_{i}^{\prime\prime}\) are the subjective weight and the objective weight, respectively.