# Mdpj _sciences_
## 3 Method
### Multi-Source Information Fusion and Prediction  
During vehicle maintenance, a single session often involves executing multiple distinct projects simultaneously. For instance, activities such as oil change and air filter replacement often occur concurrently, indicating an interdependence among various maintenance projects. To fully utilize the correlations between maintenance projects, we propose a representation based on the co-occurrence matrix. We create a global co-occurrence graph for all maintenance projects with weighted edges, each node serving as a representation of a maintenance project \(\{p_{i}\}_{i=1,2,\ldots,|P|}\) sourced from the set \(P\). If a pair \((p_{i},p_{j})\) co-occurs in a vehicle's maintenance record, two equal weights \(\overrightarrow{(i,j)}\) and \(\overrightarrow{(j,i)}\) are integrated into \(G\). We then count the total co-occurrence frequency \(t_{ij}\) of \((p_{i},p_{j})\) in all vehicle maintenance records for further calculation of edge weights. Additionally, we aim to identify important and common project pairs. Consequently, we define a threshold \(\delta\) to filter out combinations with low frequency, resulting in a qualified set \(\Delta_{i}=\left\{p_{i}\mid\frac{t_{ij}}{\sum_{n=1}^{|P|}t_{ij}}\geq\delta\right\}\) for \(p_{i}\). Let \(q_{i}=\sum_{p_{j}\in\Delta_{i}}t_{ij}\) represent the total frequency of qualified projects co-occurring with \(p_{i}\). We used an adjacency matrix \(G\in\mathbb{R}^{|P|\times|P|}\) to represent the co-occurrence graph as defined in Equation (7). \[G_{ij}=\left\{ \begin{array}{l}0\text{ if }i=j\text{ or }\frac{t_{ij}}{\sum_{j=1}^{|P|}t_{ij}}<\delta\\ \frac{t_{ij}}{q_{i}}\text{ otherwise}\end{array} \right. \tag{7}\]  
Note that \(G\) is designed to be symmetric, representing the influence of two maintenance projects. As a static matrix, \(G\) quantifies the frequency of global maintenance project co-occurrence. However, the occurrence and disappearance of various maintenance projects happen at different stages. Even if a specific maintenance project is absent from current records, a related project may emerge in the future due to correlations among various projects. Consequently, to account for the correlations among maintenance projects, the correlation representation \(\{R_{t}\}_{t=1,2,\ldots,T}\) of each project is derived from each vehicle's historical maintenance projects \(\{V_{t}\}_{t=1,2,\ldots,T}\), utilizing \(F_{2}(V_{t},G)\). The definition of \(F_{2}(V_{t},G)\) is provided in Equation (8). \[F_{2}(V_{t},G)=G\cdot V_{t} \tag{8}\]  
By the operation of \(F_{2}(V_{t},G)\), \(\{R_{t}\}_{t=1,2,\ldots,T}\) contains not only the information of the original maintenance projects, but also implies the information on the previous related maintenance projects. To better integrate historical maintenance projects and mileage data, we propose an information fusion module based on a gated unit [22] to achieve a more comprehensive integration of projects and mileages on an item-by-item basis. First, we perform a matrix dot product on \(M_{t}\) and \(N_{t}\) to obtain \(S_{t}\). Then, we subtract \(S_{t}\) from \(N_{t}\) to obtain \(X_{t}\). Next, \(X_{t}\) is activated by a Sigmoid function to yield \(Z_{t}\). Finally, \(S_{t}\) and \(Z_{t}\) are multiplied to produce \(L_{t}\). The detailed computational procedure is illustrated in Equation (9). \[ \begin{split} S_{t}&=M_{t}\cdot N_{t}\\ X_{t}&=[S_{t},N_{t}]\\ Z_{t}&=\text{Sigmoid}(W_{Z}Z_{t}+b_{Z})\\ L_{t}&=S_{t}\cdot Z_{t}\end{split}  \tag{9}\]  
where \(W_{Z}\in\mathbb{R}^{2*|P|\times|P|}\) and \(b_{Z}\in\mathbb{R}^{|P|}\) denote the weights and biases, respectively. The integration of project and mileage information learned through gated unit enhances the model's representation. Subsequently, \(L_{t}\) and \(R_{t}\) are fused using the attention mechanism outlined in Equation (5), as demonstrated in Equation (10).