## 3 Methods
### The Proposed Algorithm
\[SUM_{1}=D_{a}+D_{b}+D_{c} \tag{1}\]  
\[A_{j}=\frac{D_{i}}{sum_{1}}(i=a,b,c,j=1,2,3) \tag{2}\]  
The volume \(V\), surface area \(S\), and the parameters \(D_{x}\), \(D_{y}\), and \(D_{z}\) of the maximum bounding box in the \(x\), \(y\), and \(z\) directions are obtained and normalized, as shown in the following formulas. \[SUM_{2}=D_{x}*D_{y}*D_{z} \tag{3}\]  
\[ \begin{cases}A_{4}=\frac{V}{sum_{2}}\\ A_{5}=\frac{S}{sum_{2}}\end{cases}  \tag{4}\]  
The moments of inertia \(J_{xx}\), \(J_{yy}\), and \(J_{zz}\) along the x, y, and z axes are extracted, and these parameters are normalized, as shown in the following formulas. \[SUM_{3}=J_{xx}+J_{yy}+J_{zz} \tag{5}\]  
\[ \begin{cases}A_{6}=\frac{J_{xx}}{sum_{3}}\\ A_{7}=\frac{J_{yy}}{sum_{3}}\\ A_{8}=\frac{J_{zz}}{sum_{3}}\end{cases}  \tag{6}\]  
Finally, the processed sub-level node vector data are integrated into the model parameter vector set \(N\), which serves as the descriptor for the parent-level model. The elements of the dataset \(N\) are determined by Formula (7):  
\[N=(A_{1},A_{2},A_{3},A_{4},A_{5},A_{6},A_{7},A_{8}) \tag{7}\]  
Figure 5 shows the assembly model of a refrigerated van, which includes eight module sub-levels. Model parameter information is obtained through SolidWorks API functions, followed by normalization of the data to generate vectors and establish the vector set \(N_{w}\) to describe the body assembly model. To ensure the accuracy of similarity matching, the vector set parameters are uniformly retained up to three decimal places. Step 3: Calculation of Rotation Matrix and Translation Vector  
First, K-D Tree is used to find the nearest neighbor \(q_{i}\) of each point \(p_{i}\) in the set \(N_{W}\) within the set \(N_{p}\). By using K-D Tree, the nearest neighbor search is accelerated, reducing the time complexity of the search to \(\text{O}\text{I}\text{o}\text{I}\text{o}\text{I}\text{o}\text{I}\text{o}\text{I}\text{o}\text{I} \text{o}\text{I}\text{o}\text{I}\text{o}\text{  
Then, each point is translated from the centroid so that the centroid is positioned at the origin (0,0,0):  
\[P_{i}^{\prime}=p_{i}-C_{W},q_{j}^{\prime}=q_{j}-C_{p} \tag{9}\]  
Using the centralized point sets \(P_{i}^{\prime}\) and \(q_{j}^{\prime}\), the covariance matrix is calculated as follows:  
\[H=\sum_{i=1}^{m}\left(p_{i}^{\prime}\right)\left(q_{i}^{\prime}\right)^{T} \tag{10}\]  
Next, perform Singular Value Decomposition (SVD) on the covariance matrix H:  
\[H=U{\sum V^{T}} \tag{11}\]  
Then, compute the rotation matrix and translation vector. The calculation formulas are as follows:  
\[R=VU^{T} \tag{12}\]  
\[t=C_{p}-R{\cdot}C_{W} \tag{13}\]  
The rotation matrix \(R\) minimizes the rotational misalignment between the point sets \(N_{W}\) and \(N_{p}\). To ensure \(R\) is a valid rotation matrix, its determinant must be checked. If \(\det(R)<0\), the last column of \(V\) is multiplied by \(-1\) to guarantee the orthogonality of the rotation matrix. The translation vector t then translates the rotated point set \(N_{W}\) to align with \(N_{p}\). After each iteration, the point set \(N_{W}\) is updated using the newly computed \(R\) and \(t\). The update formula is as follows:  
\[P_{i}^{\prime}=R{\cdot}P_{i}+t \tag{14}\]  
In the rotational alignment optimization, a normal vector consistency term is introduced to minimize the positional error between the two point sets (\(N_{W}\) and \(N_{p}\)) after  
Figure 5: Parameter vector set for van-type refrigerated truck model. alignment using the rotation matrix and translation vector. The error formula is expressed as follows:  
\[\text{TSE}=\min_{R,t}\sum_{i=1}^{m}\left\|p_{i}-(Rq_{i}+t)\right\|^{2}+\alpha \big{(}1-n_{p_{i}}\cdot Rn_{p_{i}}\big{)}^{2} \tag{15}\]  
The updated point set will be used for the next iteration until convergence criteria are met. Step 4: Model Similarity Calculation  
The refrigerated van assembly model's vector set (\(N_{w}\)) is compared with the historical case model's vector set (\(N_{p}\)) using the ICP algorithm to measure the distance between the sets.