## 2 Constructing Virtual Prototype
### Construction of the Mesh Solid Model Layer
#### 2.1.4 System Error Analysis  
Error Analysis of the Feature Parameter Detection Process  
In this study, GoogLeNet is used to classify the parts corresponding to the image according to the sample image of the part; YoloV4 Tiny is used to detect all part features in the sample image according to the type of features contained in the part. Their dataset is classified according to the types of parts and their characteristics summarized in Table 1. There are about 1500 samples of each type of parts. The training set, test set, and verification set are divided according to the quantity ratio of 8:1:1 to construct the data set of GoogLeNet image classification network. This data set, according to the relationship between parts and their feature types summarized in Table 1, frames the data features in various parts' image samples, and constructs the data set of YoloV4 Tiny. The schematic diagram of the data set is shown in Figure 13. Their recognition and detection accuracies are both higher than 99.6%. In this study, approximately 10,000 three-dimensional models are used to construct its training set. Some of its data and the PR curve of network training are as shown in Table 3 and Figures 13 and 14. Figure 12: Arc feature mesh solid model. Figure 13: The training dataset of the deep-learning network. On the other hand, the error unit of the image-processing algorithm is the unit length of pixels. We randomly selected several three-dimensional models with known part parameters, compared them with the system detection data, and solved the relative error of the data. The results are as shown in Table 4.  
From the data in Table 4, it can be concluded that the relative errors of some feature parameters are below \(2\times 10^{-5}\), which is better than the measurement results of the feature recognition network (see the detection results in Figure 3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Part Name** & **Part Feature Parameters** & \begin{tabular}{c} **Theoretical** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Detection** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Relative** \\ **Error** \\ \end{tabular} \\ \hline \multirow{6}{*}{Second driven gear} & Radius of addendum circle & 49 & 48.9997 & \(6.12\times 10^{-6}\) \\  & Tooth width & 26 & 26.0003 & \(1.15\times 10^{-5}\) \\  & Centroid of feature segment & \((-68.6,0)\) & \((-68.5998,0)\) & \(2.92\times 10^{-6}\) \\  & Inner arc radius & 29 & 29.0008 & \(2.76\times 10^{-5}\) \\  & Inner arc thickness & 39 & 38.9998 & \(5.13\times 10^{-6}\) \\  & Centroid of inner contour & \((-68.6,0)\) & \((-68.5999,0)\) & \(1.46\times 10^{-6}\) \\  & feature segment & & & \\ \hline Inner bore bearing of fourth driven & External diameter & 37 & 37.0004 & \(1.08\times 10^{-5}\) \\  & Internal diameter & 25 & 24.9999 & \(4.00\times 10^{-6}\) \\  & Width & 30 & 30.0005 & \(1.67\times 10^{-5}\) \\  & Centroid of feature segment & (6,0) & (6.0001,0) & \(1.67\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical table of error verification data. Figure 14: The loss and accuracy curve of the deep-learning network. Error Analysis of Mesh Solid Modelling  
The error of differential calculation will occur in the arc fitting of the mesh solid model. Increasing the values of \(A_{r},A_{T},A_{a}\), which are in Formulas (13), (15), and (17), can improve its contour accuracy. Using the error analysis method of curve fitting [29; 30; 31], we selected any vector diameter in the cylindrical coordinate system to intersect the mesh solid model and the 3D model, obtained two surface contour points \((r,\theta,h),(r_{r},\theta_{r},h_{r})\), and then solved the relative error \(\sigma_{i}\) of their spatial position to evaluate the fitting accuracy of the mesh solid model. The average frame rate data are used to evaluate the consumption of computing resources of mesh solid models with different division accuracies.