## 4 System Implementation and Verification  
### Application Case  
This paper takes the centring machining system as the application object. It carries out the digital twin system design based on the above digital twin system framework, and the configuration information of the system operation platform is shown in Table 1.  
PixyzStudio and other tools were used to develop a digital twin system for centring and machining lathes for high-precision optical components. The development process is as follows: draw a high-fidelity CAD model that reflects the spatial features of the centring lathe according to the actual drawings through Solidworks2019, then import the model into PixyzStudio, simplify the non-critical features to reduce the rendering consumption, triangulate the CSG model using the Tessellate method, merge the parts, unify the pivot, create UVs and export them to Unity3D, create a digital twin of a high-precision optical component, and export as an FBX model. Then the FBX model is imported into Unity, the digital twin scene is created, objects and textures are added, the physics engine provided by Unity is used to add components, and the physical and motion simulation is performed; a script is written in C# to control the simulation and interaction, OPC UA is registered, and the socket object is created in the hand to complete the TCP connection. The interface is connected through the OPC UA transfer protocol to get the centring lathe, including spindle position coordinates, speed, power, and other equipment state information, to complete the data connection. It will accept the data by the information model into a CRUD such as a database, using C# scripts to call MySQL for the data interaction connection. The centring lathe digital twin system is shown in Figure 10.  
This paper uses the public dataset PHM2010 to construct the VMD-GRU deep learning model to verify the prediction effect of the equipment machining state. Repeat six trials under the above cutting conditions to obtain six sets of data, C1, C2, C3,..., C6. In this paper, C1 is selected as the training data, and C4 is selected as the test data. Each data group consists of two parts with 316 files, including one prediction output file and 315 prediction input files. The input files include 315 groups of tool wear values in X, Y, and Z directions, respectively, and each input file contains seven signal channels: force signal, vibration \begin{table}
\begin{tabular}{c c} \hline Machine name & DESKTOP-ISW5J \\ Operation system & Windows 10 64-bit \\ Processor & Intel(R) Core(TM) i5-9400F CPU @ 2.90 GHz (6 CPUs), \(\sim\)2.9 GHz \\ Memory & 32768 MB RAM \\ Video card & NVIDIA GeForce GTX 1050 Ti \\ \hline \end{tabular}
\end{table} 
Table 1: Development Platform Configuration Information. Figure 10: The main interface of the digital twin system for the high-precision lens-centring process. signal, and acoustic emission signal in XYZ direction. Some of the VMD decomposition results are shown in Figure 11.  
The prediction results are shown in Figure 12. Figure 13 shows the RMSE and MAE of the different models in the three experiments. It is easy to see that the VMD-GRU method proposed in this paper exhibits good prediction performance. However, the LSTM has more parameters than the GRU to capture more temporal features and learn more complex patterns, thus showing better performance. It requires more data and computational resources, and in the case of a relatively short sequence, its performance is not stable enough, and it is prone to overfitting. The VMD-GRU method can mine more sequence information through VMD signal decomposition and effectively suppress the influence of noise in the original signal to obtain more relevant features, so it shows better prediction performance. At the same time, in terms of training time, it performs superior to that of the LSTM and close to that of the GRU, which meets the real-time requirements of the system's intelligent monitoring. Figure 11: The result of VMD decomposition.