## 3 Materials and Methods
### Overall Architecture Design of the Digital Twin for the Wind Turbine Gear Transmission System  
The overall design of the digital twin for the wind turbine gear transmission system is shown in Figure 6. The system primarily comprises six modules: the physical module, virtual module, data module, application module, information interaction module, and visualization module. (1) The physical module comprises the wind farm environment, the physical wind turbine, and all the devices equipped on it, mainly including the wind turbine entity, sensors, controllers, a remote data acquisition and transmission system, the SCADA system, and wireless communication modules. Coordination among these components ensures the proper operation and real-time condition monitoring of the wind turbine. Sensors primarily collect dynamic operational data from the wind turbine; the controller, upon detecting an anomaly, receives control commands to intervene in the turbine's operating status; the wireless communication module primarily handles wireless data transmission. The physical module serves as the foundation for the mathematical models. All other modules are built around the physical module and ensure its normal and sound operation. (2) The virtual module is a high-fidelity mathematical representation of the physical module, consisting of three types of models: a geometric model, a mechanistic model, and an AI algorithm model. The geometric model's information is obtained from the physical wind turbine and its associated devices, enabling visualization within a virtual environment. The mechanistic model describes the underlying mechanism changes during operation. The AI algorithm model is a mathematical model used to solve high-dimensional, nonlinear, complex problems. As the twin of the physical module, the virtual module must accurately map the actual status of the physical module. (3) The data module is primarily responsible for managing the data generated by the physical module during actual operation, handling tasks such as data acquisition, processing, interaction, and storage. It manages both inherent static data and dynamic data from operations. Static data refers to inherent information that generally does not change significantly over time, whereas dynamic data is generated by the physical entity during operation and can be stored as historical data for fault warning, diagnosis, and status  
Figure 5: Three-dimensional view of the gearbox. assessment. Unlike static data, dynamic data changes over time. When combined with specific models, different types of dynamic data can be utilized for targeted diagnosis and warning for the system. Historical data can be used to evaluate the operational condition of the equipment. (4) The application module is responsible for executing specific functions. All algorithms and mathematical models used in the twin system are encapsulated in this module. It uses dynamic and historical data from the data module to drive the mathematical models, enabling visual monitoring of the wind turbine's real-time motion state, power output, wind speed, etc. Additionally, it can perform fault diagnosis, prediction, maintenance, and lifetime prediction for the wind turbine, ensuring reliable operation throughout its entire lifecycle to maximize economic benefits. (5) The visualization module serves as the interface through which users interact with the entire system; it is the visual representation of all functions in the application module. Users can access the designed digital twin system via tablets, computers, mobile phones, or VR clients to monitor its overall operational status in real time. (6) The information interaction module functions as the intermediary that links the various modules within the digital twin system. It facilitates bidirectional data transmission through specified transport protocols and monitoring transmission ports.