## 1 Introduction  
An inertially stabilized platform (ISP) is a mechanical device that uses a gyroscope to sense the attitude of the platform in inertial space and isolates carrier disturbance based on a servo control system to ensure the stability of its visual axis. It is widely used in ships, tanks, launch vehicles, spacecraft, and other fields [1, 2, 3, 4, 5]. As the basic component of an ISP servo system, the transmission performance of a precision drive transmission device directly affects the servo performance of the system and has a decisive influence on the high-precision pointing control of the ISP. The mapping relationship between the transmission performance and servo performance of the drive transmission components has important guiding significance for the selection of ISP drive components, the distribution of servo performance indicators, and the prediction of servo performance. In the research on the influence of mechanical system servo performance, the main focus is on studying the influence patterns of single factor variables, and verifying relevant conclusions through simulation or experiments [6, 7, 8]. As the servo system performance is affected by multiple factors, and the influence factors are coupled with each other, it is impossible to obtain the influence law of multiple factors through theoretical analysis. Therefore, relying on experimental means to study the changes in servo performance becomes the most direct and reliable method [9]. [PERSON] et al. [10] studied the impact of a precision reducer on the performance of an industrial robot through an accelerated degradation test to study the trend of static and dynamic performance of the reducer,and through the evaluation of the robot machine's performance obtained the five factors that affected its performance. An experimental study has the disadvantage of being time-consuming and expensive, and the mapping relationship obtained is not comprehensive, as the performance parameters of the reducer cannot be changed on demand. Due to the shortcomings of experimental methods, simulation analysis has become the preferred method for studying the servo performance of mechanical systems. In order to make the simulation results true and reliable, the accuracy of the system dynamic model plays a decisive role. With the increasing demand for the accuracy of system dynamic models, the accurate modeling of nonlinear factors has become the focus and difficulty of research. The traditional nonlinear factor modeling method is based on simplifying the model structure and using an analytical equation form for least squares fitting. For example, in the modeling of nonlinear factors such as friction [11; 12; 13; 14], transmission error [15; 16; 17], and backlash [18; 19; 20; 21], the model structure is simplified into a combination of several analytical functions. This analysis model has the characteristics of simple structure, low computational complexity, and easy parameter identification, but the nonlinear model structure is simplified, making it difficult to accurately describe the nonlinear characteristics of the system. The data-driven hybrid modeling methods based on data-driven modeling make up for the shortcomings of analytical models [22; 23], which show high accuracy and strong generalization ability in system dynamics modeling with the help of intelligent algorithms, such as artificial neural networks, which are powerful in nonlinear data fitting and prediction [24]. [PERSON] et al. [25] used deep neural networks for the first time to build an inverse dynamics model for a robotic manipulator, which showed better performance in terms of generalization ability and convergence. [PERSON] [26] used a BP neural network to establish the nonlinear mapping relationship between the magnetic chain, rotor position, and phase currents, opening up a new approach for establishing the switched reluctance motor model.