## 1 Introduction  
Direct-drive electro-hydraulic servo valves are an essential control element in both aerospace and remote control. In modern industrial control, fluid-hydraulic control or pneumatic control occupies the primary control strategy market, so the study and application of one of its essential control components, the direct-drive electro-hydraulic servo valve, is also a major research point. For example, in the field of remote sensing, for the design of monitoring mobile scanning systems in thermal systems [1], control valves such as servo valves, as the leading equipment for the thermal components of the thermal system, have a non-negligible impact on the accuracy of the final scanning system. The Spanish scholar [PERSON] et al. [2] evaluated the performance of an urban park irrigation system where water consumption was used as the main argument factor. In contrast, water consumption was related to the control of the valve element of the servo valve, another great application of their research in conjunction with the evaluation system. In thermal power plants [3, 4], servo valves, as the main components of their digital electro-hydraulic control systems, leak, and other failures are also one of the main causes of control system failure in thermal power plants. [PERSON] et al. [5] have also studied servo valves used in fighter jet wing and robot control systems, combining simulations and experiments to verify their internal flow in such industrial applications. In aerospace and aircraft or missile control [6], where servo valves are widely used, their internal fluid conditions and pressure characteristics are also important influencing factors in such areas. In addition, life prediction is closely related to the physical failure and degradation of components and is a significant focus of attention in both the aerospace and remote control sectors. For electro-hydraulic servo valve life prediction, most of them are applied to the Bayesian tracking method and others [7; 8] for diagnosis and prediction. However, this relies mainly on models, mechanical components, or wear experience for analysis and does not lead to a regular diagnosis and projection method. The accuracy of the results has too large an upper and lower accuracy limit for routine use in the modern control industry. In recent years, more life prediction methods have been devised. [PERSON] et al. [9] proposed a load-based prediction method that combines multiple forces such as load, structural properties, and material properties through the specific use and industrial conditions of the system to which the part is subjected, which is then monitored to form a set of life prediction parameters. Scholars [PERSON] [10] and others have also proposed a new fatigue damage model for the life prediction of wind turbine blades that cascades and expands the various loss behaviors of the components. The process is also available in the ABAQUS software user material subroutine. [PERSON] et al. [11] updated and extrapolated a novel mathematical model for the lifetime prediction of rechargeable battery cells, allowing the model to describe the evolution of the battery capacity decay trend while retaining its desirable characteristics such as uncertainty quantification. [PERSON] et al. [12] describe a method for life prediction from static fatigue measurements for life prediction from the plastic material of the part itself and suggest that its most critical factor is the assumed dependence of the time to failure on stress, and then validated the validity of their method. [PERSON] et al. [13] in Korea combined the initial strain parameter method and the Larsen-Miller parameter method to study the remaining service life of automotive engine components made from the metallic material Alloy 718 at high temperatures. They experimentally verified the validity of such practices under high temperatures and continuous pressure at 550 \({}^{\circ}\)C to 700 \({}^{\circ}\)C. In addition, [PERSON] et al.