## 1 Introduction
An electro-hydraulic actuator is a high frequency action part, and its action frequency is directly related to the compressor speed. The high frequency action inevitably leads to the fatigue degradation of the reset spring of the unloader in long-term operation. The solenoid valve dynamic characteristics also offset due to continuous charging and discharging. Unfortunately, since the SCRS is a complex system with mechanical, electrical, and hydraulic coupling, the characteristic parameters of the reset spring and solenoid valve cannot be directly measured during system operation. Therefore, if there is a decrease in system regulation performance, it is extremely challenging, even impossible, to locate the fault through the technical method of single factor analysis. To address this issue, it is necessary to study the influence law between the system regulation performance and each coupling component and explore the degradation law of system performance caused by valve leakage, characteristic parameter deviation of the solenoid valve, and reset spring stiffness degradation. Therefore, this paper develops a multi-subsystem coupling model to analyze the relationship between the system regulation performance and the parameters of each component. Some research has been done on system modeling. [PERSON] et al. proposed a mathematical model that is coupled with a control system, hydraulic system, actuator, buffer tank, and other components [12]. However, the coupling model did not take the influence of the gas pipeline between compressor and buffer tank and the valve leakage into account. The opening and closing processes of the solenoid valve were also ignored. Based on the coupling multi-system model established in [12], an improved multi-subsystem integrated mathematical model, including compressor, gas pipeline, buffer tank, and actuator, was established, which took the solenoid valve dynamics and valve leakage into consideration. Here, the framework of degradation-based optimization (DBO) was developed. The flow diagram of the developed DBO framework for SCRS is shown in Figure 1. In the operation of the SCRS, the load prediction model predicts the actual load of the compressor, and the degradation model calculates the degradation rate of the system based on the prediction results. At the initial time, the degradation rate of the system was very low and close to zero. With the degradation of the system's regulating performance, the degradation rate gradually increased. The adaptive optimization compensation model generates control parameter compensation to compensate for the degraded part, which minimizes the degradation rate of the whole system and ensures the acceptable regulation accuracy and performance of the system. The load prediction model is the most important part of the whole compensation-based optimization framework. Generally speaking, the load prediction model can be realized through mechanism modeling, but the mechanism model requires a large number of system structure parameters and process parameters which are not even measurable. Therefore, these models are unsuitable for engineering applications, especially in real-time control systems. Encouragingly, artificial neural networks (ANNs) have been widely used in reciprocating compressor modeling and system optimization due to their advantages of being adaptive, self-learning, and fault-tolerant and working with nonlinear mapping. [PERSON] et al. set up a physical mechanism model and an artificial neural network model of a reciprocating compressor, respectively, with an experimental refrigeration device as the research object and analyzed and compared these models through parameters such as exhaust volume, exhaust temperature, and energy consumption [13]. [PERSON] et al. developed two models: one using an artificial neural network and another one using a probabilistic neural network to predict and simulate the behavior of a reciprocating compressor [14]. The artificial neural network models for the non-injection, vapor