## 1 Introduction
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Factors** & **Location** & **Effect** \\ \hline reset spring stiffness & electro-hydraulic actuator & affects actuator withdrawal resulting in decreased precision or regulation failure \\ \hline solenoid valve response & electro-hydraulic actuator & affects actuator withdrawal resulting in decreased precision or regulation failure \\ \hline partial actuator failure & electro-hydraulic actuator & regulation accuracy decreases or fails \\ \hline oil supply pressure too low & hydraulic system & fails to regulate \\ \hline valve leakage & compressor & regulation accuracy decreases \\ \hline controller failure & computer-controlled system & fails to regulation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main factors that affect the regulation performance. Figure 1: Proposed framework for compensation optimization. injection, and two-phase injection heat pumps were developed to predict the performance indexes during cooling and heating seasons [15]. An ANN was trained and validated with the experimental data and the same was proposed for the predicting performance of a work recovery scroll expander in closed-loop operation with a CO\({}_{2}\) refrigeration system in the sub-critical zone [16]. In addition, artificial neural networks are also widely used in parameter and system optimization. [PERSON] et al. assigned an ANN to investigate a logical interaction among dependent and independent variables and to define a cost function based on the empirical data; then the function was optimized by Genetic Algorithm to determine the best amount for each parameter [17]. A hybrid ANN model was trained as well as tested with experimental data sampled from statistical methods, and the model was used to predict the optimal process parameters of injection molding process of a bi-aspheric lens [18]. Hence, this study proposes an ANN-based model to predict the load of a compressor for evaluating the degradation rate of the SCRS. Although various methods have been developed to improve the prediction accuracy of ANN models, a back propagation (BP) neural network is still one of the most popular techniques in this field [19]. A gradient descent algorithm is usually used in a typical BP neural network. However, the typical BP neural network has the limitation of slow convergence speed and is easy to fall into a local extremum. As is well known, the particle swarm optimization (PSO) has the advantages of good global search capability and fast convergence speed. Therefore, PSO is used to optimize the initial connection weight and threshold of BP neural networks. Comparing an ANN model with and without PSO, the prediction error of an ANN model with PSO is lower than without using PSO. Since the optimization is a steady-state optimization, an adaptive optimization method based on the degradation rate is proposed to avoid the over-optimization caused by the load prediction error. In this work, a multi-subsystem coupling mathematical model including compressor, gas pipeline, buffer tank, actuators, and other components is developed to study the performance degradation law of the SCRS caused by changes in the actuator's dynamic characteristic parameters and valve leakage. Then the degraded performance of the SCRS is optimized based on the developed DBO framework. The objective of performance optimization is to minimize the degradation rate of the SCRS. The key outcomes resulting from the proposed DBO framework are the control parameter compensation which leads the SCRS to operate at minimum degradation rate and to guarantee acceptable regulation accuracy. The effectiveness of the proposed DBO framework was verified by the implementation results. This paper is organized as follows: Section 2 introduces the composition and working principle of the SCRS. Section 3 describes the multi-subsystem coupling model. The law of performance degradation is analyzed in Section 4. Section 5 provides the load prediction model based on improved PSO-BP and proposes an optimization method.