## 1 Introduction
The models established in the abovementioned studies were based on the parameters of a single system model or the parameters between subsystems, which cannot truly reflect the mutual influences between subsystems. Since the reciprocating compressor stepless flow control system is a typical mechatronics-hydraulic integrated system, it demonstrates the characteristics of multi-system coupling and multi-parameter crossover. Moreover, any change in a particular coupling parameter in the system affects the performance of the other subsystems. Therefore, the establishment of a relatively simple single system or two-system simulation model can no longer accurately reflect the overall performance changes of a system. For this reason, it is important to determine the key coupling parameters and establish a multi-system model that can reflect the coupling relationship between systems. Co-simulation is an effective method of solving this type of problem, involving multiple disciplines and fields [13]. [PERSON] [14] established a joint simulation model of a hydraulic-mechanical system of an aircraft landing gear and verified the reliability of the model. [PERSON] [15] established a semi-active suspension system for an 8 \(\times\) 8 multi-axle armored vehicle, based on co-simulation technology, and analyzed characteristic values such as ride comfort and maneuverability when a vehicle passed through different obstacles. [PERSON] [16] established a joint simulation model of electro-hydraulic integration for a shearer cutting drum, then analyzed the dynamic characteristics of key components in the coal-mining process. [PERSON] [17] established a mechatronics model of rail vehicles based on the collaborative simulation method. For electromechanical hydraulic integration systems involving multiple disciplines and fields, owing to the complexity of the model, it is difficult to obtain a clear mathematical relationship between the key parameters of a system and the objective function, and there are contradictory relationships between multiple objective functions. Therefore, researchers use the optimization proxy model to approximate the mathematical relationship between the key parameters and the objective function, using the multi-objective optimization method to determine the Pareto front and then obtain an optimal solution. Common methods for establishing mathematical models of optimization agents include radial basis neural network models [18], Kriging models, and response surface models (RSM) [19]. The most commonly used method is the response surface method, which can not only establish the relationship between multiple influencing factors and the objective function but also analyze the sensitivity of each factor to the objective function, as well as the interaction between the two factors [20]. He [21] used the RSM to establish an accurate approximate mathematical model between three new honeycomb shape parameters and shock resistance performance parameters; they established the best shape using the multi-objective particle swarm optimization algorithm (MOPSO). [PERSON] and [PERSON] [22] used the RSM to establish the porosity coefficient, the ratio of core to total thickness, and the weight fraction of graphene nanosheets to express the mathematical equation of the buckling ability of the sandwich plate, which was then used to evaluate the relationship between the critical buckling capacity of sandwich panels and input variables. [PERSON] [23] used the parameters of cone height Lc (X1), suction angle \(\alpha\) (X2), and vortex meter insertion depth Lv (X3) as input variables, and the output separation efficiency E and total pressure drop \(\Delta\)P as response values. Based on the response surface method, a regression equation was established. The proxy mathematical model was used to obtain the best combination of input variables.