**1. Introduction**

Using a pump as the driver in an electro-hydrostatic actuator (EHA) has the advantages of compact integration, high output force, and ease of maintenance [1]. Therefore, it has become part of a developing trend in fluid power transmission. They have been used in aerospace applications, to replace traditional hydraulic actuators in more-electric aircraft (MEA) Rongjie et al. [2], such as the A380 Van Den Bossche [3]. It is also emerging as a preferable solution for industrial applications, as their design combines the best of both electro-mechanical and electro-hydraulic technologies.

The schematic diagram of a typical EHA is illustrated in Figure 1. The basic function of an EHA is as a servo motor to drive a bi-directional hydraulic pump to generate a pressured cyclic flow rate, to control the cylinder extend/retract. The EHA has the advantage of being electric-powered, which can eliminate heavy, messy, and fault-liable hydraulic pipes; which makes them preferable in more-electric aircraft (MEA). Therefore, they can can make the system much more easy to maintain and reduce the system weight. In Kulshreshtha and Charrier [4], it was demonstrated, in the A380, that using more electric actuators saved over 450 kg. EHA have become a hot topic, and have been developed significantly in many aspects. However, they still have some issues which to be solved before they can be applied with high performance and reliability, such as high speed hydraulic pumping [5], and over-heating. In order to overcome the over-heating problem, some interesting works have been reported recently, such as using a load-sense pump in Chao et al. [6], and a novel control method with energy feedback in Shang et al. [7].

**Figure 1.** Schematic diagram of an electro-hydrostatic actuator (EHA).

In the early phases of an EHA design project, only a few design parameters are available, but a lot design parameters have to be decided and several properties should be considered simultaneously. It is well-known that early verification and virtual validation of the system design in the preliminary design phase, based on advanced simulations and computational tools, can significantly reduce the cost and enhance the quality of the design process. Some researchers have studied simulation-based preliminary design methods for aircraft actuator design, sizing, analysis, and optimization in recent years. A simulation-based preliminary design and optimization method of an electro-mechanical and hydraulic actuation system for an aircraft flight control surface was proposed by Fraj et al. [8], where the weight was the optimized objective and the weight estimation models of major components of actuator were presented. An improved integrated methodology for the preliminary design of electromechanical actuators in a redundant electro-mechanical nose-gear steering system was published by Liscouët et al. [9]. In order to obtain the properties of an electro-mechanical actuator (EMA) for multi-objective optimization in preliminary design, the estimation models for power size, thermal balance, dynamics, and reliability were studied by Budinger et al. [10]. After that, Budinger et al. [11] presented a methodology for the optimal preliminary design of EMAs. A MATLAB/Simulink-based methodology for the sizing, simulation, analysis, and optimization of both EHAs and EMAs, for the primary and secondary control surfaces of a more-electric aircraft (MEA), was proposed by Chakraborty et al. [12]. After that, in Chakraborty et al. [13], an electric control surface actuator design optimization and allocation for MEA was studied. Recently, a multi-level virtual prototyping of EMAs, using bond-graph modeling method, was proposed by Fu et al. [14], FU et al. [15]. However, most of these studies did not take advantage of intelligent

optimization methods to find optimal design parameters; therefore, they cannot provide strong support for designers.

The most important properties of EHA includes light-weight, less energy consumption, quick response, and high stiffness to disturbance. These objectives usually conflict with each other and are hard to balance. Therefore, using a multi-objective optimization (MOO) method to design an EHA leads to more preferable solutions. MOO methods usually obtain a set of Pareto-optimal solutions, instead of a single optimal solution Marler and Arora [16]. The Pareto front is able to indicate the relations between the design parameters and the desired performance, which is very useful for the engineer to achieve an optimal design. In order to offer support for preliminary design of MEA, Wu et al. [17] proposed estimation models for the weight and efficiency of EHA, and a multi-objective optimization algorithm to get the Pareto front of considered performances. In the following work by Yu et al. [18], an estimation model of stiffness was considered and a synthesis decision-making method, based on an analytic hierarchy process (AHP), was used to choose the best solution in the Pareto front. This method can offer significant support to engineers in system design. However, it didn't integrate with a simulation tool and, thus, could not evaluate the dynamic performance.

The present work aims to offer an efficient and powerful simulation-based multi-objective optimization design method for fast and easy preliminary design of EHA. This methodology can search the design parameters automatically, which will make the EHA have Pareto-front performances. This study considered the four important indexes of weight, energy consumption, dynamic response, and stiffness. The weight of the actuator is predicted, based on a scale law according to the design parameters. The performances of energy consumption, dynamic response, and stiffness are obtained by dynamic simulation with AMESim. The intelligent optimization program sent the parameters to the AMESim model, and then ran the simulation and analyzed the dynamic performances (according to the simulation results) automatically. The MOO method of the program in present study is the multi-objective particle swarm optimization (MOPSO) method. The results present the mapping between parameters to the performance and the relations between these objectives. It also illustrated that the proposed method has the significant benefits in the design of EHA and other similar systems.
