## 1 Introduction  
Mounts are elastic connections between the powertrain and body/chassis. They are key components for isolating and attenuating the vibration of the powertrain and reducing structurally borne noise. The passive hydraulic engine mount with an inertia track and decopler membrane (PHM-IT-DM) has been extensively investigated because of its excellent performance, which can provide high stiffness and strong damping in the low-frequency band. Expanding upon the advantages of strong damping in the low-frequency band of the PHM-IT-DM, an active hydraulic mount with an inertia track, decopler membrane, and oscillating coil actuator (AHM-IT-DM-OCA) has been studied and applied to refine noise and vibration with an active force to cancel the force transmitted to the vehicle body through the primary path. Compared with active hydraulic mounts with magnetostrictive actuators [1], piezoelectric actuators [2], and shape memory alloys [3], the AHM-IT-DM-OCA has the advantages of a compact structure, low energy consumption, sensitive response, large actuating displacement, and linear actuating force. The investigation of active hydraulic mounts (AHMs) involves three aspects: the model, its parameters, and control algorithm [4; 5]. The model and its parameters form the basis of the control algorithm. Active and passive hydraulic mounts are generally modeled using a lumped-parameter model. The accuracy of the parameters is essential for controlling the stability and capability of an algorithm. Methods for acquiring parameters include numerical calculations, direct testing, and parameter identification. The numerical calculation methods are based on virtual prototypes. The conventional method is the finite element method (FEM), which focuses on the super-elastic constitutive of rubber [6; 7] and multiple physics coupling fields [8; 9]. Considering the limitations of convergence and accuracy of fluid-solid interaction (FSI) at high frequencies, FEM with FSI is always performed in the lower frequency band. Direct testing methods [10; 11; 12] are generally used to study specific components when a physical prototype exists. Special fixtures or test rigs are required for the parameter acquisition of different components, such as the main rubber spring, upper fluid chambers, inertia tracks, and decoupler membranes. Therefore, direct testing is time consuming and labor intensive. Moreover, mount element-level tests cannot accurately reflect the operating boundary condition in the way assembly level tests can. Therefore, direct testing is inappropriate for identifying the key parameters of the decoupler membrane attached to the actuator, which significantly influences the accuracy of the model for active control. Parameter identification methods are based on the external dynamics of the mount assembly when a physical prototype is available. Depending on whether the acquired parameters have a specific physical meaning, parameter identification can be performed based on curve fitting or distinct features. Curve fitting, which does not require physical meaning, can be carried out based on the Freudenberg hydromount equations [13] and quadratic polynomials [14; 15] to simulate the dynamic behaviors. Focusing on frequency-variant dynamics, the curve fitting method can be applied in the low- and high-frequency bands using two different sets of parameters [16; 17]. Regardless of whether the mathematical model is linear or nonlinear, curve fitting can achieve good agreement with the experimental results [18]. Parameter identification methods based on the distinct features of dynamics identify parameters based on the relationship between external dynamics and internal physical parameters, focusing on the physical meanings of the parameters. For hydraulic engine mounts, the key physical parameters mainly include the bulk stiffness, equivalent piston area, and natural frequency, which can be identified by a fixed point and a horizontal segment [19; 20; 21].