## 6 Conclusions  
1. Distinct features of the dynamics and key parameter identification were systematically investigated based on a nonlinear lumped parameter model of the AHM-IT-DM-OCA. A method for simplifying the mathematical model is proposed in the low-, mid-, and high-frequency bands, which are divided into two resonance frequencies of the fluid channel and actuator mover. The simplified model in the mid- and high-frequency bands is linear, which is attributed to the negligible nonlinear factors of the fluid channel and the linear output of the actuator.
2. The distinct features of the dynamics, which include three resonances and seven horizontal segments, are revealed. Experimental validations based on a series of tests have shown only three resonances of the fluid channel and actuator mover, and the 1 st, 4 th, and 6 th horizontal segments can be applied to identify all key parameters owing to the limitations of the test equipment and low fixture modalities.
3. The distinct features of passive and active dynamics in fluid-filled and non-fluid states should be analyzed successively rather than independently. Passive dynamics are the foundation that provide a method for model simplification and basic parameters. The active dynamics in the non-fluid state are extensions of the identification of all key parameters, which decouples the complex items composed of multiple key parameters. A complete procedure for the identification of all six key parameters is established based on the distinct features of the dynamics. This is compared with previous study's identification of only two parameters based on the fixed point of passive dynamics.  
Figure 8: Simulation validation of the active FRF of \(|F_{1}/I|\) at 25–400 Hz for the **fluid-filled state**. _Key:_ Measured (); Simulated ().  
Figure 9: Simulation validation of the active FRF of \(\left|\tilde{Y}_{3}/I\right|\) at 0–1000 Hz for the **non-fluid state**. _Key:_ Added masses \(m_{\rm ad}=8.90\) g; Measured (); Simulated ().  
4. The consistency of the key parameters identified by the procedure is presented based on experiments with different added masses. The physical rationality is presented by comparing the results under fluid-filled and non-fluid states. The correctness is demonstrated by the agreement between the simulated active dynamics and the experimental ones. All key parameters identified by this systematic method are sufficiently accurate to be applied for future research on algorithms and the performance of active control.  
Conceptualization, R.-L.F.; methodology, R.-L.F. and Z.-N.F.; software, R.-L.F. and Z.-N.F.; validation, R.-L.F.; formal analysis, R.-L.F. and Z.-N.F.; investigation, R.-L.F.; resources, R.-L.F.; data curation, R.-L.F.; writing--original draft preparation, R.-L.F.; writing--review and editing, R.-L.F. and Z.-N.F.; visualization, R.-L.F.; supervision, R.-L.F.; project administration, R.-L.F.; funding acquisition, R.-L.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Anhui Eastar Auto Parts Co., Ltd. (No. 2017-092), the National Natural Science Foundation of China (No. 51175034) and the Scientific and Technological Innovation Foundation of Shunde Graduate School, USTB (No. BK19 CE002).  
Not applicable.  
We are grateful to [PERSON] (Anhui Eastar Active Vibration Control Technology Co., Ltd. and Anhui Eastar Auto Parts Co., Ltd.) for financial and experimental support and [PERSON] (Anhui Zhongding NVH Technology Co., Ltd.) for experimental support. We are also grateful to the National Natural Science Foundation of China (No. 51175034) and the Scientific and Technological Innovation Foundation of Shunde Graduate School, USTB (No. BK19 CE002) for supporting this work.  
The authors declare no conflict of interest.