In recent decades, quasi-zero stiffness (QZS) vibration isolation systems with nonlinear characteristics have aroused widespread attention and strong research interest due to their enormous potential in low-frequency vibration isolation. This work comprehensively reviews recent research on QZS vibration isolators with a focus on the principle, structural design, and vibration isolation performance of various types of QZS vibration isolators. The negative-stiffness mechanism falls into two categories by different realization methods: passive and active/semi-active negative-stiffness mechanisms. Representative design, performance analysis, and practical application are elaborated for each category. The results show that passive vibration isolation systems have excellent low-frequency vibration isolation performance under specific payload and design parameters, whereas active/semi-active vibration isolation systems can better adapt to different environmental conditions. Finally, the development trends and challenges of QZS vibration isolators are summarized, and the solved and unsolved problems are highlighted. This review aims to give a comprehensive understanding of the QZS vibration isolation mechanism. It also provides guidance on designing new QZS vibration isolators for improving their vibration isolation performance and engineering applicability.

The study focuses on the fault signals of rolling bearings, which are characterized by nonlinearity, periodic impact, and low signal-to-noise ratio. The advantages of entropy calculation in analyzing time series data were combined with the high calculation accuracy of Multiscale Fuzzy Entropy (MFE) and the strong noise resistance of Multiscale Permutation Entropy (MPE), a multivariate coarse-grained form was introduced, and the coarse-grained process was improved. The Composite Multivariate Multiscale Permutation Fuzzy Entropy (CMvMPFE) method was proposed to solve the problems of low accuracy, large entropy perturbation, and information loss in the calculation process of fault feature parameters. This method extracts the fault characteristics of rolling bearings more comprehensively and accurately. The CMvMPFE method was used to calculate the entropy value of the rolling bearing experimental fault data, and Support Vector Machine (SVM) was used for fault diagnosis analysis. By comparing with MPFE, the Composite Multiscale Permutation Fuzzy Entropy (CMPFE) and the Multivariate Multiscale Permutation Fuzzy Entropy (MvMPFE) methods, the results of the calculations show that the CMvMPFE method can extract rolling bearing fault characteristics more comprehensively and accurately, and it also has good robustness.

The propulsion shaft system, as the core of the ship’s power system, has attracted widespread attention in terms of vibration. This paper is dedicated to the study of the dynamic response characteristics of the ship propulsion shafting system, with a particular focus on the impact of the shaft-driven generator supported by bearings on the dynamic torque of the shafting system. A classic lumped-parameter equivalent system model is adopted, and the time domain transient response simulation calculation is conducted based on the Newmark-β method. A comprehensive analysis is made of the vibration torque and vibration stress in the propulsion shaft system under different rotational speeds and working conditions, with or without the shaft-driven generator connected to the load. Dynamic vibration torque measurements are also taken on a 16100TEU ship for the propulsion shaft system to analyze the consistency between simulation results and experimental results. The results show that at the rated speed of the main engine at 80 rpm and adjacent speeds, the error between the simulation calculation results and the actual measured torque results at the pre- and post-motor measurement points is less than 10% and is much less than the continuous allowable torque of 4.01 × 10⁶ N·m and the instantaneous torque. This installation state, including the propulsion shaft system with the shaft-driven generator supported by bearings, can safely navigate during normal operation. This provides theoretical and experimental support for the future installation of the propulsion shaft system with the shaft-driven generator supported by bearings. In addition, the actual ship experiment enhances the universality and reliability of the research.

In order to effectively control the low-frequency vibration of ship machinery, based on the improved multi-line spectrum adaptive control algorithm, a two-degree-of-freedom (two-DOF) active-passive hybrid vibration isolator composed of an electromagnetic actuator, rubber spring, and the hydraulic device is proposed. The dynamic model of the two-DOF vibration isolation system is established and the main control force demand of the vibration isolation system at different damping forces is analyzed. By introducing the improved wavelet packet decomposition algorithm with the Hartley block least mean square algorithm to the filter-x least mean square (FxLMS) algorithm, an improved wavelet packet Hartley block filter-x least mean square (IWPHB-FxLMS) algorithm is established. The experimental results show that the IWPHB-FxLMS algorithm has better control performance. Compared with the traditional FxLMS algorithm, the IWPHB-FxLMS control algorithm improves the convergence speed by 91.7% and the line spectrum power spectrum attenuation by 58.1%. The active-passive hybrid vibration isolator is based on multi-line spectrum adaptive control and can achieve good control effects under the excitation of multi-frequency line spectrum and constant frequency line spectrum.

In recent times, there has been a significant focus on electromagnetic resonant shunt damping (ERSD) and quasi-zero-stiffness vibration isolators (QZS VI) as prominent solutions for vibration mitigation or energy harvesting. In this paper, an innovative retrofittable model is proposed for dual-functional energy harvesting and low-frequency vibration attenuation by combining the ERSD and two-stage quasi-zero-stiffness vibration isolator (TQZS VI). The viscous dissipative element between the TQZS VI upper and lower layers is implemented using an electromagnetic shunt transducer that is connected in parallel with a resonant RLC (resistor–inductor–capacitor) circuit. Firstly, the mathematical model of the electromagnetic resonant shunt series quasi-zero-stiffness isolator (ERS-TQZS VI) is developed. Then, the magnitude-frequency response equations of the ERS-TQZS VI system are approximately solved using the harmonic balance method (HBM) in combination with the pseudo-arc-length method (PLM). The analytical approach is validated using numerical simulations. Moreover, the force transmissibility and output power of the ERS-TQZS VI are defined, and detailed parametric analysis for energy harvesting and low-frequency vibration attenuation is performed to assess the critical design parameters that result in optimal performance of the ERS-TQZS VI. The results demonstrate that the ERS-TQZS VI exhibits a significant reduction in resonance peaks of low-frequency vibration while simultaneously enabling effective vibration energy harvesting.

The strong coupling between the ship’s sway and yaw motion increases the complexity of identifying hydrodynamic derivatives in mathematical models and reduces accuracy. To solve this problem, this paper proposes an identification method Alpha Evolution Multi-output Support Vector Regression (AE-MSVR) based on MSVR combined with AE. This method approaches the yaw and sway motion equations as a multi-input and multi-output (MIMO) problem, utilizing MSVR for modeling and optimizing hyperparameters with AE. It reduces parameter drift by restructuring the regression model’s input–output. Identification data is obtained via zigzag test simulation. The AE-MSVR method successfully identifies linear and nonlinear hydrodynamic derivatives in the 3 degree of freedom (DOF) Abkowitz model. Using clean simulation data, the results show promising agreement with experimental values from planar motion mechanism (PMM) tests and achieve improved accuracy compared with the standard SVR identification method. To assess robustness, simulated noise is introduced at different levels; maneuvering characteristics are evaluated using turning circle tests. Results demonstrate that AE-MSVR achieves promising accuracy in identifying ship hydrodynamic derivatives and shows encouraging robustness against noise. The method provides potential support for ship motion prediction and maneuverability forecasting.