Variational mode decomposition (VMD) and its variants are widely used to decompose multicomponent signals into intrinsic mode functions (IMFs). However, they may exhibit mode mixing and limited noise robustness when processing modes with closely spaced center frequencies, sideband structures, or local multi-peak spectra. To address these issues, this paper proposes reassembly variational mode decomposition (ReVMD), which performs mode extraction through a two-stage procedure. In the first stage, the signal is successively decomposed into a sufficient number of spectrally compact preliminary mode functions (PMFs), allowing closely spaced local spectral components to be separated and thereby reducing mode mixing. In the second stage, PMFs belonging to the same mode are adaptively reassembled into final IMFs through fuzzy clustering based on center frequency and spectral energy. This two-stage procedure enables modes with closely spaced center frequencies to be separated and reduces noise contamination in the final IMFs, thereby mitigating mode mixing and improving noise robustness. Simulation results demonstrate that ReVMD achieves lower decomposition errors when the center frequencies of different modes are closely spaced, provides more accurate decomposition of complex multicomponent signals, and exhibits better performance under different noise conditions. Planetary gearbox experiments further demonstrate the effectiveness of ReVMD for bearing fault diagnosis.
Sound intensimetry can be used for the localization of the sound source by utilizing a compact-sized probe system. While vector sensors are advantageous due to their small size and elimination of finite difference errors, their high initial cost and lack of measurement traceability present implementation challenges. As a result, microphone arrays remain widely used for estimating sound intensity vectors despite their limitations, including a limited frequency range due to the spatial bias error at high Helmholtz numbers. In this study, the spatial bias error is explained theoretically, and the localization errors for different Helmholtz numbers are analyzed using the proposed error model. In addition, the collimation error and its effect on the localization result are analyzed, which was not explained in the error compensation model in previous studies. As an effective configuration, this study proposes an octahedron microphone array consisting of six microphones for sound source localization using acoustic intensimetry. The closed-form solution to calculate one-dimensional intensity vector coefficients based on the microphone position is applied to implement acoustic intensimetry. The microphone array combination method is applied to compensate for spatial bias error, with its validity explained by analyzing the directional response and experimental test results. A double tetrahedron array module and phase and amplitude gradient estimating methods, proposed in previous studies to compensate for spatial bias error, are compared with the suggested method through numerical simulations. The causes of errors at the narrow frequencies found in experimental results and the space efficiency in the practical implementation of the microphone array are discussed. Finally, it is shown that by applying an octahedron microphone array consisting of six microphones and an array combination method, the direction of arrival of the sound source can be accurately estimated, even at high Helmholtz numbers.
Gear root cracks alter both the free and forced responses of the measured signal. While established gear crack diagnostic methods have been based on one of those responses, methods based on free responses have not yet been developed for variable speed applications. This study provides insights into the differences between methods based on free and forced responses and their suitability for practical application. The paper investigates gear root crack diagnosis using three different techniques for both constant and variable speed: a classical approach based on Stewart’s analysis of TSA signals, transfer function removal, and the angle cepstrum comb liftering (ACCL) method. The application of ACCL is extended to transmission error (TE) and displacement signals, which have not previously been investigated. In addition, the paper systematically examines the choice of tine width (TW) in the ACCL method to optimise the signal-to-noise ratio of the ACCL spectrum over this broader application area. These techniques are applied to two crack cases: a single crack with the same number of hunting tooth periods for all situations, and two cracks for which the data have different numbers of hunting tooth periods, to assess the effect of this parameter on the ACCL method. The optimisation of the TW value indicates that TE requires a higher value of TW than the acceleration and displacement signals, even though the overall shape of the displacement spectrum is more similar to that of TE (angular displacement). Using data collected under healthy conditions as the baseline, the comparative results indicate that TE was the strongest discriminator between healthy and cracked conditions. This study has made the following contributions to the research field. First, this is the first paper that systematically documents the differences between forced and free responses, and between additive and multiplicative (i.e. modulation) effects. Second, it advances speed-robust gear diagnostics through a comparative assessment of TF removal and ACCL methods, while extending the application of ACCL to both TE and vibration signals.
This study proposes a single-channel broadband Nonlinear Wave Modulation Spectroscopy (NWMS) strategy for baseline-free full-field damage imaging in composite structures, markedly simplifying the experimental configuration required by conventional approaches. The key idea is to excite the structure using a mixed-frequency signal formed by the linear superposition of two continuous waves, thereby eliminating the need for a second excitation chain. Under sufficiently intense excitation, strong wave/defect interactions give rise to multiple nonlinear components triggered at defects, from which sensitive nonlinear damage maps are constructed through time–frequency filtering and bandpower calculation.The feasibility of the proposed single-channel strategy is first verified through numerical simulations. The practical imaging performance is further assessed through experiments on a delaminated cross-ply composite plate under varying excitation conditions. The results demonstrate that the single-channel dual-actuator excitation scheme manifests pronounced defect detectability and superior robustness in damage imaging, while effectively mitigating the influence of source nonlinearities under high mechanical input power (MIP) levels. Moreover, the nonlinearity evolution analysis confirms the existence of a nonlinear activation threshold for delamination, above which the nonlinear bandpower at defects exhibits an approximately positive linear correlation with the MIP delivered by the actuators. Finally, the applicability of the proposed strategy to different layups and damage types is further validated on an impacted quasi-isotropic CFRP plate.
Periodic impact loads exhibit transient and broadband characteristics, making it difficult for fixed-parameter vibration damping devices to simultaneously address different response stages. To address this issue, this paper proposes an intermittent multi-segment nonlinear energy sink (IM-NES) with multi-segment gaps, segmented stiffness, and segmented damping, and establishes a dynamic model coupling it with a linear oscillator. Periodic half-sine acceleration impacts are used as external excitation, and the system response is obtained through numerical integration. The effects of the number of segments, segmented gaps, segmented damping, segmented stiffness, and asymmetric parameters on vibration reduction performance are investigated by combining indicators such as root mean square acceleration, vibration reduction efficiency, short-time Fourier transform, segment activation rate, and segmented dissipated energy. Results show that the multi-segment structure can progressively activate different segments according to the relative motion amplitude. By adjusting the restoring force and damping energy dissipation, the velocity and acceleration responses of the main structure are effectively reduced, and the adaptability to different impact intensities is improved. The segment gaps mainly determine the activation conditions, while segmented damping and segmented stiffness affect the control effect by influencing relative motion and energy transfer. Excessive constraints weaken the participation of higher-order segments. Asymmetric parameters can adjust the segment participation and energy distribution in both forward and reverse motions. Experimental results verify the proposed device’s ability to suppress periodic impact vibrations, providing theoretical and experimental basis for the structural design and parameter matching of IM-NESs.
