In recent years, many studies on variational mode decomposition (VMD) have mainly focused on choosing the number of modes and balancing parameter, while less research focuses on the internal properties of VMD. This paper proposes an adaptive single-mode VMD (ASMVMD) method based on the convergence characteristics of VMD and the adaptivity of particle swarm optimization (PSO). Firstly, we study the convergence characteristics of single-mode VMD and find that the U-shaped convergence region related to fault impact is very wide in the whole frequency domain. Secondly, based on the characteristics of the U-shaped convergence region, a new population position initialization strategy is proposed. Finally, the improved PSO is used to optimize the initial center frequency and balancing parameter of single-mode VMD. The effectiveness of the proposed method is verified by analyzing the simulated signal and wheelset bearing fault signals. Compared with the fast kurtogram and Autogram, it is shown that ASMVMD has a stronger capability of fault feature extraction.

A wheelset bearing is one of the main components of the train bogie frame. The early fault detection of the wheelset bearing is quite important to ensure the safety of the train. Among numerous diagnostic methods, envelope analysis is one of the most effective approaches in the detection of bearing faults which has been amply applied, but its validity greatly depends on the informative frequency band (IFB) determined. For the wheelset bearing faulty signal, it is often difficult to identify the IFB and extract fault characteristics due to the influence of complex operating conditions. To address this problem, a novel method to select optimal IFB, called the Mkurtogram, is proposed for railway wheelset bearings fault diagnosis. It takes the multipoint kurtosis (Mkurt) of unbiased autocorrelation (AC) of the squared envelope signal generated from sub-bands as assessment indicator for the first time. The fundamental concept which inspires this proposed method is to make full use of regular periodicity of AC of squared envelope signal. In the AC domain, the impulsiveness and periodicity, two distinctive signatures of the repetitive transients, have achieved a united representation by Mkurt. A simulated signal with multiple interferences and two experimental signals collected from wheelset bearings are applied to verify its performances and advantages. The results indicate that the proposed method is more effective to extract the wheelset bearings fault feature under complex interferences. It can not only decrease the influence of large impulse interference and the discrete harmonics interference, but also effectively overcome the influence of amplitude fluctuation caused by variable working conditions. Moreover, based on the periodic directivity of Mkurt, the proposed method also can be applied to the compound faults diagnosis of the wheelset bearing.

Due to the influence of the wheel-rail excitation and complex transmission path, the fault signature of wheelset bearings is often obscured by complex background noise, which brings great challenges to the adaptive determination of the informative frequency band (IFB) in envelope analysis. In this paper, the vibration response characteristics of the axle box under wheel–rail excitation are revealed through full-scale bench tests. The experimental results show that tread damage will provoke periodic transient impacts and it has an obvious sparsity in the frequency domain. Inspired by this feature, a DTMSgram method is proposed to enhance the fault feature components of vibration signals through time-domain and frequency-domain noise reduction technology, and improve the accuracy of demodulation frequency band selection. Firstly, the amplitude spectrum of different weight coefficients is used to preprocess the vibration signal and adjust the full band component of the vibration signal. Then, the autocorrelation process is performed on each layer’s narrowband filtered signal envelope in kurtogram to further reduce noise interference from a time-domain perspective. Moreover, a two-dimensional color map is constructed showing the normalized squared envelope spectrum of the IFBs determined simultaneously from the modified signal. Finally, the effectiveness of the proposed method is verified by simulated signal and experimental data of three sets of full-size wheelset bearing systems. The analysis results indicate this proposed method can effectively overcome the influence of complex wheel–rail excitation interference and can diagnose multi-source faults simultaneously.

Aiming at the difficulty of accurate diagnosis of wheelset-bearing system composite faults, a multi-fault feature extraction method based on self-adaptive variational mode extraction (SAVME) was proposed. Variational mode extraction (VME) can extract a specific sub-signal from a multi-component signal. The key to the success of this algorithm is to determine appropriate initial parameters in advance, including initial center frequency (ICF) and penalty factor. To determine the key parameters of VME adaptively, the convergence characteristics of VME are analyzed deeply, and the VME convergence tendency diagram is proposed creatively according to the trend of the iterative curve of the center frequency of the desired mode. By analyzing the test signal with the VME convergence tendency diagram, the number of main latent sub-signals in the test signal and the ICF of each sub-signal corresponding to the VME can be determined efficiently. Then, according to the position of the ICF of each sub-signal in the frequency domain, the empirical formula of the penalty factor is used to quickly obtain the appropriate penalty factor. The proposed SAVME method not only improves the parameter selection adaptability of the traditional VME algorithm but also extends the VME algorithm to the field of multi-fault diagnosis. By analyzing the simulated signal and two experimental signals, the effectiveness of the SAVME algorithm is verified. Compared with the fast kurtogram method and the adaptive variational mode decomposition method, the proposed method is more accurate and superior in the multi-fault feature extraction of the wheelset-bearing system.

Studies on wheel flatness and polygonal wear have demonstrated that wheel defects cause severe impact forces at the wheel–rail interfaces. This study investigated the dynamic contact mechanical behaviour of high–speed train transmission gears when subjected to wheel defects. First, a train-track coupling dynamics model was established, considering the localized contact characteristics of transmission gears. This model was developed using the slice method and the Hertz contact model, exploring the spatial coupling effects between the gear contact interface and the train–track interface. Subsequently, the dynamic model was employed to extract essential contact mechanical parameters of the transmission gear under the influence of wheel defects, including gear meshing load, gear contact stress, and sliding velocity. Furthermore, an analysis was conducted to uncover and elucidate the mechanism by which wheel flatness and polygonal wear impact the dynamic contact behaviour of the transmission gear. This study underscores the importance of considering wheel defects when assessing the contact fatigue and wear performance of high-speed train transmission gears.