The bearing fault diagnosis is of vital significance in maintaining the safety of rotation machine. Among various fault detection techniques, the diagnosis based on vibration signal is widely applied in monitoring the condition of rotation machine. Variational mode decomposition (VMD) is a novel signal analysis method, which can decompose a multi-component signal into a certain number of band-limited intrinsic mode functions (BLIMFs) nonrecursively. VMD could overcome some problems such as mode mixing, the inference of noise, the determination of wavelet base, which exist in empirical mode decomposition, ensemble empirical mode decomposition, wavelet transform, respectively. However, the empirical selection of the parameters for VMD would affect the result of the decomposition. This paper presents an adaptive VMD method with parameter optimization for detecting the localized faults of rolling bearing. Kurtosis, sensitive to transient impulsive components, is employed as optimization index to evaluate the performance of the VMD. Two parameters in the VMD, namely the number of decomposition modes and data-fidelity constraint, are optimized synchronously based on the kurtosis index through artificial fish swarm algorithm. Executing VMD with the acquired parameters, the optimal BLIMF is obtained. The spectrum analysis of the optimal BLIMF could identify the characteristic frequency caused by the localized crack effectually. The validity of the proposed method is proved by means of a cyclic transient impulse response signal and two experiments with practical vibration signals of rolling bearings. Compared to several existing methods, the proposed method demonstrates reinforced results.

Stochastic resonance (SR) has been proved to be an effective approach for weak sensor signal detection. This study presents a new weak signal detection method based on a SR in an underdamped system, which consists of a pinning potential model. The model was firstly discovered from magnetic domain wall (DW) in ferromagnetic strips. We analyze the principle of the proposed underdamped pinning SR (UPSR) system, the detailed numerical simulation and system performance. We also propose the strategy of selecting the proper damping factor and other system parameters to match a weak signal, input noise and to generate the highest output signal-to-noise ratio (SNR). Finally, we have verified its effectiveness with both simulated and experimental input signals. Results indicate that the UPSR performs better in weak signal detection than the conventional SR (CSR) with merits of higher output SNR, better anti-noise and frequency response capability. Besides, the system can be designed accurately and efficiently owing to the sensibility of parameters and potential diversity. The features also weaken the limitation of small parameters on SR system.

The condition of locomotive bearings, which are essential components in trains, is crucial to train safety. The Doppler effect significantly distorts acoustic signals during high movement speeds, substantially increasing the difficulty of monitoring locomotive bearings online. In this study, a new Doppler transient model based on the acoustic theory and the Laplace wavelet is presented for the identification of fault-related impact intervals embedded in acoustic signals. An envelope spectrum correlation assessment is conducted between the transient model and the real fault signal in the frequency domain to optimize the model parameters. The proposed method can identify the parameters used for simulated transients (periods in simulated transients) from acoustic signals. Thus, localized bearing faults can be detected successfully based on identified parameters, particularly period intervals. The performance of the proposed method is tested on a simulated signal suffering from the Doppler effect. Besides, the proposed method is used to analyze real acoustic signals of locomotive bearings with inner race and outer race faults, respectively. The results confirm that the periods between the transients, which represent locomotive bearing fault characteristics, can be detected successfully.

A fault diagnosis strategy based on the wayside acoustic monitoring technique is investigated for locomotive bearing fault diagnosis. Inspired by the transient modeling analysis method based on correlation filtering analysis, a so-called Parametric-Mother-Doppler-Wavelet (PMDW) is constructed with six parameters, including a center characteristic frequency and five kinematic model parameters. A Doppler effect eliminator containing a PMDW generator, a correlation filtering analysis module, and a signal resampler is invented to eliminate the Doppler effect embedded in the acoustic signal of the recorded bearing. Through the Doppler effect eliminator, the five kinematic model parameters can be identified based on the signal itself. Then, the signal resampler is applied to eliminate the Doppler effect using the identified parameters. With the ability to detect early bearing faults, the transient model analysis method is employed to detect localized bearing faults after the embedded Doppler effect is eliminated. The effectiveness of the proposed fault diagnosis strategy is verified via simulation studies and applications to diagnose locomotive roller bearing defects.

Measured vibration signals from rolling element bearings with defects are generally nonstationary, and are multiscale in nature owing to contributions from events with different localization in time and frequency. This paper presents a novel approach to characterize the multiscale signature via empirical mode decomposition (EMD) for rolling bearing localized defect evaluation. Vibration signal measured from a rolling element bearing is first adaptively decomposed by the EMD to achieve a series of usable intrinsic mode functions (IMFs) carrying the bearing health information at multiple scales. Then the localized defect-induced IMF is selected from all the IMFs based on a variance regression approach. The multiscale signature, called multiscale slope feature, is finally estimated from the regression line fitted over logarithmic variances of the IMFs excluding the defect IMF. The presented feature reveals the pattern of energy transfer among multiple scales due to localized defects, representing an inherent self-similar signature of the bearing health information that is embedded on multiple analyzed scales. Experimental results verify the performance of the proposed multiscale feature, and further discussions are provided.

The phenomenon of Doppler shift in the acoustic signal acquired by a microphone amounted beside the railway leads to the difficulty for fault diagnosis of train bearings with a high moving speed. To enhance the condition monitoring performance of the bearings on a passing train using stationary microphones, the elimination of the Doppler shift should be implemented firstly to correct the severe frequency-domain distortion of the acoustic signal recorded in these conditions. In this paper, a Doppler shift removal method is proposed based on instantaneous frequency (IF) estimation (IFE) for analyzing acoustic signals from train bearings with a high speed. Specifically, the IFE based on short-time Fourier transform is firstly applied to attain the IF vector. According to the acoustic theory of Morse, the data fitting is then carried out to achieve the fitting IFs with which the resampling sequence can be established as the resampling vector in time domain. The resampled signal can be finally reconstructed to realize fault diagnosis of train bearings. To demonstrate the effectiveness of this method, two simulations and an experiment with practical acoustic signals of train bearings with a crack on the outer raceway and the inner raceway have been carried out, and the comparison results have been presented in this paper.