Owing to the nonlinearity and nonstationarity of the bearing fault signal, it is difficult to identify fault characteristics under the influence of a strong noise environment. The extraction of early weak fault features is critical for the reliability of bearing operations. Therefore, an urgent problem is reasonable noise reduction and feature enhancement in weak-signal processing. Traditional variational modal decomposition (VMD) and stochastic resonance (SR) are commonly applied to detect weak signals in fault diagnosis. The VMD method can decompose the signal into several intrinsic mode functions (IMFs) to effectively reduce the modal aliasing problem. However, uniform standards for the key parameters of decomposition and the selection of the optimal IMF after decomposition are lacking. Meanwhile, some disadvantages of SR still exist; for example, the interference of multiscale noise may lead to false detection by incorrect selection of high-pass filter parameters, and the system parameters are not adaptive to different signals to achieve the best response output. To better address the weak signal feature enhancement, a novel rolling bearing fault diagnosis method combining adaptive VMD and SR by improved differential search (IDS) optimization is proposed. First, the bearing fault signal is decomposed into several IMFs using the IDS-VMD. Second, the feature information of the fault signal is retained and reconstructed using the correlation kurtosis for sensitive modal extraction. Furthermore, the fault features of the reconstructed signal are effectively enhanced by the variable-step IDS-SR, which can reasonably transfer the noise energy of the input components to the fault characteristic frequency. Finally, the periodic pulse can be observed in the corresponding envelope spectrum. The simulated and experimental data show that the proposed method can not only effectively extract the signal feature information in the actual fault but also realize early weak fault diagnosis of rolling bearings more accurately.

Variational mode decomposition (VMD), a recently developed adaptive mode decomposition technique, has attracted much attention in various fields. However, due to the assumption that the obtained intrinsic mode functions should be band-limited and separable in the Fourier domain, VMD has experienced many obstacles when processing wideband nonstationary signals. In this paper, a new method named fractional iterative variational mode decomposition (FrIVMD) is proposed for the decomposition of a multicomponent linear frequency modulation signal. By accurately estimating the chirp rate of the linear frequency modulation (LFM) component, the original signal is mapped to the fractional Fourier domain by the fractional Fourier transform (FRFT), where the corresponding LFM component is narrowly banded. Then, the conventional VMD is applied to separate the components. Finally, the signal mode in the time domain is obtained by the inverse FRFT. Numerical and real-world vibration signals are employed to validate the effectiveness of the FrIVMD technique. The results prove that the proposed method performs well for noisy signals and even signals containing weak components.

To ensure a long-time stable operation of the rolling bearing, it is important to accurately assess their working performance, especially the incipient degradation based on the massive service process data. As a new and effective tool, deep learning model is applied widely in the field of fault diagnosis but limited to rare labeled data. In this paper, a bearing performance assessment method based on signal component tracking is proposed to realize the bearing degradation detection. More general features are obtained by local convolution operation to represent the local characteristics in the spectrum or time-frequency distribution of vibration signal, which follows the forward features mapping process of the convolutional neural network (CNN). Then, a novel quantification criterion based on the comparison of those local features is used to provide the selection strategy of optimal fault components. The proposed method takes into account the abnormal information in degradation monitoring and utilizes it to achieve bearing incipient fault diagnosis. The experimental results prove that the features extracted by the proposed method possess high recognition efficiency when being used in incipient failure detection and diagnosis. INDEX TERMS Local feature, incipient fault diagnosis, performance assessment. I. INTRODUCTION