Envelope analysis is one of the most useful methods in localized fault diagnosis of rolling element bearings. However, there is a challenge in selecting the optimal resonance band. In this paper, a novel method based on kurtogram and frequency domain correlated kurtosis is proposed. To obtain the correct relationship between the node and frequency band in wavelet packet transform, a vital process named frequency ordering is conducted to solve the frequency folding problem due to down sampling. Correlated kurtosis of envelope spectrum instead of correlated kurtosis of envelope signal or kurtosis of envelope spectrum is utilized to generate the kurtogram, in which the maximum value can indicate the optimal band for envelope analysis. Several cases of experimental bearing fault signals are used to evaluate the immunity of the proposed method to strong noise interference. The improved performance has also been compared with two previous developed methods. The results demonstrate the effectiveness and robustness of the method in fault diagnosis of rolling element bearings.

In data-driven bearing fault diagnosis, it is unrealistic to obtain enough labeled data, and the data used for training and testing often have different distributions. Existing methods typically address this issue by either marginal distribution adaptation or conditional distribution adaptation. However, most studies fail to consider both distributions simultaneously and overlook the relative importance between them, resulting in suboptimal diagnostic performance. To address this limitation, this paper introduces a novel unsupervised domain adaptation network called the balanced deep transfer network (BDTN). BDTN employs a one-dimensional convolutional neural network (1-D CNN) as its backbone and leverages the maximum mean discrepancy (MMD) and pseudo-labels to map data with distinct marginal and conditional distributions onto the same feature subspace. To ensure practical applicability, a balance factor is proposed to dynamically adjust the relative importance of the marginal distribution adaptation and conditional distribution adaptation. Finally, transfer learning experiments across sensors at different places using the Case Western Reserve University (CWRU) dataset and the axlebox bearing dataset are conducted to validate the effectiveness and superiority of BDTN.

Vibration signals are widely applied in mechanical fault diagnosis methods. Strong and non-stationary noise can easily affect vibration signals, and the vibration signals will differ depending on the load conditions. Additionally, there aren’t many vibration signals with faults that can be employed because mechanical equipment typically operates as intended. A brand-new data augmentation and composite multi-scale network (DACMSN) for mechanical fault identification is proposed as a solution to these issues. The method of data augmentation is to generate samples simply and efficiently through a mathematical permutation and combination method. Each generated sample consists of two original samples, and each generated sample contains all fault information of the original sample. The dense multi-scale convolution neural network (DMSCNN) and the multi-scale residual network (MSRN) make up the composite multi-scale network (CMSN). The CMSN has rich multi-scale feature extraction capabilities and coarse-fine feature extraction capabilities. Convolutional kernels of various sizes are used in DMSCNN, which also takes into account the results of previous layers to initially discover fault features. MSRN further performs multi-scale feature extraction on each sub network of DMSCNN, achieving the effect of fully exploring fault features and effectively accelerating loss backpropagation. The proposed model can demonstrate unique advantages through the use of these mechanisms, such as a wider feature extraction scale and a more complete ability to extract coarse-fine features. This article compares the proposed method with different methods using noise and variable load dataset for tests. The experimental results demonstrate that the proposed method can perform well for fault diagnosis even in noisy environments.

Wavelet filter is widely used in extracting fault features embedded in the noisy vibration signal, especially the complex Morlet wavelet. In most occasions, the filter parameters are optimized adaptively with a suitable objective function. And then, with the Hilbert transform demodulation analysis, the single localized fault in rolling element bearings can be detected. To extend it for compound faults detection, a novel index deduced from the different intervals of the prominent bearing fault frequencies and subsequent harmonics in the envelope spectrum is proposed. By maximizing the ratio of correlated kurtosis to kurtosis of the envelope spectrum amplitudes of the filtered signal, the optimal complex Morlet wavelet filters corresponding to the different faults are designed by the particle filtering method, respectively. Two cases of real signals are analyzed to evaluate the performance of the proposed method, which include one case of experiment signal with artificial outer race fault coupled with roller fault, as well as one case of engineering data with outer race fault coupled with inner race fault. Furthermore, some comparisons with a previous method are also conducted. The results demonstrate the effectiveness and robustness of the method in compound faults diagnosis of the rolling element bearings.