The performance of the activation function in convolutional neural networks is directly related to the model’s image classification accuracy. The rectified linear unit (ReLU) activation function has been extensively used in image classification models but has significant shortcomings, including low classification accuracy. The performance of a series of parametric activation functions has made parameter addition a popular research avenue for improving the performance of activation functions in recent years, and excellent progress has been achieved. Existing parametric activation functions often focus on assigning a different slope to the negative part of the activation function and still involve the negative value alone in the activation function calculation, without considering the impact of linking the negative value to the positive value on the performance of the activation function. As a result, this work proposes a novel parametric right-shift activation function, the adaptive offset activation function (AOAF). By inserting an adaptive parameter (the mean value of the input feature tensor) and two custom ReLU parameters, the negative parameters previously driven to zero by ReLU can be turned into positive parameters with lower weight and participate in CNN feature extraction. We compared the performance of the suggested activation function to the performance of a selection of typical activation functions using four distinct public datasets. Compared with ReLU, the average classification accuracy of our proposed activation function improved by 3.82%, 0.6%, 1.02%, and 4.8% for the four datasets, respectively.

In response to the problems of low accuracy and poor noise immunity of the traditional fault diagnosis method for rolling bearing fault diagnosis due to the complex and variable operating conditions of rolling bearings and the large noise interference during bearing signal acquisition, a rolling bearing fault diagnosis model based on VMD–RP–CSRN is proposed. Firstly, the initial feature extraction of the bearing signal is carried out by variational modal decomposition (VMD), which is then converted into a two-dimensional image with fault features by recurrent plot (RP) coding, and then the feature images are input to a channel split residual network (CSRN) for feature extraction and fault classification. In order to verify the accuracy and noise immunity of the proposed method for the diagnosis of bearing faults under complex working conditions, experiments on the selection of parameters in the CSRN model were conducted on the bearing dataset of Jiangnan University, and experiments on the diagnosis of bearing faults under complex working conditions and noise immunity of CSRN were carried out and compared with other commonly used methods. The proposed bearing fault diagnosis method based on VMD–RP–CSRN combines VMD and RP to retain the fault features in the original signal to the maximum extent and stress the hidden features in the signal. The proposed channel split operation realizes the extraction of hidden features by selecting the main operating channel of the three-channel feature image, and makes more fault features participate in the feature extraction of the diagnosis model. The experimental results demonstrate that the proposed method is at least 1.2% better than the comparison method, and has better noise immunity. In addition, experiments on the fault diagnosis capability of the model with different data set sizes and the diagnosis of variable speed bearing data by the model show that the proposed method has better generalization performance and diagnosis capability.

To address the problems of poor model diagnosis and poor noise immunity caused by inconsistent distribution of bearing fault features and difficulty in feature extraction in multi-condition environments, a multi-condition bearing fault diagnosis method based on a channel segmentation improved residual network is proposed. A channel segmentation mechanism is designed for channel information highlighting, by selecting one channel of the three-channel feature image as the main operation channel, stacking it with the secondary operation channel after convolution, and then inputting the stacked feature map into the convolutional neural network to realize the extraction and classification of bearing fault features. Four different network models were selected to verify the diagnostic performance of the channel segmentation mechanism on the Case Western Reserve University bearing dataset and the Jiangnan University bearing dataset, and noise immunity experiments were conducted on the Jiangnan University bearing dataset. The experiments show that the proposed diagnostic model on the Case Western Reserve bearing dataset has a minimum improvement of 6.8% compared to the comparison method for multi-case bearing fault diagnosis experiments. In terms of noise immunity, the diagnostic accuracy of the fault diagnosis model with the addition of the channel cut-off mechanism improves the diagnostic accuracy of the noisy data by an average of 4.3% compared to that without the addition. The proposed model still has excellent diagnostic performance when diagnosing variable speed bearing faults.

As a core component of automobile transmission, rolling bearings play a main role in the safety and reliability of vehicles. Existing diagnostic models often treat all features equally after feature extraction, without effectively distinguishing the importance of fault features, resulting in low accuracy and poor robustness in bearing fault diagnosis. To address this issue, a fault diagnosis model for bearings under multiple operating conditions based on feature parameterization weighting is proposed. The model utilizes a feature parameterization weighting module to categorize faults into two classes based on differences in means and implements different feature processing methods. The experimental results validate that the proposed feature parameterization weighting module effectively improves the diagnostic accuracy of the model by 8.95%. In terms of noise resistance, on two multi-condition datasets, the proposed diagnostic model achieves diagnostic accuracy of 98.79% and 98.36%. The diagnostic accuracy is improved by 15.7% and 22.48%, which indicates that the model has strong anti-noise ability.

To address the challenge of extracting invariant bearing fault features under multi-working conditions, an enhanced multi-branch bias residual network (MBRN) based on multi-branch bias and folding calculation is proposed. First, in constructing the fault dataset, the original bearing fault signal is transformed into two-dimensional feature images using recurrent plot. Second, to replace the original residual connection, a multi-branch bias structure is constructed, and the feature tensors in different branches are transformed by idle operation and folding operation. This strategy has improved the diagnostic model’s ability to extract invariant bearing fault features under multi-working conditions. Finally, MBRN is trained using the above fault dataset to achieve fault diagnosis under different bearing conditions. The performance of the proposed diagnostic model was validated on two multi-condition bearing fault datasets and two variable condition bearing datasets. The experimental results demonstrate that the average diagnostic accuracy of the proposed MBRN is 4.05% higher than that of the original MBRN. Furthermore, even when reducing the size of the fault dataset to 20% of its original size, the proposed MBRN still improves diagnostic accuracy by an average of 2.2%.