Owing to complex operational and measurement conditions, the data available to realize the effective training of deep models are often inadequate. Compared with traditional deep networks, Transformer exhibits a unique and excellent pattern recognition ability and has thus emerged as the de facto standard for processing tasks in many research fields. However, the application of Transformer architectures to fault diagnosis remains limited. To overcome these limitations and achieve highly accurate fault diagnosis, a novel Transformer convolution network (TCN) based on transfer learning is proposed. First, signal data are split into fixed-size patches, and the sequence of the linear embeddings of these patches is used as an input to a Transformer encoder. Subsequently, a convolutional neural network with a classifier layer is constructed to decode and classify patterns. The TCN is pretrained in the source domain and fine-tuned in the target domain by using a transfer learning strategy. Experiments to diagnose rotating machinery faults are conducted using bearing and gearbox datasets. The average diagnostic results for four transfer experiments are 99.71%, 99.97%, 99.83%, and 100.00%, and the proposed approach significantly outperforms state-of-the-art methods. The results demonstrate the exceptional robustness and effectiveness of the proposed method.

Effective steel surface defect classification with low computational cost is essential for online quality inspection. The challenge of this task is large intra-class differences and unclear inter-class distances shown in various surface defects. This paper proposes a novel feature extraction method based on Legendre multi-wavelet transform and Auto-Encoder network (LWT-AE) for effectively recognizing the steel surface defects categories. More precisely, the finite element approximation theory is implemented to address the strong capacity of LW bases with various regularities and vanish moments for thoroughly matching the complex geometry characteristics of the steel surface defects, which provides strict theory foundation for the feature extraction in LWT frequency domain without losing any defect information due to its orthogonality. Then, the statistical and texture parameters are utilized to sparsely extract the defect features from LWT frequency domain, resulting in removing the redundancy components corresponding to the defects. AE network is utilized to further reduce the dimension of the extracted features and automatically select the most valuable defect features. Furthermore, two classifiers (SVM and BPNN) are used to rectify the generalization ability of the proposed method. Finally, extensive experiments are conducted on two datasets to verify the effectiveness and robustness of the proposed method. The highest classification accuracies 99.44% and 95.37% compared with other methods are attained on the NEU-CLS dataset and X-SDD dataset, respectively. To summary, the proposed method not only has simple structure, but also can reliably identify different types of the steel surface defects, which provides a suitable online application technique for the actual steel surface defect classification.

This paper focuses on the fault diagnosis problem in the scenario of scarce bearing samples, facing two main challenges: complex noise background and variations in operating conditions. While deep learning-based fault diagnosis methods have achieved significant progress, they heavily rely on large amounts of samples. This paper proposes a few-shot learning fault diagnosis method based on siamese networks (SN), which classify samples based on the similarity between pairs rather than end-to-end classification. Tested on two bearing datasets, the proposed method outperforms SVM, DCNN, WDCNN, and CNN-BiGRU. The influence of factors such as parameter regularization, noise, and load variation on the proposed method is also discussed. Experimental results demonstrate that double parameter regularization contributes more to the model’s generalization ability, maintaining good stability and generalization even under noise interference or load variation.

The application of edge computing combined with the Internet of Things (edge-IoT) has been rapidly developed. It is of great significance to develop a lightweight network for gearbox compound fault diagnosis in the edge-IoT context. The goal of this paper is to devise a novel and high-accuracy lightweight neural network based on Legendre multiwavelet transform and multi-channel convolutional neural network (LMWT-MCNN) to fast recognize various compound fault categories of gearbox. The contributions of this paper mainly lie in three aspects: The feature images are designed based on the LMWT frequency domain and they are easily implemented in the MCNN model to effectively avoid noise interference. The proposed lightweight model only consists of three convolutional layers and three pooling layers to further extract the most valuable fault features without any artificial feature extraction. In a fully connected layer, the specific fault type of rotating machinery is identified by the multi-label method. This paper provides a promising technique for rotating machinery fault diagnosis in real applications based on edge-IoT, which can largely reduce labor costs. Finally, the PHM 2009 gearbox and Paderborn University bearing compound fault datasets are used to verify the effectiveness and robustness of the proposed method. The experimental results demonstrate that the proposed lightweight network is able to reliably identify the compound fault categories with the highest accuracy under the strong noise environment compared with the existing methods.

Efficiently diagnosing bearing faults is of paramount importance to enhance safety and reduce maintenance costs for rotating machinery. This paper introduces a novel bearing fault diagnosis method (LW-BPNN), which combines the rich properties of Legendre multiwavelet bases with the robust learning capabilities of a BP neural network (BPNN). The proposed method not only addresses the limitations of traditional deep networks, which rely on manual feature extraction and expert experience but also eliminates the complexity associated with designing and training deep network architectures. To be specific, only two statistical parameters, root mean square (RMS) and standard deviation (SD), are calculated on different Legendre multiwavelet decomposition levels to thoroughly represent more salient and comprehensive fault characteristics by using several scale and wavelet bases with various regularities. Then, the mapping relation between the extracted features and the health conditions of the bearing is automatically learned by the simpler BPNN classifier rather than the complex deep network structure. Finally, a few experiments on a popular bearing dataset are implemented to verify the effectiveness and robustness of the presented method. The experimental findings illustrate that the proposed method exhibits a high degree of precision in diagnosing various fault patterns. It outperforms other methods in terms of diagnostic accuracy, making it a viable and promising solution for real-world industrial applications in the field of rotating machinery.

Wavelet neural networks have been widely applied to dynamical system identification fields. The most difficult issue lies in selecting the optimal control parameters (the wavelet base type and corresponding resolution level) of the network structure. This paper utilizes the advantages of Legendre multiwavelet (LW) bases to construct a Legendre multiwavelet neural network (LWNN), whose simple structure consists of an input layer, hidden layer, and output layer. It is noted that the activation functions in the hidden layer are adopted as LW bases. This selection if based on the its rich properties of LW bases, such as piecewise polynomials, orthogonality, various regularities, and more. These properties contribute to making LWNNs more effective in approximating the complex characteristics exhibited by uncertainties, step, nonlinear, and ramp in the dynamical systems compared to traditional wavelet neural networks. Then, the number of selection LW bases and the corresponding resolution level are effectively optimized by the simple Genetic Algorithm, and the improved gradient descent algorithm is implemented to learn the weight coefficients of LWNN. Finally, four nonlinear dynamical system identification problems are applied to validate the efficiency and feasibility of the proposed LWNN-GA method. The experiment results indicate that the LWNN-GA method achieves better identification accuracy with a simpler network structure than other existing methods.