Bearings frequently operate under time-varying working conditions where speed profiles may be unseen for intelligent diagnostic models. Frontier research succeeds in extracting discriminative and invariant features for accurate diagnosis. However, their extraction and generalization mechanisms lack physical interpretations, resulting in dubious generalizability and high data dependency. To tackle the challenges in practical scenarios, this study incorporates fault mechanism, proposing a fully interpretable network for credible fault diagnosis across unseen time-varying working conditions, called convolutional sparse modal unrolling network (CSMUNet). For interpretable time-varying feature extraction, a novel sparse coding algorithm is conceived and forms CSMUNet via algorithm unrolling. The algorithm utilizes modal response as convolutional dictionary for sparse vector optimization, under a masking constraint of time-varying impulsive moments. To generalize across unseen working conditions, an interpretable domain-invariant representation is conceived based on impulsive fault mechanism. The input is divided by equiangular span instead of time length, enabling impulses of different samples to have constant numbers for accurate moment recognition in CSMUNet. The proposed model is tested under unseen time-varying speed with simulation and experiment data. Results demonstrate the superior discriminative feature extraction, with key metrics rising to 3.2 times higher than raw inputs and classical convolutional models reaching over 35% accuracy improvement. The performance of CSMUNet is interpreted with the domain-invariant representation, which enhances its diagnostic credibility.

The demand for disruption-free fault diagnosis of mechanical equipment under a constantly changing operation environment poses a great challenge to the deployment of data-driven diagnosis models in practice. Extant continual learning-based diagnosis models suffer from consuming a large number of labeled samples to be trained for adapting to new diagnostic tasks and failing to account for the diagnosis of heterogeneous fault types across different machines. In this paper, we use a representative mechanical equipment -rotating machinery – as an example and develop an uncertainty-aware continual learning framework (UACLF) to provide a unified interface for fault diagnosis of rotating machinery under various dynamic scenarios: class continual scenario, domain continual scenario, and both. The proposed UACLF takes a three-step to tackle fault diagnosis of rotating machinery with homogeneous-heterogeneous faults under dynamic environments. In the first step, an inter-class classification loss function and an intra-class discrimination loss function are devised to extract informative feature representations from the raw vibration signal for fault classification. Next, an uncertainty-aware pseudo labeling mechanism is developed to select unlabeled fault samples that we are able to assign pseudo labels confidently, thus expanding the training samples for faults arising in the new environment. Thirdly, an adaptive prototypical feedback mechanism is used to enhance the decision boundary of fault classification and diminish the model misclassification rate. Experimental results on three datasets suggest that the proposed UACLF outperforms several alternatives in the literature on fault diagnosis of rotating machinery across various working conditions and different machines.Note to Practitioners—This paper presents a continual fault diagnosis methodology for mechanical equipment under various working conditions across different machines with homogeneous-heterogeneous faults. On the application side, the proposed UACLF can be applied to facilitate diagnosis across a broad range of complex industrial equipment, including aerospace, automobile transmission, and wind turbines, among others. With the uncertainty-aware pseudo labeling, the proposed framework is empowered to select the samples in the new phase that we are able to reliably assign their labels. Hence, it can effectively improve mechanical equipment fault classification accuracy in the case that only a small portion of labeled fault samples is available. When training the model, given the model architecture, fault samples collected from multiple accelerometers are fed into the developed model. Four different loss functions, supervision loss, inter-class classification loss, intra-class discrimination loss, and uncertainty estimation loss, are employed to train the diagnostic model. Experiments conducted on three different laboratory datasets have demonstrated the effectiveness of the proposed framework, but have not been tested in the practical industrial applications. We will consider testing the proposed UACLF in an actual plant in future research.

In mechanical fault diagnosis (MFD), intelligent fault diagnosis (IFD) methods perform excellently regarding diagnosis accuracy. However, those methods are generally constructed with an excessive number of unprincipled parameters, resulting in uninterpretable architecture, ambiguity in the diagnosis process, and unclear decision-making basis. Thus, a traceable algorithm unrolling (TAU) network for interpretable MFD is proposed to overcome the above limitations. First, a mechanism-driven feature extractor (FE) is constructed by unrolling the iterative algorithm of sparse coding, aiming at encoding interpretable features from vibration signals. Second, a theory-based feature clustering (FC) algorithm is executed through the dynamic routing mechanism of the capsule network (CN), where the inner product serves as a measure for the association between input and output features. Finally, a post hoc interpretability strategy based on the coupling matrix is introduced to investigate how the TAU generates diagnostic results from the learned features and to verify whether these features are associated with faults, thereby enhancing the credibility of the diagnosis results. In addition, the simulation and experiment are designed to verify the decision-making mechanism and diagnostic performance of TAU. The results demonstrate that TAU makes diagnostic decisions based on the high-dimensional feature mapping associated with fault characteristic frequencies. Meanwhile, TAU outperforms the compared methods in fault diagnosis performance.

Due to high-transmission efficiency, gearboxes have become indispensable components of industrial mechanical equipment. It is paramount for gearbox fault diagnosis to extract discriminant features under strong interferences of industrial scene. However, the extraction performance of current methods is not satisfactory in interpretability and robustness. In this article, an interpretable approach named mechanism-informed neural network (MINN) is proposed for robust impulsive fault feature (IFF) extraction. First, standard auto-encoder is modified based on sparse representation to construct an unsupervised MINN. Second, a mechanism-informed dictionary is designed and embedded into MINN, which brings physical interpretability for the IFF extraction. Third, a two-stage IFF extraction framework is formulated, in which the network parameters are adaptively updated with the proposed joint optimization algorithm to achieve robust IFF extraction. Finally, comparative studies in simulation and experiment are conducted. The results demonstrate that MINN performs better in IFF extraction under strong harmonic interferences. Moreover, the extracted IFF of MINN has been analyzed and interpreted from the view of impulsive fault mechanism, which enhances the reliability.

Impulsive feature (IF) response is an essential indicator for rolling bearing fault. However, it is overwhelmed by strong noise and difficult to extract in real scenes. Although deep learning-based methods are powerful in feature extraction, their logic and extracting principles possess weak interpretability and credibility. Their further implementation is hampered. In this article, a natural modal sketching network (NMSNet) is constructed to achieve robust and credible bearing IF extraction. First, the modal response is designed as a convolutional kernel of NMSNet, and the forward propagation logic is interpreted as natural modal sketching, including modal response recovery and weighted superposition. The logic derives from the fault mechanism and brings solid credibility to NMSNet. Second, a novel correction algorithm is developed to interpret the extraction principle of NMSNet in theory and achieve noise elimination due to its filter nature. Third, NMSNet realizes adaptive modal sketching via the formulated weighted fusion strategy and training constraint. Finally, simulation and experiment have been carried out to verify the effectiveness and noise robustness of NMSNet. The fault-related interpretability analysis confirms the knowledge acquisition of NMSNet, which strengthens the credibility of IF extraction.

Rotatory machinery commonly operates in complex environments with strong noise and variable working conditions. Time-frequency representation offers a valuable method for capturing and analyzing nonstationary characteristics, making it particularly suitable for identifying transient fault-related features. However, despite these advantages, extracting robust and interpretable fault features in machinery operating under variable speeds remains a challenge with existing techniques. In this article, a novel sparse time-frequency representation (STFR) method, named matching pursuit network (MPNet) is proposed for mechanical fault diagnosis. First, a deep network structure with signal decomposition capability is constructed by well-defined interpretable matching pursuit (MP) units to automatically learn discriminative features from time-frequency inputs. Then, the weights of each effective component signal to reconstruct the raw input are designed to measure their contributions. Accordingly, the optimization criterion with structural similarity metric is produced to realize the model parameter update in an end-to-end manner. Finally, phenomenological model-based fault simulation signals and real fault signals from gearbox experiments are used for model training and testing, respectively. The results show that the proposed approach can well extract robust and interpretable time-frequency features and obviously outperforms the state-of-the-art time-frequency representation methods.

The development of Internet of Things technology provides abundant data resources for prognostics health management of industrial machinery, and data-driven methods have shown their powerful ability in the field of fault diagnosis. However, these methods have several limitations: 1) Using less labeled data to obtain higher accuracy is a challenging task, which limits the application of diagnostic models in practical applications. 2) Physics-informed knowledge is largely ignored during the modeling process, which contains a wealth of information that can reflect the harmonic drive’s health status. To address these challenges, a self-supervised fault diagnosis framework is developed by integrating prior knowledge with deep learning to improve the accuracy and reliability of diagnosis models in industrial applications. Specifically, the physics-based knowledge including 32-dimensional time domain, frequency domain, and time-frequency domain features, is first designed to provide fault information and significantly reduce the amount of data required for deep learning. Furthermore, a self-supervised knowledge embedded auto-encoder network is built by employing the prior knowledge in the multi-scale convolutional auto-encoder. With the ability to integrate prior knowledge and the self-supervised learning mechanism, the proposed method can provide a strong tool for knowledge representation and an effective solution for fault diagnosis under a few-shot industrial scenario. The experimental results conducted on a real harmonic drive fault dataset prove that the proposed network framework provides effective insights on fault diagnosis and has excellent generalizability in practical industrial applications.

Industrial Internet of Things (IIoT) improving by leaps and bounds has brought new possibilities for industrial manufacturing. Meanwhile, it does bring some serious challenges with the increasing number of devices. In which massive connectivity and multiservice are two major challenges for IIoT, in order to address the two main issues, in this article, we jointly consider nonorthogonal multiple access (NOMA) and wireless network slicing scenario, where multiservice devices share the same communication resources. To connect devices as many as possible, we formulate the connectivity maximization problem with joint subcarrier association and power allocation as a mixed-integer nonlinear programming (MINLP) problem, under the constraints of limited communication resources. To solve the problem effectively, we first split the MINLP problem into two subproblems by introducing a power allocation weight. Then, we analyze the theoretical approach for a special case and propose the layered access (LA) algorithm for general cases. Furthermore, a bisection search (Bisearch) algorithm is devised to find out the optimal power allocation weight. Simulation results show that the proposed LA algorithm has better performance compared to other benchmark schemes.

In real industries, there often exist application scenarios where the target domain holds fault categories never observed in the source domain, which is an open-set domain adaptation (DA) diagnosis issue. Existing DA diagnosis methods under the assumption of sharing identical label space across domains fail to work. What is more, labeled samples can be collected from different sources, where multisource information fusion is rarely considered. To handle this issue, a multisource open-set DA diagnosis approach is developed. Specifically, multisource domain data of different operation conditions sharing partial classes are adopted to take advantage of fault information. Then, an open-set DA network is constructed to mitigate the domain gap across domains. Finally, a weighting learning strategy is introduced to adaptively weigh the importance on feature distribution alignment between known class and unknown class samples. Extensive experiments suggest that the proposed approach can substantially boost the performance of open-set diagnosis issues and outperform existing diagnosis approaches.

Lane detection is a fundamental task for autonomous driving. Most existed deep learning-based methods use a combination of semantic segmentation and post-processing for lane information extraction. Such methods not only tend to ignore global lane information but also bring the problem of low efficiency due to the complex models. To solve these problems, a novel global lane detection method based on key-point regression and multi-scale features fusion (KP-MFF) is proposed in this study. Firstly, a regression strategy is presented to generate key-point sequences in each grid of the image for locating the lane. Moreover, a multi-scale feature fusion module is proposed to merge feature maps of different scales. Additionally, a rule-based fast post-processing method is proposed to deal with the series of key-point sequences output by the CNN model, which further improves the lane detection accuracy. Experiments on CULane and TuSimple datasets demonstrate that the proposed method performs more effectively (417 FPS on NVIDIA 2080Ti and 91 FPS on NVIDIA Jetson AGX Xavier) while maintaining competitive accuracy compared with state-of-the-art methods. The road test also validates the practicability and effectiveness of the proposed method.

Recently, domain adaptation techniques have achieved great attention in solving domain-shift problems of mechanical fault diagnosis. However, existing methods mostly work under assumption that source domain and target domain share identical label spaces, which fail to handle those issues, where a large set of source data classes are available and target data only cover a subset of classes. To address this problem, a novel weighted adversarial transfer network (WATN) is proposed for partial domain fault diagnosis, in this article. Adversarial training is introduced to learn both class discriminative and domain invariant features, and a weighting learning strategy is adopted to weigh their contributions to both source classifier and domain discriminator. As such, the irrelevant source examples can be identified and filtered out, and the distribution discrepancy of shared classes between domains can be reduced. Experiments on two diagnosis data sets demonstrate that the proposed WATN achieves satisfactory performance and outperforms state-of-the-art methods.

Deep neural networks present very competitive results in mechanical fault diagnosis. However, training deep models require high computing power while the performance of deep architectures in extracting discriminative features for decision making often suffers from the lack of sufficient training data. In this paper, a transferable convolutional neural network (CNN) is proposed to improve the learning of target tasks. First, a one-dimensional CNN is constructed and pretrained based on large source task datasets. Then a transfer learning strategy is adopted to train a deep model on target tasks by reusing the pretrained network. Thus, the proposed method not only utilizes the learning power of deep network but also leverages the prior knowledge from the source task. Four case studies are considered and the effects of transfer layers and training sample size on classification effectiveness are investigated. Results show that the proposed method exhibits better performance compared with other algorithms.

In practical industrial applications, the working conditions of machinery are changing with long-term operation, and the health status is declining with the degradation of crucial components. When the working condition changes, prior diagnosis models cannot be generalized from one condition to another. To solve this challenging issue, in this article a robust weight-shared capsule network (WSCN) is introduced for intelligent fault diagnosis of machinery under varying working conditions. First, taking raw accelerometer signals as inputs, one-dimensional convolutional neural network is constructed to extract discriminative characteristics. Second, various capsule layers based on multistacked weight-shared capsules are developed to enhance the generalization performance for further fault classification. Finally, margin loss function as well as agreement-based dynamic routing algorithm are employed to optimize the WSCN. In this article, two diagnosis cases are carried out to demonstrate the generalization performance of the WSCN which obtains higher accuracy under varying working conditions than that of other state-of-the-art methods.

It is a big challenge to identify the most effective features for enhancement of fault classification accuracy in rotating machines due to nonstationary and nonlinear vibration characteristics of the machines under varying operating conditions. To find discriminative features, a novel dimension reduction algorithm, referred to as the nearest and farthest distance preserving projection (NFDPP), is proposed for machine fault feature extraction and classification. With the NFDPP, both the nearest and farthest samples of the data manifold can be analyzed simultaneously to identify features leading to fault classification. Additionally, we denoise the features directly in the feature space to save computation time and storage space, and prove its equivalence to denoising the signals in the time domain. Through analysis of measured vibration data for bearings with different defects, it is demonstrated that the proposed NFDPP approach can effectively classify different bearing faults and identify the severity of the bearing ball defect, and the direct denoising of features yield a significant improvement in fault classification. The effectiveness of the proposed method is further validated in identifying compound faults in locomotive bearings in an industrial setting.