Accurate fault classification in rotating machinery under changing speeds and loads is a critical challenge in industrial predictive maintenance, where vibration signatures shift across operating regimes and black-box decisions are difficult to trust. This paper presents a hybrid architecture that combines Transformers with Logic Tensor Networks (LTNs), used here as the neuro-symbolic learning framework because they ground first-order rules into differentiable satisfiability terms optimized directly in the training objective, for fault diagnosis on two public benchmarks: the Drivetrain Dynamics Simulator (DDS) (multiple speed/load regimes) and the University of Connecticut (UoC) gear-fault dataset. A compact 1-D Transformer encodes raw vibration windows, and an LTN layer imposes soft first-order constraints during training. We introduce a dynamic rule module that induces, merges, and prunes centroid-based similarity rules as the embedding geometry evolves, enabling the constraint set to adapt to within-class variability. Unlike prior LTN-based approaches such as LogicLSTM, which reweight a fixed rule set, our rules are induced and updated dynamically during training. Experiments show improvements over strong neural and neuro-symbolic baselines on DDS (average accuracy 94.01% vs 88.20%), and gains over a strong Transformer baseline on UoC (macro F1 0.939). Beyond accuracy, the induced rules provide compact, queryable explanations by identifying prototypical vibration-window patterns that support a prediction. Confidence calibration improves versus baselines under the same evaluation protocol. Because LTN supervision acts only during training, inference latency matches the base Transformer. The results support neuro-symbolic fusion as a practical path to accurate and explainable fault diagnosis under varying operating conditions.

The intelligent fault diagnosis (IFD) methods based on graph neural networks (GNNs) have achieved great success in machine fault diagnosis. However, the following two drawbacks of the existing GNN-based methods have greatly limited their application in industry: 1) poor interpretability in model structure and the extracted features and 2) difficulty in extracting robust fault features in nonstationary machine states. To address the above issues, a Kolmogorov–Arnold-informed interpretable graph wavelet activation network (GWAN) is proposed for machine fault diagnosis in this work. In GWAN, two critical components are designed, that is, graph wavelet activation convolutional (GWAConv) layer and wavelet attention (WavAtt) layer. In GWAConv, the graph message passing is achieved using the wavelet Kolmogorov–Arnold (WKA) layer with learnable scale and translation parameters to capture the robust fault features, while WavAtt layer decomposes the raw signal into low-frequency and high-frequency components to force the model to focus on the low-frequency components, which is helpful for fault diagnosis. Experiments under stationary, nonstationary, and noisy conditions were implemented to verify the effectiveness of GWAN. The experimental results show the superiority of GWAN among comparison methods, and the interpretability of the extracted features is demonstrated through post-hoc feature visualization. The code library is available at: https://github.com/HazeDT/GWAN

Incremental learning (IL) provides a dynamic framework for expanding the classification capacity of data-driven systems, thereby facilitating unknown fault diagnosis (UFD) in motor systems. However, the necessity for a manually established training set with unknown fault samples for the retraining of IL models, combined with insufficient consideration of real time, presents significant challenges. To address these challenges, this article proposes an automatic IL method based on edge computing (AILEC) for UFD of motors. First, the method introduces a convolutional encoder based on a training guide-separation module (CETGM) and a feature similarity match (FSM) technique. These components are designed to function effectively at the edge after initial training. An IL method, based on edge joint training (EJT), is then proposed to extend the classifiable quantity of the model at edge end, based on UFD results derived from CETGM and FSM. The superiority of the proposed method is validated through experiments on a motor test rig. The results demonstrate that the approach achieves 99.99% accuracy for UFD, with an average accuracy of 98.84% across 4 to 10 incremental states. Additionally, the system delivers a model size of 0.5 MB, an inference time of 2.09 ms, and a model update time of 164 s. The proposed method outperforms several existing approaches in terms of accuracy and real-time processing capabilities. It provides an intelligent solution for UFD of motors, featuring continuous model updates and real-time IL.

Domain adaptation (DA) techniques are becoming increasingly proficient in cross-domain fault diagnosis tasks. However, DA-based methods are not always applicable due to the target domain data is not always accessible. Although there have been some interesting domain generalization methods for fault diagnosis under unseen conditions, most of them can only be used to mine the fault features on source domain distributions, and the improvement of model generalization performance is limited. To solve this problem, the multiplicative noise Gaussian perturbation strategy and the additive noise linear fusion strategy are proposed to capture fault information beyond source domain distributions. The former is used to randomly perturb feature statistics of multisource domains to simulate the uncertainty of domain shift, while the latter is used to perform the additive noise linear operation on feature statistics of multiple source domains to ensure the authenticity of the generated feature styles. Further, the feature statistics generated by both strategies are mixed with random convex weights to obtain new feature styles, achieving the best compromise between reliability and diversity. The network can learn more fault information from features with diversified styles. Extensive experimental results on both public and real datasets verify the effectiveness of our approach.

Intelligent anomaly detection (AD) methods have achieved much successes in machinery condition monitoring. However, the underlying independent and identically distributed assumption restricts their application scopes to steady operating conditions. False and missing alarms would occur when machines operate under time-varying circumstances. In this work, a more challenging time-varying setting is studied, where the working conditions are continuously changing, such that few or no samples are available for model training at one single condition. To tackle this issue, we propose a unified flowing normality learning (UFNL) framework, which aims to capture the flowing normal conditional distribution of time-varying samples and assigns dynamic decision boundary for AD. Specifically, a manifold-based probability density estimation is utilized to guide the adversarial learning process of generative adversarial networks, where adjacent samples are aggregated to approximate the conditional distribution by a conditional generator. Then, a latent normality inversion is proposed to extract the manifold structure from the pretrained generator and to map it into the latent space via a conditional encoder. The reconstruction errors from the encoder and generator can reveal the deviation of signals to the flowing normality. Finally, a condition-aware adaptive threshold selection strategy is proposed, where different thresholds are adaptively assigned for different conditions. Experiments are carried out under two typical continuous time-varying scenarios. The results demonstrate that the proposed framework can realize accurate fault detection at any operating condition within continuously changing environments.

Sparse representation-based interpretable algorithm unrolling is one of promising techniques for mechanical anomaly detection. In order to enhance the learning and representation capabilities of the algorithm unrolling model, this article proposes a learnable sparse regularization network (LSR-Net). Instead of imposing explicit regularization constraints on the encoding and dictionary during modeling, two subnetworks are designed to learn prior information:$\mathbf{Net}_{\mathbf{X}}$and$\mathbf{Net}_{\mathbf{D}}$. The model is solved using the half quadratic splitting algorithm, and further unrolls the process of iterative computation into the form of a network. The architecture for encoding learning is structured as input convex neural networks, ensuring LSR-Net can learn meaningful encoding priors. Through the analysis of simulated and experimental data, it has been demonstrated that LSR-Net has strong feature extraction and noise resistance capabilities, and the design of its prior learning architecture is both reasonable and effective. In addition, the visualization of LSR-Net's overall reconstruction and the reconstruction of different dictionary atoms allows for both global and local interpretation of the learning results, thereby providing post hoc interpretability to LSR-Net. The visualization results confirm that LSR-Net is capable of learning features that align with mechanical vibration characteristics.

Nowadays, transfer learning (TL) is widely used in fault diagnosis of machinery, which greatly broadens its application in scenarios with variable operating conditions. However, existing TL-based fault diagnosis methods usually emphasize on the research of domain adaptation (DA) mechanisms, and neglect the impact of the expressiveness of the classifier on DA. To overcome this limitation of existing DA-based diagnosis methods, the dynamic softmax with angular margin penalty is designed to dynamically adjust the expressiveness of the embeddings learned by the encoder network. In this way, the diagnosis network can learn more representative features, which improves the robustness of the network on the target data. Furthermore, a trend block is designed to learn trend features in the vibration signal, so that the fault features learned by the feature extractor are more abundant. Comprehensive experiments on real and public datasets show that our approach outperforms other well-established cross-domain fault diagnosis algorithms.

Terahertz (THz) time-domain spectroscopy gains its popularity in internal defect detection of nonpolar dielectrics, and emerges as a promising inspection technique for delamination defects in composite materials due to its submillimeter level resolution and high penetrability. However, the contrast of THz images decreases significantly with an increasing number of layers due to dramatic signal attenuation and severe multiple reflections, which degrades the temporal and spatial resolution and subsequently hinders the accuracy of defect characterization. In this article, we propose a novel THz defect characterization framework for inspecting ultralayered glass fiber-reinforced polymer composites. The framework reconstructs the laminate structure by utilizing the local symmetry characteristic of the reflected THz pulses and the point cloud density. Then, THz images are extracted from both the reflected time-domain signal and local symmetry function. Pixel-level clustering of THz images is performed for accurate defect characterization. The defect intersection over union for 25 delamination defects in a 31-layer composite can reach more than 0.87. Our proposed strategy offers a promising route for accurate delamination assessment in ultralayered composites, and can be extended to automatic THz characterization in industrial applications.

In the case of label space alignment, the existing domain adaptation (DA)-based fault diagnosis approaches have achieved high accuracy. In real industrial scenarios, however, the label space of the target domain is usually a subset of the label space of the source domain, called partial DA (PDA). The main challenge of PDA lies in how to separate common samples from private samples. In existing works, different weights are usually assigned to different samples based on the prediction score of the classifier, but the negative transfer caused by the data distribution alignment of private and common samples is ignored. To address this problem, class-consistency matching is proposed in this article, which uses label consensus score to identify classes in target clusters to discover common and private samples. In addition, parameter-free cosine attention wavelet blocks (PCAWBs) are designed to learn the complementary spatial-domain and frequency-domain features to enrich the domain-invariant features extracted by the shared encoder. Experiments on the real motor system demonstrate that the proposed method significantly outperforms state-of-the-art PDA fault diagnosis approaches.

Deep learning has attracted much attention in bearing fault diagnosis because of its high precision and end-to-end modules. However, in real industrial scenarios, some complex mechanical structures and working environments hinder data collection and fault reproduction, which makes bearing fault diagnosis with few samples a practical but challenging issue. As a data-driven approach, the standard deep learning method cannot extract features from a few samples due to overfitting. Neuroscience research has shown that the learning mechanism of the biological brain is more adaptable to learning tasks with few samples. Motivated by this, we propose a brain-inspired meta-learning (BIML) strategy for diagnosing few-shot bearing faults. Specifically, we design a brain-like learning algorithm for spiking neural networks (SNNs) based on the biological nervous system's learning mechanism and introduce a meta-learning strategy to apply it to the fault diagnosis task of bearing with few samples. Experimental results show that BIML is better than existing few-shot bearing fault diagnosis methods. Subsequently, we conduct a theoretical analysis of the effectiveness of BIML strategies and verify our analysis through experiments.

Anomaly detection is a task of identifying samples that significantly differ from the majority. However, most typical anomaly detection methods often prioritize accuracy over interpretability. To address this limitation, we propose an explainable anomaly detection approach using a deep learnable M-band wavelet packet network constructed from the frequency perspective. This network could flexibly decompose a signal into different frequency bands and learn its frequency representation. Then the learnable threshold function is designed to learn the distribution of the normal signal in each frequency band and corrupt the abnormal representation. As a result, the abnormal signal can not be reconstructed from its corrupted representation. We evaluate the proposed method on both simulation data and real acoustic data.

Bearings are crucial components of rotating machines, and accurately predicting their remaining useful life is paramount for ensuring machine safety and maintenance. Existing prognostic studies predominantly rely on limited monitoring data collected under specific operating conditions for modeling, often overlooking valuable degradation characteristics contained under other conditions. To tackle these challenges, this study proposes a federated learning (FL)-based prognostic method that aims to collaboratively construct personalized prognostic models for bearings operating under different conditions within the FL framework. Specifically, a client selection strategy is initially adopted to identify clients with closely related high-level degradation features, guiding effective aggregation among relevant clients. This strategy significantly improves the accuracy and convergence of the prediction model. Subsequently, based on the obtained similarity parameters, a personalized aggregation enhancement scheme is proposed to aggregate models in the subgroup of selected clients, further enhancing the prognostic performance of the prediction model. This study represents a novel attempt at constructing personalized prognostic models in scenarios involving data heterogeneity. Experimental results on two bearing data sets jointly verify the improved accuracy and convergence of the proposed method.

Remaining useful life (RUL) prediction technology is a crucial task in prognostics and health management (PHM) systems, as it contributes to the enhancement of the reliability of equipment operation. With the development of Industrial Internet of Things (IIoT) technologies, it becomes possible to efficiently coordinate data collection for mechanical equipment, enabling real-time monitoring of device status and performance. This could provide more accurate estimations of the RUL. While current RUL prediction techniques predominantly rely on deep learning (DL), these approaches often neglect the temporal correlation within training samples, resulting in unstable prediction outcomes. To address this issue, a novel RUL prediction method is introduced, leveraging deep reinforcement learning (DRL). This method combines the effective feature extraction ability of DL with the preservation of temporal correlation between samples through reinforcement learning. Firstly, an autoencoder (AE) is employed to extract key features that are most relevant to degenerative process from the original signals collected from mechanical equipment. Secondly, state variables in reinforcement learning are constructed using the extracted features and the predicted RUL value of the sample at the previous time step. Finally, a deep reinforcement learning model based on the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3) is trained after setting an appropriate action space and reward function. Validation using XJTU-SY bearing dataset demonstrates that the DRL method yields lesser Root Mean Square Error (RMSE) and more stable prediction results compared to alternative methods.

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use of the inductive bias of the interdependencies between the different sensor measurements. However, there are some limitations with these GNN-based fault diagnosis methods. First, they lack the ability to realize multiscale feature extraction due to the fixed receptive field of GNNs. Second, they eventually encounter the over-smoothing problem with increase of model depth. Finally, the extracted features of these GNNs are hard to understand due to the black-box nature of GNNs. To address these issues, a filter-informed spectral graph wavelet network (SGWN) is proposed in this article. In SGWN, the spectral graph wavelet convolutional (SGWConv) layer is established upon the spectral graph wavelet transform, which can decompose a graph signal into scaling function coefficients and spectral graph wavelet coefficients. With the help of SGWConv, SGWN is able to prevent the over-smoothing problem caused by long-range low-pass filtering, by simultaneously extracting low-pass and band-pass features. Furthermore, to speed up the computation of SGWN, the scaling kernel function and graph wavelet kernel function in SGWConv are approximated by the Chebyshev polynomials. The effectiveness of the proposed SGWN is evaluated on the collected solenoid valve dataset and aero-engine intershaft bearing dataset. The experimental results show that SGWN can outperform the comparative methods in both diagnostic accuracy and the ability to prevent over-smoothing. Moreover, its extracted features are also interpretable with domain knowledge.

Recently, the remaining useful life (RUL) prediction of bearings driven by deep learning (DL) technology has gained massive attention. However, there are significant differences in the degradation processes from different bearings, which makes it difficult to adapt the model to unseen data. Moreover, the training paradigm of DL assumes that samples are independent, ignoring the ordinal relationships within feature space. This work considers that generalizable features in RUL prediction should possess two characteristics: domain invariance and continuous ordering. To this end, a domain invariant and consistent ordinal representation learning (DICORL) method is proposed for RUL estimation of bearings. DICORL employs maximum mean discrepancy to align feature distributions of multiple bearings in the training set. To alleviate the overfitting problem of the model in given domains, a distribution encoding–decoding framework is designed to project aligned features into the latent space that is constrained by a Gaussian mixture distribution. Moreover, ordinal loss and local consistency loss are constructed to encourage the model to learn ordered and locally consistent low-dimensional manifolds. Extensive experiments indicate that DICORL obtains superior prognostic performance compared to other domain generalization approaches.

Federated learning (FL) has emerged as an effective machine-learning paradigm for collaborative machine fault diagnosis in a privacy-preserving scheme. However, due to the perception limitation and different annotation criteria of annotators, the data in clients may have noisy labels with varied noise levels, leading to degraded FL performances. Most existing methods in FL for tackling the label noise issue, assume that there is label noise in all clients and treat all clients with the same denoising training. However, these methods may result in sub-optimization and even training instability of local models, so that they cannot perform well on heterogeneous label noise across clients in FL. To address this issue, we propose a curriculum-based federated learning (called FedCNL) method to combat the heterogeneous label noise in FL settings. First, our proposed FedCNL exploits a noise modeling module to adaptively estimate the clean clients and noisy clients, and identify the clean samples and noisy samples in noisy clients in an unsupervised manner. Then, a multi-stage curriculum learning is designed by regarding the noise level as learning complexity, where the model learns from clean to noisy samples, gradually improving the performance of the global model. Moreover, a mixed loss correction method is explored in the curriculum stage to maximize the utilization of data with noisy labels. Experiments performed on fault datasets in non-identically and independently distributed settings indicate that our proposed method addresses the label noise issue for machine fault diagnosis in heterogeneous FL with favorable effectiveness, achieving state-of-the-art performances.

Convolutional neural network (CNN)-based fault detection approaches based on multisource signals have attracted increasing interest from the research community and industrial practices, thanks to the powerful feature representation capability of CNN and the rapid development of sensor technology. Various strategies have been applied in existing CNN-based diagnostic models to learn features from 1-D real-valued multivariate data. However, the distribution gap and the intrinsic correlations among multisource mechanical signals during the learning process have been rarely considered, which may lead to suboptimal fault identification results. To tackle this issue, this article proposes a cross-modal fusion convolutional neural network (CMFCNN) for mechanical fault diagnosis, which performs modality-specific and cross-modal feature representation on multisource data. Specifically, CMFCNN adopts two parallel modality-specific networks and a cross-modal knowledge-sharing network to fully explore independent and shared features from the multisource mechanical signals. To achieve effective feature propagation and fusion, a cross-modal fusion module is introduced to integrate cross-modal features and pass the fused information to the next layer. Moreover, to alleviate overfitting and achieve a better diagnostic performance of the framework, an online soft-label training algorithm is adopted in the CMFCNN training phase. Extensive experimental results on the cylindrical rolling bearing dataset and the planetary gearbox dataset validate that the proposed CMFCNN outperforms seven state-of-the-art methods significantly, especially under strong noise conditions.

In mechanical anomaly detection, algorithms with higher accuracy, such as those based on artificial neural networks, are frequently constructed as black boxes, resulting in opaque interpretability in architecture and low credibility in results. This article proposes an adversarial algorithm unrolling network (AAU-Net) for interpretable mechanical anomaly detection. AAU-Net is a generative adversarial network (GAN). Its generator, composed of an encoder and a decoder, is mainly produced by algorithm unrolling of a sparse coding model, which is specially designed for feature encoding and decoding of vibration signals. Thus, AAU-Net has a mechanism-driven and interpretable network architecture. In other words, it is ad hoc interpretable. Moreover, a multiscale feature visualization approach for AAU-Net is introduced to verify that meaningful features are encoded by AAU-Net, helping users to trust the detection results. The feature visualization approach enables the results of AAU-Net to be interpretable, i.e., post hoc interpretable. To verify AAU-Net's capability of feature encoding and anomaly detection, we designed and performed simulations and experiments. The results show that AAU-Net can learn signal features that match the dynamic mechanism of the mechanical system. Considering the excellent feature learning ability, unsurprisingly, AAU-Net achieves the best overall anomaly detection performance compared with other algorithms.

As an important component of the rotating machinery, rolling bearings usually work under the condition of variable speed and load, and vibration signals in the same health state are significantly different due to the change in operating conditions. To address the problem that the existing deep learning (DL) methods have fixed nonlinear transformations for all input signals in cross-domain fault diagnosis, we propose a new activation function, i.e., parameter-free adaptively rectified linear units (PfAReLU). The proposed activation function performs adaptive nonlinear transformations according to the input data and can better capture the fault features of vibration signals in the same fault state under different operating conditions. Furthermore, the number of PfAReLU parameters is zero, so that the risk of network overfitting is reduced. At the same time, deep parameter-free reconstruction-classification networks with PfAReLU (DPRCN-PfAReLU) are also constructed for cross-domain fault diagnosis. Specifically, DPRCN-PfAReLU consists of a shared encoder, a target domain decoder, and a source domain classifier. The shared encoder adds a parameter-free attention module at the output to enhance the weight of domain-invariant features without increasing network parameters. The shared encoded representation of source domain and target domain is learned by target domain decoder and source domain classifier. Compared with other methods under nine different operating conditions via real experiment studies, the proposed method shows superiority for cross-domain fault diagnosis.

Deep learning (DL) has present great diagnostic results in fault diagnosis field. However, the poor interpretability and noise robustness of DL-based methods are still the main factors limiting their wide application in industry. To address these issues, an interpretable wavelet packet kernel-constrained convolutional network (WPConvNet) is proposed for noise-robust fault diagnosis, which combines the feature extraction ability of wavelet bases and the learning ability of convolutional kernels together. First, the wavelet packet convolutional (WPConv) layer is proposed, and constraints are imposed to convolutional kernels, so that each convolution layer is a learnable discrete wavelet transform. Second, a soft threshold activation is proposed to reduce the noise component in feature maps, whose threshold is adaptively learned by estimating the standard deviation of noise. Third, we link the cascaded convolutional structure of convolutional neutral network (CNN) with wavelet packet decomposition and reconstruction using Mallat algorithm, which is interpretable in model architecture. Extensive experiments are carried out on two bearing fault datasets, and the results show that the proposed architecture outperforms other diagnosis models in terms of interpretability and noise robustness.

Deep learning (DL)-based intelligent fault diagnosis methods have greatly promoted the development of the field of fault diagnosis due to their powerful feature extraction ability for handling massive monitoring data. However, most of them still suffer from the following three limitations. First, many existing DL-based intelligent diagnosis methods cannot extract proper discriminative features from signals with strong noise. Second, the interactions or relationships between signals are ignored, while they mainly focus on extracting temporal features from the signal. Third, owing to their black-box nature, the learned features lack interpretability, which hinders their application in the industry. To tackle these issues, an explainable graph wavelet denoising network (GWDN) is proposed to achieve intelligent fault diagnosis under noisy working conditions in this article. In GWDN, the collected signals are first transformed into graph-structured data to consider the interactions among signals. Then, the graph wavelet denoising convolution (GWDConv) is proposed based on the discrete graph wavelet frame, which allows GWDN to achieve multiscale feature extraction for graph-structured data and realize signal denoising. Extensive experiments are implemented to verify the efficacy of the proposed GWDN, and the experimental results show that GWDN can achieve state-of-the-art performance among the comparison methods. Besides, by using the square envelope spectrum to analyze the extracted features of GWDConv, we find that it can well retain the fault-related components of the signal and realize signal denoising, which further proves that GWDN is explainable.

Deep learning technology provides a promising approach for rotary machine fault diagnosis (RMFD), where vibration signals are commonly utilized as input of a deep network model to reveal the internal state of machinery. However, most existing methods fail to mine association relationships within signals. Unlike deep neural networks, transformer networks are capable of capturing association relationships through the global self-attention mechanism to enhance feature representations from vibration signals. Despite this, transformer networks cannot explicitly establish the causal association between signal patterns and fault types, resulting in poor interpretability. To tackle these problems, an interpretable deep learning model named the variational attention-based transformer network (VATN) is proposed for RMFD. VATN is improved from transformer encoder to mine the association relationships within signals. To embed the prior knowledge of the fault type, which can be recognized based on several key features of vibration signals, a sparse constraint is designed for attention weights. Variational inference is employed to force attention weights to samples from Dirichlet distributions, and Laplace approximation is applied to realize reparameterization. Finally, two experimental studies conducted on bevel gear and bearing datasets demonstrate the effectiveness of VATN to other comparison methods, and the heat map of attention weights illustrates the causal association between fault types and signal patterns.

Most current data-driven prognosis approaches suffer from their uncontrollable and unexplainable properties. To address this issue, this article proposes a physics-constraint variational neural network (PCVNN) for wear state assessment of the external gear pump. First, a response model of the pressure pulsation of the gear pump is constructed via a spectral method, and a compound neural network is utilized to extract features from the pressure pulsation signal. Then, the response model is formulated into an objective function to softly constrain the learning process of the neural network, forcing the learned features to have explicit physics meaning. Meanwhile, to characterize the system uncertainty, the variational inference is utilized to extend a Kullback-Leibler (KL) divergence into the objective function. Finally, the wear state is evaluated based on the distance of learned physics features. Experimental results on an external gear pump validate the merits of the proposed method in explainable representation learning and system uncertainty estimation. It also offers a controllable and explainable perspective to understand the dynamic behavior of the system.

Transformer has shown impressive performance on global feature modeling in many applications. However, two drawbacks induced by its intrinsic architecture limit its application, especially in fault diagnosis. First, the quadratic complexity of its self-attention scheme extremely increases the computation cost, which poses a challenge to apply Transformer to a computationally limited platform like an industry system. In addition, the sequence-based modeling in the Transformer increases the training difficulty and requires a large-scale training dataset. This drawback becomes serious when Transformer is applied in fault diagnosis where only limited data is available. To mitigate these issues, we rethink this common approach and propose a new Transformer, which is more suitable for fault diagnosis. In this article, we first show that the attention module can be actually replaced with or even surpassed by a convolution layer under some conditions in mathematics and experiments. Then, we adopt the convolutions into the Transformer, where the computation burden issue is alleviated and the fault classification accuracy is significantly improved. Furthermore, to increase the computation efficiency, a lightweight Transformer called LiteFormer, is developed by utilizing the depth-wise convolutional layer. Extensive experiments are carried out on four datasets: Case Western Reserve University dataset; Paderborn University dataset; and two gearbox datasets of drivetrain dynamic simulator. Through our experiments, our LiteFormer not only reduces the computation cost in model training, but also sets new state-of-the-art results, surpassing other counterparts in both fault classification accuracy and model robustness.

Recent researches on intelligent fault diagnosis algorithms can achieve great progress. However, considering the practical scenarios, the amount of labeled data is insufficient in face of the difficulty of data annotation, which would raise the risk of overfitting and hinder the model from its industrial applications. To address this problem, in this article, we propose an interinstance and intratemporal self-supervised learning framework, where self-supervised learning on massive unlabeled data is integrated with supervised learning on few labeled data to enrich the capacity of learnable data. Specifically, we design a time-amplitude signal augmentation technique and conduct interinstance transform-consistency learning to obtain domain-invariant features. Meanwhile, an intratemporal relation matching task is promoted to improve the temporal discriminability of the model. Moreover, to overcome the single task domination problem in this multitask framework, an uncertainty-based dynamic weighting mechanism is utilized to automatically distribute weight for each task according to its uncertainty, which ensures the stability of multitask optimization. Experiments on open-source and self-designed datasets demonstrate the superiority of the proposed framework over other supervised and semisupervised methods.

Surface damage detection is vital for diagnosis and monitoring of aeroengine blade. At present, borescope inspection is the dominant technology. Several inspectors hold borescope to inspect the blades one by one through naked eyes on the apron. The inspection of turbine blades even requires drilling into narrow aeroengine tail nozzle. The manual visual inspection is high cost and low efficiency. To improve detection efficiency and economic benefit, we propose an intelligent borescope inspection method in this article. Facing the problem of weak damage information caused by background noise and unsatisfactory illumination, local window transformer network efficiently models pixel-to-pixel relations with the help of global self-attention mechanism, and shifted window strategy is used to conduct information exchange. The capacity of global modeling is beneficial for capturing detailed damage outline. Besides, to learn label relations as prior and embed it into model, semantic information of different damages is aggregated by a two-layer graph convolution network. The global label graph network provides global prior by modeling label dependencies based on the samples in dataset. Finally, the image features and label features are fused to provide rich feature representation for mode recognition and damage localization. We validate the effectiveness of the proposed method on three datasets, including simulated blade, aluminum, and real blade datasets. The results demonstrate that the proposed method has superior performance with 84.9 mAP on simulated blade dataset and satisfactory visualization results on real blade dataset.

Multiple signal classification (MUSIC) has gained prominence in frequency estimation with the virtue of overcoming the undersampling problem of blade tip timing (BTT). However, as a crucial vibration feature, the amplitude cannot be estimated by MUSIC. Existing amplitude extraction methods for MUSIC are performed as postprocessing methods not related to MUSIC. Additionally, existing derivations of MUSIC for real signals use Euler’s formula to transform real signals into complex exponential signals. Therefore, this article rederives MUSIC based solely on real signals and further proposes an amplitude-identifiable MUSIC (Aid-MUSIC) approach to recover the amplitude information hidden in the eigenvalue decomposition of MUSIC. Combined with the proposed formulaic explanation of MUSIC’s asynchronous-pass ability, Aid-MUSIC is adapted according to the characteristics of BTT signal. The simulations and experiments show that Aid-MUSIC can achieve the simultaneous and stable extraction of amplitude and frequency for asynchronous frequency components without the interference of synchronous frequency components.

Multi-sensor information acquisition system can reflect the operation status of machinery more comprehensively and reliably, but also demands higher requirements on data analysis algorithms. Unlike previous deep learning models, the emerging Graph Neural Network (GNN) has a remarkable performance in mining graph structure and patterns, effectively integrating multiple node relationships and features. This paper presents a fault diagnosis algorithm based on multi-sensor information fusion using the modified Graph Attention Network-GATv2. Firstly, the dependencies between multi-sensor signals are explicitly extracted by the Grow-Shrink (GS) algorithm, where the topology of the constructed graph can characterize different failure states of the equipment. During the aggregation process, the attention mechanism in the GATv2 assigns higher weights to informative nodes for the effective fusion of multi-sensor information. Experiments show that the proposed diagnosis framework can yield more expressive multi-sensor representations, and the diagnostic accuracy is improved significantly compared to the single-sensor graph.

Convolutional neural network (CNN), with the ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, an explanation on the physical meaning of a CNN architecture has rarely been studied. In this article, a novel wavelet-driven deep neural network, termed as WaveletKernelNet (WKN), is presented, where a continuous wavelet convolutional (CWConv) layer is designed to replace the first convolutional layer of the standard CNN. This enables the first CWConv layer to discover more meaningful kernels. Furthermore, only the scale parameter and translation parameter are directly learned from raw data at this CWConv layer. This provides a very effective way to obtain a customized kernel bank, specifically tuned for extracting defect-related impact component embedded in the vibration signal. In addition, three experimental studies using data from laboratory environment are carried out to verify the effectiveness of the proposed method for mechanical fault diagnosis. The experimental results show that the accuracy of the WKNs is higher than CNN by more than 10%, which indicate the importance of the designed CWConv layer. Besides, through theoretical analysis and feature map visualization, it is found that the WKNs are interpretable, have fewer parameters, and have the ability to converge faster within the same training epochs.

Enabling precise forecasting of the remaining useful life (RUL) for machines can reduce maintenance cost, increase availability, and prevent catastrophic consequences. Data-driven RUL prediction methods have already achieved acclaimed performance. However, they usually assume that the training and testing data are collected from the same condition (same distribution or domain), which is generally not valid in real industry. Conventional approaches to address domain shift problems attempt to derive domain-invariant features, but fail to consider target-specific information, leading to limited performance. To tackle this issue, in this article, we propose a contrastive adversarial domain adaptation (CADA) method for cross-domain RUL prediction. The proposed CADA approach is built upon an adversarial domain adaptation architecture with a contrastive loss, such that it is able to take target-specific information into consideration when learning domain-invariant features. To validate the superiority of the proposed approach, comprehensive experiments have been conducted to predict the RULs of aeroengines across 12 cross-domain scenarios. The experimental results show that the proposed method significantly outperforms state-of-the-arts with over 21% and 38% improvements in terms of two different evaluation metrics.

Anomaly detection is one of the most fundamental and indispensable components in predictive maintenance. In this article, anomaly detection is modeled as a one-class classification problem. Based on the scenario that the training data only include healthy state data, a fault-attention generative probabilistic adversarial autoencoder (FGPAA) is proposed to automatically find low-dimensional manifold embedded in high-dimensional space of the signal. Benefited from the characteristics of autoencoder, the signal information loss in feature extraction is reduced. Then, the fault-attention abnormal state indictor can be constructed with the distribution probability of low-dimensional feature and reconstruction error. Effectiveness of the model is verified with fault classification datasets and run-to-failure experimental datasets. The results show that FGPAA outperforms both GPAA and other traditional methods and can be processed in real time. It not only can obtain high accuracy for both classification data and run-to-failure data, but also achieve a certain trend index for run-to-failure data.

In wireless sensor networks, unbalanced energy consumption may shorten network lifespan. In this paper, a multi-objective distributed clustering algorithm using the analytic hierarchy process is developed to ensure that the energy expenditure of the cluster head nodes is balanced and the network lifespan is enhanced. By adopting the analytic hierarchy process model, our proposed algorithm aggregates multiple factors such as the node energy, the node centrality, and the node degree to search for an optimal clustering structure. Furthermore, a super cluster head is selected among the cluster head nodes based on the distance from the cluster head to the base station, which further minimizes the energy dissipation. Simulation results indicate that the proposed algorithm outperforms the other existing ones in terms of clustering structure and network lifespan.

The cutting tool is a key part of a machine system, which plays an important role in modern manufacturing systems. To avoid an unexpected tool failure, it is necessary to carry out health condition assessment of cutting tools. In this paper, a deep coupled restricted Boltzmann machine (DCRBM) is proposed for health state assessment of cutting tools based on fusion of vibration signals and acoustic emission (AE) signals. Because of the complementary of multisensory signals, it is necessary to develop a fusion strategy for the fusion of multisource signals. The proposed DCRBM is symmetric with each side consisting of several hidden layers and one coupled layer, which is constructed by two basic restricted Boltzmann machines with similarity constraints. Vibration signals and AE signals, which are connected with the two sides of DCRBM, respectively, are mapped into a feature space, where similar representations are learned. The parameters of the deep architecture are learned by optimizing the new objective function. Experimental results on fusion of vibration signals and AE signals demonstrate the promising performance of DCRBM for health state assessment of cutting tools compared with other fusion strategies.

We develop a novel deep learning framework to achieve highly accurate machine fault diagnosis using transfer learning to enable and accelerate the training of deep neural network. Compared with existing methods, the proposed method is faster to train and more accurate. First, original sensor data are converted to images by conducting a Wavelet transformation to obtain time-frequency distributions. Next, a pretrained network is used to extract lower level features. The labeled time-frequency images are then used to fine-tune the higher levels of the neural network architecture. This paper creates a machine fault diagnosis pipeline and experiments are carried out to verify the effectiveness and generalization of the pipeline on three main mechanical datasets including induction motors, gearboxes, and bearings with sizes of 6000, 9000, and 5000 time series samples, respectively. We achieve state-of-the-art results on each dataset, with most datasets showing test accuracy near 100%, and in the gearbox dataset, we achieve significant improvement from 94.8% to 99.64%. We created a repository including these datasets located at mlmechanics.ics.uci.edu.

Deep learning with ability to feature learning and nonlinear function approximation has shown its effectiveness for machine fault prediction. While, how to transfer a deep network trained by historical failure data for prediction of a new object is rarely researched. In this paper, a deep transfer learning (DTL) network based on sparse autoencoder (SAE) is presented. In the DTL method, three transfer strategies, that is, weight transfer, transfer learning of hidden feature, and weight update, are used to transfer an SAE trained by historical failure data to a new object. By these strategies, prediction of the new object without supervised information for training is achieved. Moreover, the learned features by deep transfer network for the new object share joint and similar characteristic to that of historical failure data, which is beneficial to accurate prediction. Case study on remaining useful life (RUL) prediction of cutting tool is performed to validate effectiveness of the DTL method. An SAE network is first trained by run-to-failure data with RUL information of a cutting tool in an off-line process. The trained network is then transferred to a new tool under operation for on-line RUL prediction. The prediction result with high accuracy shows advantage of the DTL method for RUL prediction.

Fingerprinting based on Wi-Fi Received Signal Strength Indicator (RSSI) has been widely studied in recent years for indoor localization. While current algorithms related to RSSI Fingerprinting show a much lower accuracy than multilateration based on time of arrival or the angle of arrival techniques, they highly depend on the number of access points (APs) and fingerprinting training phase. In this paper, we present an integrated method by combining the deep neural network (DNN) with improved K-Nearest Neighbor (KNN) algorithm for indoor location fingerprinting. The improved KNN is realized by boosting the weights on K-nearest neighbors according to the number of matching access points. This will overcome the limitation of the original KNN algorithm on ignoring the influence of the neighboring points, which directly affect localization accuracy. The DNN algorithm is first used to classify the Wi-Fi RSSI Fingerprinting dataset. Then these possible locations in a certain class are also classified by the improved KNN algorithm to determine the final position. The proposed method is validated inside a room within about 13 ⁎ 9 m2 . To examine its performance, the presented method has been compared with some classical algorithms, i.e., the random forest (RF) based algorithm, the KNN based algorithm, the support vector machine (SVM) based algorithm, the decision tree (DT) based algorithm, etc. Our real-world experiment results indicate that the proposed method is less dependent on the dense of access points and indoor radio propagation interference. Furthermore, our method can provide some preliminary guidelines for the design of indoor Wi-Fi test bed.

This paper aims to unveil a collaborative sparsity structure for rigorously describing the universal self-similarity property of mechanical feature information, which is an important task in the field of adaptive feature recognition. The self-similarity pattern among all local feature segments is first highlighted by an elaborately designed partition strategy, and then a row-wise group sparsity penalty is enforced under an appropriate dictionary to effectively capture the latent self-similarity features from noisy observations. Incorporating dictionary learning techniques, a collaborative sparsity learning model (CSLM) is further proposed, and meanwhile solved by a nonconvex optimization solver generated from a block proximal gradient descend framework. Moreover, the convergence property and computational complexity of the developed solver are discussed comprehensively. The advantage of this model is to adaptively achieve a satisfying sparse level to concentrate the underlying feature information and simultaneously enforce that all segments share a same active atom set to retain the desired self-similarity pattern. The proposed CSLM is profoundly evaluated through implementing feature detection for wind turbine gearbox, and it shows superior performances to many state-of-the-art feature recognition techniques.

A convolutional discriminative feature learning method is presented for induction motor fault diagnosis. The approach firstly utilizes back-propagation (BP)-based neural network to learn local filters capturing discriminative information. Then, a feed-forward convolutional pooling architecture is built to extract final features through these local filters. Due to the discriminative learning of BP-based neural network, the learned local filters can discover potential discriminative patterns. Also, the convolutional pooling architecture is able to derive invariant and robust features. Therefore, the proposed method can learn robust and discriminative representation from the raw sensory data of induction motors in an efficient and automatic way. Finally, the learned representations are fed into support vector machine classifier to identify six different fault conditions. Experiments performed on a machine fault simulator indicate that compared with the current state-of-the-art methods, the proposed method shows significant performance gains, and it is effective and efficient for induction motor fault diagnosis.

Vibration measurement has been widely applied to bearing condition monitoring and health assessment. To device a method for signal interpretation and automate the process of defect severity classification under varying operating conditions, a multilayer feed-forward neural network has been developed. A health index based on the Weibull theory has been proposed for defect severity assessment. Feature vectors extracted from the wavelet transform and spectral post-processing of the vibration data were used as inputs to the neural network. The designed neural network has shown to be able to effectively differentiate faulty bearings from a comparatively "healthy" bearing, identify defective elements, and classify the defect severity using a corresponding health index value. A classification rate of 99% and 97% were achieved for defects in the inner and outer raceways, respectively. The results encourage further exploration of various neural network structures for automated bearing health diagnosis under varying operating conditions.