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

Constructing a unified canonical pose representation for 3D object categories is crucial for pose estimation and robotic scene understanding. Previous unified pose representations often relied on manual alignment, such as in ShapeNet and ModelNet. Recently, self-supervised canonicalization methods have been proposed, However, they are sensitive to intra-class shape variations, and their canonical pose representations cannot be aligned to a coordinate system centered on the object. In this paper, we propose a category-level canonicalization method that alleviates the impact of shape variation and extends the canonical pose representation to an upright and forward-facing state. First, we design a Siamese Vector Neurons Module (SVNM) that achieves SE(3) equivariance modeling and self-supervised disentangling of 3D shape and pose attributes. Next, we introduce a Siamese equivariant constraint that addresses the pose alignment bias caused by shape deformation. Finally, we propose a method to generate upright surface labels from pose-unknown in-the-wild data and use upright and symmetry losses to correct the canonical pose. Experimental results show that our method not only achieves SOTA consistency performance but also aligns with the object-centered coordinate system. Project page: https://anon-mity.github.io/upright-facing/

Fault diagnosis is crucial in the industrial Internet of Things (IIoT), but unknown fault types lead to out-of-distribution (OOD) problems, making label prediction challenging. Various domain adaptation (DA) methods often rely heavily on prior knowledge of the target domain. This article proposes a universal DA (UDA) fault diagnosis method capable of effectively handling various DA settings. The method proposed enables diagnosis without considering the label in the target domain. This eliminates the need to switch between different diagnostic models, greatly enhancing the generalization capability of crossing various tasks and reducing both time and operational costs in engineering applications. The method utilizes clustering algorithms to leverage the changes in data density information, and then address the long-tailed imbalanced data problem to some extent. Through cycle-matching at the category and sample levels, potential unknown categories in the target domain are identified, and samples of shared classes are aligned using contrastive domain discrepancy loss. To mitigate misclassifications during the clustering, extreme-value theory (EVT) models are constructed using source domain samples to filter out incorrect samples. The proposed method is evaluated by constructing experiments with imbalanced data and cross-domain experiments under different working conditions on the WT-planetary gearbox dataset and the twin spool engine (TSE) datasets. Simultaneously, we visualize the analysis of the results. The experimental results demonstrate that the proposed approach can accurately identify unknown fault samples and make improvements in both accuracy and H-score.

Accurately predicting the state of health (SOH) of lithium-ion batteries is crucial for optimizing usage and extending battery lifespan. In the era of the Internet of Things (IoT), collaborative modeling represents a pivotal trend in future SOH estimation research. However, privacy constraints induce data isolation among battery organizations, limiting collaborative progress. Federated learning (FL) enables multi-party collaboration while preserving data privacy, but it faces the inherent challenge of data heterogeneity. To address this, we propose a novel personalized federated transfer learning (PFTL) framework to enable secure collaboration and build a reliable SOH estimation model in data heterogeneity scenarios. We develop the Residual Adaptive Kolmogorov-Arnold Network (RAKAN) as the predictive model within the framework, improving the base performance of local client models. Our framework constructs global synthetic data as a core element and achieves effective aggregation among local models through the global synthetic data-guided cross-client alignment mechanism. Additionally, we design a dynamic weighted aggregation strategy based on feature-focus similarity, allowing the global model to learn more generalized feature-focus patterns. This framework can further refine the global model to obtain personalized SOH estimation models tailored to the characteristics of each client. Experimental results confirm that our method achieves robust and accurate SOH estimation results while ensuring data privacy.

Due to coupled nonlinearities and complex measurement noise, assess the condition of the rotor system remains a challenge, particularly in cases where historical run-to-failure data is lacking. To this end, we proposed a hierarchical physics-informed neural network (HPINN) to identify/discover the ordinary differential equations (ODEs) of a healthy/faulty rotor system from noise measurements and then assess the rotor condition based on the discovered ODEs. Specifically, the ODEs of a healthy rotor system are first stably identified from noisy measurement through HPINN guided by rotor dynamics. Based on the identified healthy ODEs, the extra fault terms in the ODEs of the faulty rotor system are then sparsely regressed from the predefined library embedded in HPINN, in which the phase compensation and alternating training strategy are developed to guarantee training convergence. Moreover, with the mathematical terms of discovered fault, the potential fault and the health indicator (HI) are diagnosed and constructed to assess the condition of the rotor system, respectively. Finally, the effectiveness of the proposed method is verified with simulation and test bench datasets, showing the potential for practical industrial applications.Note to Practitioners—This paper investigates the health assessment problem (condition monitoring and fault diagnosis) of the rotor system, a critical component in large rotating machinery. The proposed HPINN provides a hierarchical framework to firstly identify the ODEs of healthy rotor system and then discover the ODEs of faulty rotor system with limited monitoring data (3-5 seconds data collected from sensor commonly, depending on the rotating speeds). With the mathematical terms of discovered fault, the fault can be diagnosed and a health indicator (HI) can be constructed to assess the condition of rotor system in a fully interpretative way. This approach is applicable to large rotating machinery in safety-critical industries, such as circulating water pumps.

Vision-based industrial inspection (VII) aims to locate defects quickly and accurately. Supervised learning under a close-set setting and industrial anomaly detection, as two common paradigms in VII, face different problems in practical applications. The former is that various and sufficient defects are difficult to obtain, while the latter is that specific defects cannot be located. To solve these problems, in this article, we focus on the few-shot semantic segmentation (FSS) method, which can locate unseen defects conditioned on a few annotations without retraining. Compared to common objects in natural images, the defects in VII are small. This brings two problems to current FSS methods: first, distortion of target semantics and second, many false positives for backgrounds. To alleviate these problems, we propose a small object few-shot segmentation (SOFS) model. The key idea for alleviating, first, is to avoid the resizing of the original image and correctly indicate the intensity of target semantics. SOFS achieves this idea via the nonresizing procedure and the prototype intensity downsampling of support annotations. To alleviate, second, we design an abnormal prior map in SOFS to guide the model in reducing false positives and propose a mixed normal dice loss to prevent the model from predicting false positives preferentially. SOFS can achieve FSS and few-shot anomaly detection determined by support masks. Diverse experiments substantiate the superior performance of SOFS.

Lithium-ion batteries are widely used in modern society. Accurate modeling and prognosis are fundamental to achieving reliable operation of lithium-ion batteries. Accurately predicting the end-of-discharge (EOD) is critical for operations and decision-making when they are deployed to critical missions. Existing data-driven methods have large model parameters, which require a large amount of labeled data and the models are not interpretable. Model-based methods need to know many parameters related to battery design, and the models are difficult to solve. To bridge these gaps, this study proposes a physics-informed neural network (PINN), called battery neural network (BattNN), for battery modeling and prognosis. Specifically, we propose to design the structure of BattNN based on the equivalent circuit model (ECM). Therefore, the entire BattNN is completely constrained by physics. Its forward propagation process follows the physical laws, and the model is inherently interpretable. To validate the proposed method, we conduct the discharge experiments under random loading profiles and develop our dataset. Analysis and experiments show that the proposed BattNN only needs approximately 30 samples for training, and the average required training time is 21.5 s. Experimental results on three datasets show that our method can achieve high prediction accuracy with only a few learnable parameters. Compared with other neural networks, the prediction MAEs of our BattNN are reduced by 77.1%, 67.4%, and 75.0% on three datasets, respectively. Our data and code will be available at: https://github.com/wang-fujin/BattNN.

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.

Remaining useful life (RUL) prediction is crucial for ensuring machine operating safety and reducing maintenance costs in nuclear power plants. Existing RUL prediction methods generally use run-to-failure data or known degradation mechanisms to establish a static model for degradation process characterization. However, the inherent degradation mechanisms of machines are time-varying, and a static model may only cover part of the degradation, resulting in an inaccurate RUL result. Hence, we propose an optimized online RUL prediction considering time-varying degradation mechanisms. The degradation model type (discrete variables) and boundary/initial conditions (continuous variables) are first set as the main variables affecting the approximation of the time-varying degradation mechanism. The RUL prediction is then formulated as a feedback-decision process through interacting with the anomaly data stream, in which variables are jointly optimized with reinforcement learning by minimizing the approximation error. Based on the degradation model established with optimized variables, the RUL can finally be deduced. The proposed method is validated by a run-to-failure dataset collected in a nuclear circulating water pump test bench.

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.

Existing data-driven fault diagnosis methods assume that the label sets of the training data and test data are consistent, which is usually not applicable for real applications since the fault modes that occur in the test phase are unpredictable. To address this problem, open set fault diagnosis (OSFD), where the test label set consists of a portion of the training label set and some unknown classes, is studied in this article. Considering the changeable operating conditions of machinery, OSFD tasks are further divided into shared-domain open set fault diagnosis (SOSFD) and cross-domain open set fault diagnosis (COSFD) in this article. For SOSFD, 1-D convolutional neural networks are trained for learning discriminative features and recognizing fault modes. For COSFD, due to the distribution discrepancy between the source and target domains, the deep model needs to learn domain-invariant features of shared classes and separate features of outlier classes. Thus, by utilizing the output of an additional domain classifier, a model named bilateral weighted adversarial networks is proposed to assign large weights to shared classes and small weights to outlier classes during the feature alignment. In the test phase, samples are classified according to the outputs of the deep model and unknown-class samples are rejected by the extreme value theory model. Experimental results on two bearing datasets demonstrate the effectiveness and superiority of the proposed method.

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.

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.

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.

A sparse deep learning method is proposed to overcome overfitting risk of deep networks with a large number of nodes and layers. Deep stacking network (DSN) is a classic and effective deep learning method, and its sparse form is presented to generate the sparse deep learning method. In DSN, output labels are encoded as a series consisted of 1 and 0. This coding strategy makes output labels to be sparse. However, sparsity of output labels is not considered in DSN model. Considering this limitation, sparse DSN (SDSN) is developed in this paper. The SDSN extends tradition DSN in sparsity characterization using a sparse regularization term. By this term, predicted output label is constrained to be similar with ideal output label that is binary and consisted of continuous 1 and 0 with a sidestep shape. The sparse regularization term is used as a soft threshold strategy to set irrelevant element to be zero, by which effectiveness of SDSN is enhanced. Case studies about fault diagnosis of motor are used to validate performance of SDSN. Comparison between SDSN and commonly used deep networks is further conducted. The results show advance of SDSN for fault classification.