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

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.

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.

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.

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.

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.

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.

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.

Health assessment and prognostics are two key tasks within the prognostics and health management frame of equipment. However, existing works are performing these two tasks separately and hierarchically. In this paper, we design and establish dual-task deep long short-term memory networks for joint learning of degradation assessment and remaining useful life prediction of aeroengines. This enables a more robust and accurate assessment and prediction results making for the increment of operational reliability and safety as well as maintenance cost reduction. Meanwhile, the target label functions that match the network training are constructed in an adaptive way according to the health state of an individual aeroengine. Experiments on the popular C-MAPSS lifetime dataset of aeroengines are employed to verify the accuracy and effectiveness. The performance of our proposed work exhibits superiority over other state-of-the-art approaches and demonstrate its application potential.

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.

Effective fault diagnosis of rotating machinery has multifarious benefits, such as improved safety, enhanced reliability, and reduced maintenance cost, for complex engineered systems. With many kinds of installed sensors for conducting fault diagnosis, one of the key tasks is to develop data fusion strategies that can effectively handle multimodal sensory signals. Most traditional methods use hand-crafted statistical features and then combine these multimodal features simply by concatenating them into a long vector to achieve data fusion. The present study proposes a deep coupling autoencoder (DCAE) model that handles the multimodal sensory signals not residing in a commensurate space, such as vibration and acoustic data, and integrates feature extraction of multimodal data seamlessly into data fusion for fault diagnosis. Specifically, a coupling autoencoder (CAE) is constructed to capture the joint information between different multimodal sensory data, and then a DCAE model is devised for learning the joint feature at a higher level. The CAE is developed by coupling hidden representations of two single-modal autoencoders, which can capture the joint information from multimodal data. The performance of the proposed method is evaluated by two experiments, which shows that the DCAE model succeeds in efficiently utilizing multisource sensory data to perform accurate fault diagnosis. Compared with other methods, the proposed method exhibits better performance.

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.

In most current intelligent diagnosis methods, fault classifiers of electric machine are built based on complex handcrafted features extractor from raw signals, which depend on prior knowledge and is difficult to implement intelligentization authentically. In addition, the increasingly complicated industrial structures and data make handcrafted features extractors less suited. Convolutional neural network (CNN) provides an efficient method to act on raw signals directly by weight sharing and local connections without feature extractors. However, effective as CNN works on image recognition, it does not work well in industrial applications due to the differences between image and industrial signals. Inspired by the idea of CNN, we develop a novel diagnosis framework based on the characteristics of industrial vibration signals, which is called dislocated time series CNN (DTS-CNN). The DTS-CNN architecture is composed of dislocate layer, convolutional layer, sub-sampling layer and fully connected layer. By adding a dislocate layer, this model can extract the relationship between signals with different intervals in periodic mechanical signals, thereby overcome the weaknesses of traditional CNNs and is more applicable for modern electric machines, especially under nonstationary conditions. Experiments under constant and nonstationary conditions are performed on a machine fault simulator to validate the proposed framework. The results and comparison with respect to the state of the art in the field is illustrated in detail, which highlights the superiority of the proposed method in industrial applications.

The aero-engine is the heart of an airplane. Operational reliability assessment that aims to identify the reliability level of the aero-engine in the service phase is of great significance for improving flight safety. Traditionally, reliability assessment is carried out by statistical analysis on large failure samples. Because the operational reliability of a specific aero-engine is an individual problem lacking statistical sample data, traditional reliability assessment methods may be insufficient to assess the operational reliability of an individual aero-engine. The operational states of the aero-engine can be identified by its condition information. Changes in the condition information reflect the performance degradation of the aero-engine. Aiming at the assessment of the operational reliability of individual aero-engines, a novel similarity index (SI) is proposed by analyzing the condition information from the fault-free state, and the current state. A condition subspace is first obtained by kernel principal component analysis (KPCA). Subspace similarity is then represented by subspace angles, i.e., kernel principal angles (KPAs). The cosine function is finally utilized as a mapping function to transform the subspace angles into a similarity index. The index can be used as a non-probabilistic metric for operational reliability assessment. Only the condition information is needed for computation of the similarity index, thus it can be performed conveniently for online assessment. The effectiveness of the proposed method is validated by three case studies regarding the health assessment of aero-engines subjected to system-level and component-level degradation. The positive results demonstrate that the proposed SI is an effective metric for operational reliability assessment of individual aero-engines.