Internet of Things technology has greatly advanced the development and application of data-driven fault diagnostics and prognostics for industrial equipment. Industrial streaming data processing remains a challenge for intelligent fault diagnosis to continuously learning fault knowledge while retaining strong anti-forgetting ability. Recently, class-incremental learning has gained attention in data-driven fault diagnosis, since it enables to sequentially integrate new fault modes from industrial streaming data while maintaining previously learned knowledge. However, incremental transfer diagnosis in industrial streaming data and time-varying working conditions remain largely unexplored, and challenges such as the stability–plasticity dilemma and limited replay techniques still constrain diagnostic performance. To tackle these issues, we propose a generalized class-incremental lifelong transfer diagnosis (GCILTD) framework. First, a dynamic network expansion strategy is developed to overcome the stability-plasticity dilemma effectively, enabling the incremental model to capture new fault information while preserving prior knowledge. Then, a multi-stage training strategy is proposed to enhance the generalization of the dynamic network, further boosting both knowledge retention and adaptability. Furthermore, a dual-level memory buffer is first designed to enhance the class-incremental transfer diagnosis under time-varying working conditions. Finally, the proposed GCILTD framework is verified on two mechanical fault datasets. Experiment results demonstrate that our proposed GCILTD framework achieves advantageous diagnostic accuracies of 93.88% and 88.51% along with the lowest forgetting rates of 2.41% and 6.09% in different class-incremental transfer scenarios under industrial streaming data and time-varying working conditions, outperforming cutting-edge class-incremental learning approaches.

As typical and complex mechatronic system, health state of the wind turbine (WT) is of significant importance to the sustained and reliable service. However, it is noted that influenced by the seasonal or fitful wind, WTs unavoidably serve in the dynamically varying environment. In this event, most of the currently available indicators expose deficiency in regard of the false or missed alarms due to the coupled condition interference. To address this issue and improve the reliability of the mechatronic system, a novel statistic discrepancy oriented cyclo-non-stationary (CNS) indicator is developed in this article. First, characteristics of the recorded degradation samples are revealed by a multiparametric model, during which the consistency is verified and improved by the hypothesis test. Second, a specific speed-dependent slicing (SDS) operator is then designed, aiming to alleviate the varying-speed-induced modulation interference at the different degradation stages. With this developed SDS operator, a CNS indicator, which can well adapt to the dynamically varying environment during the operating process, is subsequently developed by incorporating the resampling-based statistic discrepancy evaluating mechanism. Experiments indicate that the proposed method can effectively characterize the health state of the transmission parts of the industrial WT under varying speed conditions.

Recently, feature mode decomposition (FMD) has been proposed and has demonstrated robust performance in the application of rotating machinery fault diagnosis. However, FMD does not have parameter adaptability, and its influencing parameters (i.e., segment number, mode number and filter length) need to be defined in advance. Inspired by the decomposition mode of wavelet packet transform, this article cleverly proposes a binary decomposition structure of FMD to form the concept of FMD packet (FMDP). Furthermore, the tiling structure of FMDP is constructed, thus forming the FMDPgram. In FMDPgram, the frequency band of the raw signal is evenly divided into 2 segments, and each FMD generates two submode components (SMCs), thus simplifying the hyperparameter optimization into a single-parameter optimization. Additionally, an indicator called narrowband peak-to-average ratio (NPAR) is proposed for optimal SMC positioning, and which is displayed in the FMDPgram tile map. First, performing FMDPgram with NPAR on the raw signal. Then, the optimal SMC is located based on the NPAR in the FMDPgram tile map. Finally, the envelope power spectrum of the optimal SMC is calculated to characterize the fault characteristic information. FMDPgram is tested on simulated and experimental data, and compared with FMD, spectral kurtosis, VMD and improved Kurtogram to evaluate its performance in rolling bearing diagnosis under low signal-to-noise ratio and non-Gaussian interference.

Diagnostic models based on deep transfer learning hold the potential to apply diagnostic knowledge across relevant machinery. However, existing methods suffer from several drawbacks. First, the random initialization of convolutional kernels lacks interpretability and may lead to suboptimal solutions, affecting diagnostic accuracy and training convergence. Second, treating all channels equally limits the ability of the model to capture crucial information. Third, traditional domain alignment methods do not effectively utilize high-order features for matching global or local feature information. To address these issues, a novel domain adaptation method named multiorder statistics matching sparse wavelet convolutional neural network (MSM-SWCNN) is proposed in this article. In MSM-SWCNN, a multichannel feature extraction module is proposed to utilize sparse wavelet convolutional kernels for comprehensive feature extraction from both time and frequency domain. In addition, a novel generalized distribution matching measure is proposed to align features and distribution between two domains. For eight transfer tasks in two datasets of bearings and gears, the diagnostic accuracy can reach more than 96.6%. The results demonstrate that the proposed method outperforms other methods for rotating machinery fault diagnosis.

In previous studies, the VMDPgram was creatively proposed by combining variational mode decomposition (VMD) with wavelet packet transform (WPT). Although the VMDPgram demonstrates excellent performance in bearing fault diagnosis, there are still some issues that need to be further studied. In light of this, this work conducts the in-depth studies of VMDPgram for the unresolved issues. First, in view of the obvious second-order cyclostationarity of vibration signal of rotating machinery such as bearing, especially in the presence of localized faults, the unbiased autocorrelation (AC) function is introduced. Here, the kurtosis value of the unbiased AC of the squared envelope of each sub-intrinsic modal function (sub-IMF) within the constrained range is calculated, generating the new method named AutoVMDPgram. Second, the modified adaptive resonance bandwidth (MARB) is introduced to constrain the decomposition depth of the AutoVMDPgram. Third, the cumulative evaluation index based on the unbiased AC kurtosis of the square envelope of the sub-IMF is proposed as a measure to locate the optimal sub-IMF without determining whether the resonant frequency range is divided into different sub-IMFs. AutoVMDPgram is tested on simulated and experimental data and compared with Autogram, spectral kurtosis (SKs), and VMD to evaluate its performance in rolling bearing diagnostics.

Convolutional neural networks and transformers have both achieved remarkable success in the field of fault diagnosis owing to their proficiency in extracting local and global features. However, in real industrial production, the diagnostic performance of many methods is often limited by factors such as environmental noise and sample quantity. To address these challenges, this article presents a novel fault diagnosis framework called MFSFormer. First, it employs embedded convolutional layers with kernels of various sizes to extract multiscale receptive field features from vibration signals. Second, a Fuse-Shuffle attention block is employed to capture dependencies between feature channels and windows, facilitating the implementation of subfeature flow. The case studies conducted on two public datasets demonstrate that the proposed method achieves an average diagnostic accuracy that surpasses the suboptimal method by 3.91% and 7.00% in noisy environments and small-sample conditions, respectively. The results indicate that the proposed method not only enhances the robustness of fault diagnosis in noisy environments, but also improves diagnostic accuracy under limited sample conditions, and the method has practical value.

Neural networks have been widely applied in the field of bearing fault diagnosis. However, many existing studies focus on bearings with constant rotational speeds, and there is a lack of research on neural networks for diagnosing faults in bearings with varying speeds. In practice, bearings are always working under varying rotational speeds. This paper proposes a one-dimensional and two-dimensional hybrid neural network combined with wavelet transform for bearings fault diagnosis under variable speeds. Instead of using one-dimensional convolutional kernels, wavelets are employed as generating a two-dimensional feature map that can represent the relationship between signal time and frequency, and the two-dimensional convolutional layer extracts features from the output of the one-dimensional convolutional layer, which is the time-frequency representation obtained through wavelet transformation of the signal. The feasibility of the proposed method is validated on a publicly available dataset from the University of Ottawa.

Condition monitoring of assets is significant to the efficiency and reliability of industrial automation systems. However, the accuracy of condition monitoring results is easily impaired by variational environments and volatile operations, especially for complex automation systems. In this article, an environmentally adaptive and contrastive representation learning method is proposed to address the problem. To suppress the unexpected effects of environmental variations on operating data, a regression model between the operational and environmental variables is developed. The variable regression adjustment is achieved by solving a penalized optimization problem based on spline functions, and the solution is explicitly derived. Then, negative samples and pseudo labels are generated based on the designed pattern of data augmentation, and valid data representations for asset condition monitoring can be obtained by contrastive learning. Moreover, the reference statue of healthy assets is established by kernel density estimation, and control charts are employed for online monitoring with alarm thresholds. Taking wind turbine blades as examples, the remarkable performance of the developed method is demonstrated with real-world measurements from wind farms. Furthermore, comparative analysis with benchmark approaches and ablation study are conducted to reveal the superiority and effectiveness of the proposed method.

The advent of Industry 4.0 has heightened the demand for the interpretability of intelligent diagnostics, especially for high-risk industrial assets. However, the comprehensive interpretation of neural networks remains inadequately explored. To address this challenge and develop a fully interpretable network, we propose a transparent operator network incorporating a parameterized signal operator node. This node is realized by a learnable Morlet wavelet operator in frequency domain with signal-wise gated matrix and skip connection. By stacking multichannel and multilayered nodes as signal operator layers, along with incorporating statistical features and a linear classifier, all modules are physically understandable. A case study demonstrates that despite having fewer parameters, the proposed model achieves better diagnosis performance. Furthermore, the learnable filters, fault signature enhancement, and physically understandable features demonstrate the transparency of the proposed model, indicating that it offers a promising tool for constructing a knowledge-informed and fully interpretable industrial decisions.

The signal-processing and intelligent diagnostic and monitoring methods based on motor current signature analysis for induction motors (IM) usually depend on preset parameters. Moreover, many of them have difficulty in achieving ideal health monitoring effect with strong noise interference and switching working conditions. To overcome these limitations, a novel digital twin architecture called the Ramanujan digital twin (RDT) is composed. This architecture uses the Ramanujan periodic transform as its computational core to detect the potential fault signatures in each monitoring frame. The quantity of interest from IM will be selected and calibrated based on the Bayesian-updated driven calibration mechanism to construct the phenomenal simulation signals with high fidelity to the potential fault signatures. These signals will provide guidance information. The effectiveness and robustness of the RDT are validated through experimental cases.

Time–frequency (TF) analysis is essential for industrial engineering applications. However, the conventional TF analysis methods suffer from blurry TF energy. This article proposes a new unified sparse TA analysis (STFA) framework to concentrate the blurry energy, restrain noise, separate condition-related components, and retain the signal reconstruction property. The STFA framework leverages the weighted elastic net sparse regularization for sparsity- inducing and energy concentration and uses the reconstruction error term for condition-related component separation and signal reconstruction, which bridges the gaps among sparsity, decomposition, transformation, and reassignment. Theoretical analysis and comprehensive investigation of the proposed framework are performed in practical cases. Comparison results with the state-of-the-art methods demonstrate that the proposed framework has superior properties for TF feature energy concentration, denoising, component separation, and reconstruction, especially for the signals with the fast-varying features.

Data-driven fault diagnosis primarily involves the identification of different fault locations and fault severities. Focusing on a challenging task for which the target fault severities do not exist in the training samples, this article proposes a generalized cross-severity bearing fault diagnosis scheme based on a novel hierarchical cross-category inference framework. The proposed method uses an outlier detection scheme based on unsupervised feature mapping and local outlier probability calculation to identify the unseen samples. A neural network embedded with a tree-structured decision layer acts as a backbone to execute fault diagnosis at different hierarchies for different sample types, seen or unseen. Additionally, the metric learning method is used to support the approximate severity inference of the unseen samples after the fault locations are identified in the hierarchical model. Experiments performed on an aeronautical bearing test rig revealed that the proposed scheme is both feasible and superior to existing methods.

This paper proposes a kinematics model with four noncoplanar points' Cartesian coordinates for a spatial parallel manipulator, which is called the tetrahedron coordinate method. The sufficient and necessary criteria of utilizing the Cartesian coordinates of the four noncoplanar points are proved. Because the constraint equations are either quadratic or linear, and the coordinates are complete Cartesian, the derivative matrix of the constraint equations only consists of linear or constant elements that are the advantages of the general natural coordinate method as well. However, the number of variables of the general natural coordinate method will increase with the increasing number of investigated points. The tetrahedron coordinate approach proposed in this paper does not need to induce any new variables when more points on the manipulator are considered. As a result, it has a prevailing advantage over the general natural coordinate method. This advantage is especially explicit when establishing the kinematics models for complex spatial parallel manipulators with three to six degrees of freedom, the virtues of which are demonstrated by a case study.

With regard to the AMFM characteristics, and especially the cyclostationarity of gear vibrations, cyclic spectral analysis is used to extract the modulation features of gearbox vibration signals to detect and assess localized gear damage. The explicit equation for the cyclic spectral density in a closed form for AMFM signals is deduced, and its properties in the joint cyclic frequency-frequency domain are summarized. The ratio between the sum of the cyclic spectral density magnitude along the frequency axis at the cyclic frequencies of modulating frequency and 0 Hz varies monotonically with the amplitude modulation magnitude. Hence it is useful to track modulation magnitude. Localized gear damage generates periodic impulses, and its growth increases the magnitude of periodic impulses. Consequently, the amplitude modulation magnitude of gear AMFM vibration signals increases. Hence the ratio can be used as an indicator of the health condition of gearboxes. The analysis of both gear crack simulation vibration signals and gearbox lifetime experiments shows a globally monotonic increase as gear damage severity increases. The proposed approach has the potential to assess the health of gearboxes, and predict severe damage.