Metric-based meta-learning has gained extensive attention in recent years due to its rapid adaptability and strong generalization capability. However, most of the existing metric-based meta-learning methods overlook the intrinsic structures of data, and the similarity evaluation methods for the few-shot scenarios are scarce, which also need to be improved. Therefore, this article proposes a novel metric-based meta-learning method, named retrospective prototype network, for few-shot fault diagnosis across both machines and operating conditions. In this method, the retrospective prototype is developed, which utilizes the interclass variability and multidimensional correlation for accurately reflecting the complex class distributions while reducing the prototype oscillation. Moreover, considering the discrepancy between data intrinsic structures, a center difference measure is designed based on the difference between the central matrix of query sample and the prototype, thus it is more suitable for few-shot scenarios, where the high-dimensional covariance matrices are not exact and full-rank. This proposed method is successfully applied to cross-bearing few-shot fault diagnosis, and the comparative results demonstrate its superiority over the typical and advanced fault diagnosis methods.

Fault diagnosis is crucial for industrial systems, with traditional methods such as CNN heavily reliant on large training datasets to achieve high accuracy. However, such datasets are often-times inaccessible in the real world. Even in few-shot learning models, such as Model-Agnostic Meta-Learning (MAML), the quantity of training data significantly impacts the stability and accuracy of the models, posing challenges for reliable fault diagnosis under limited data conditions. To address these issues, the Wavelet Transform Prototypical Network (WTPN) is proposed, which integrates discrete wavelet transform with prototypical networks for limited training dataset. There are two main structures in WTPN. Firstly, this method transforms one-dimensional vibration signals into two-dimensional distance matrices, enhancing feature extraction and classification accuracy. Secondly, a confidence weighting mechanism assigns weights to decomposed signals based on their classification reliability, thereby improving consistency and reducing performance variability. Then, results from both experimental and publicly available datasets validate that WTPN consistently outperforms existing few-shot learning models in terms of accuracy and stability. Furthermore, the contributions include enhanced feature extraction through DWT, improved stability via confidence weighting, and robust performance in scenarios with limited training data. In conclusion, WTPN represents a significant advancement in fault diagnosis, offering reliable outcomes with minimal training data, making it particularly suitable for applications where data availability is constrained.

Fault detection in mechatronic transmissions is particularly challenging due to the nonstationary nature of monitoring signals arising from complex operating conditions, coupled with the high-safety requirements that limit the availability of fault data. Sparse linear parameter varying autoregressive moving average (Spa LPV-ARMA) model is a powerful tool for dealing with nonstationary time series, and good fitting results can be achieved through the basis function expansion, where parameters of the model are associated with additional variables. However, current research on Spa LPV-ARMA model only considers single basis function, overlooking the potential complementarity of multiple basis functions. This article proposes a novel enhanced Spa LPV-ARMA model with ensemble basis for mechatronic transmission fault detection. The proposed model incorporates the concept of ensemble learning by combining models with different basis functions, and a stepwise approach is utilized to select the models to be combined. The rational choice of the combination scale allows the ensemble model to have fewer parameters with higher accuracy. Simulation and experimental studies in mechatronic transmission are conducted, verifying that the proposed ensemble basis Spa LPV-ARMA model exhibits higher modeling accuracy and fault detection performance.

The Industrial Internet of Things (IIoT) greatly facilitates prognostics and health management of complex industrial systems, wherein the vast amount of real-time data from the IIoT improves intelligent predictive maintenance of industrial systems. When processing industrial IoT data across devices, traditional subdomain adaptation-based methods ignore the local similarities across domains. Also, if fault classes are used to define subdomains, these methods may not be applicable when the target domain is unlabeled or has limited labels. To address the above challenges, a Graph-embedded Subdomain Adaptation Network (GSAN)-based approach is proposed to predict the remaining useful life under different machines in IIoT. Specifically, a manifold subdomain representation is established by manifold learning and local manifold discrepancies between each pair of manifold subdomains with the highest similarity are minimized. To maintain a divisible margin for each manifold, a self-supervised intra-manifold regularization module is developed. An extensive evaluation of six transfer scenarios is performed, and the experimental results show that GSAN can achieve more significant outcomes. This can provide some guidance for future work on prognostics across devices and subdomains.

Vold–Kalman filter (VKF) is a powerful tool for time-frequency (TF) decomposition of nonstationary signals. However, the overdependence on instantaneous frequency (IF) estimation, neglect of nonlinear initial phase, and improper bandwidth selection against noise interference limit its practical performance in mechatronic transmission fault diagnosis under variable speed conditions. This article proposes a novel signal processing method named iterative adaptive Vold–Kalman filter (IAVKF) to tackle the challenges in VKF and realize accurate IF estimation and fault dynamic feature extraction. Specifically, an improved VKF model is developed with the consideration of nonlinear initial phase and discrepancies between true and estimated IFs. Then, the estimated IF is refined by the recovered envelope to ameliorate TF resolution. Finally, an iterative bandwidth adaptation step is developed based on signal orthogonality to reduce noise interference and ensure algorithm convergence. Numerical analysis and two engineering applications in mechatronic transmission fault diagnosis are conducted, showing that IAVKF provides higher accuracy and efficiency in fault feature extraction and IF estimation.