A copula entropy enhanced mRMR feature selection method for fault diagnosis of hydropower units

Hybrid EEMD-PCA and transformer-based deep learning approach for rotating bearing fault classification

Enhanced Rotating Machinery Fault Diagnosis Using Holo-Hilbert Spectrum Analysis and Machine Learning

Reliable fault diagnosis in rotating machinery is challenging due to the nonlinear and non-stationary nature of vibration signals. Although time–frequency analysis is widely used, it cannot capture the cross-scale coupling between amplitude-modulated (AM) and frequency-modulated (FM) components that carry essential diagnostic information. This study applies Holo-Hilbert Spectrum Analysis (HHSA) to extract amplitude–frequency modulation features and integrates them with six machine learning classifiers to identify four fault conditions. Random Forest, K-Nearest Neighbors, and Logistic Regression achieve accuracies of up to 99.95%, yielding higher accuracy than Fast Fourier Transform-based features. The proposed framework employs an HHSA-based feature extraction pipeline that effectively captures AM–FM coupling in nonlinear vibration signals. It also provides higher discriminative capability than traditional spectral approaches and maintains robustness across multiple classifiers. This method offers high diagnostic accuracy and strong potential for industrial predictive maintenance. Future work will focus on improving computational efficiency and evaluating the framework under more diverse and realistic operating conditions. Received: 10 September 2025 | Revised: 20 April 2026 | Accepted: 10 June 2026 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The VBL-VA001 datasets that support the findings of this study are openly available at https://doi.org/10.1007/s42417-023-00959-9, reference number [44]. Author Contribution Statement Van-Trung Nguyen: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Ba-Tan Le: Investigation, Data curation, Writing - original draft, Writing - review & editing. Van-Phuong Dao: Methodology, Validation, Writing - review & editing.

A fault diagnosis technique using refined composite attention entropy and BWO-SVM

Rolling bearings are core components of rotating machinery, unexpected faults cause economic losses and safety risks. To solve problems of poor feature discriminability and blind parameter selection in traditional fault diagnosis, this paper proposes a method based on refined composite multi-scale attention entropy (RCMAE) and Beluga whale optimization (BWO) for multi-classification support vector machines (SVM). For feature extraction, RCMAE (avoiding hyper-parameter optimization and capturing subtle multi-scale fault information) is fused with time-domain features to form a discriminative multi-dimensional feature vector. For the diagnostic model, BWO optimizes SVM’s key parameters ( c and g ) to eliminate blind selection impacts, establishing the BWO-SVM model. Verification on Jiangnan University and Huazhong University of Science and Technology bearing datasets shows diagnostic accuracies of 99.2% and 100%, respectively. Comparative experiments with DT, RF, KNN, and LSTM confirm its superior accuracy, stability, and generalization. This study provides a reliable technical solution for engineering applications, supporting condition monitoring and predictive maintenance of rotating machinery in manufacturing, wind power, etc., to reduce costs and improve system reliability.

A Rolling Bearing Fault Diagnosis Method Using Adaptive Decomposition and Impact Feature Enhancement Fusion

To address the issues of parameter dependency on empirical settings, insufficient fault feature extraction capability, and limited classification accuracy in rolling bearing fault diagnosis using Variational Mode Decomposition (VMD), a novel fault diagnosis method based on adaptive signal decomposition and intelligent classification integration is proposed. The VMD parameters are adaptively optimized using the Subtraction-Average-Based Optimizer (SABO), and a kurtosis–correlation criterion is introduced to select a single fault-sensitive intrinsic mode function, from which time-domain features are extracted to construct fault feature vectors. The Moth-Flame Optimization Algorithm (MFOA) is employed to optimize the parameters of the Kernel Extreme Learning Machine (KELM) for fault state identification. From the perspective of methodological symmetry, the averaged population update of SABO is invariant to the ordering of search agents, VMD exhibits equivalence under permutation of mode labels, and KELM constructs the sample similarity matrix using a symmetric kernel function. These symmetry-related structures are integrated into the parameter optimization, modal decomposition, and fault classification stages of the proposed method. Experimental validation using the CWRU rolling bearing dataset demonstrates that the proposed method reaches a fault recognition accuracy of 96.73%, outperforming other comparative models and exhibiting superior diagnostic precision and robustness.

Mode entropy knowledge machine: a fully automated bearing fault diagnosis model for complex operating conditions

Accurate diagnosis of rolling bearing faults is critical to the reliability of industrial equipment. However, rolling bearings often operate under complex operating conditions, and with data imbalances and noise interference, fault diagnosis of them remains extremely challenging. To address these issues, a novel mode entropy knowledge machine (MEKM) framework for robust bearing fault diagnosis is proposed in this study. For MEKM, the mode entropy space is firstly constructed to decompose the vibration signal into intrinsic mode components, and the noise-resistant feature extraction and dimensionality reduction are realized by principal component analysis. Secondly, a fast classifier based on extreme learning machines is introduced, and its parameters are automatically adjusted through a particle swarm optimization to establish an adaptive extreme learning machine diagnosis model, ensuring optimal generalization under different load and speed levels. Then, a collaborative optimization paradigm is developed to coordinate mode entropy features and classifier parameters through fully automated learning, in which entropy-driven feature characterization guides the iterative refinement of decision boundaries, while classifier feedback dynamically improves the selectivity of entropy features. Finally, validation is performed on bearings with multiple operating conditions, and the results indicated that the MEKM outperformed conventional deep learning methods in terms of diagnostic accuracy and generalization ability. The work provides a theoretical basis and an industrially feasible solution for health monitoring of mechanical equipment.

Identification of vacuum OLTC faults using improved multimodal PKO-SVM.

Fault identification of vacuum on-load tap changers (OLTCs) is essential for reliable transformer operation and condition-based maintenance. Existing diagnostic methods often rely on single-modality feature settings or treat feature selection and SVM hyperparameter optimization as separate steps. These practices may limit the use of complementary fault information and lead to suboptimal model configurations. To address these limitations, a multimodal PKO-SVM framework is proposed by integrating vibration-acoustic feature-level fusion with joint feature selection and SVM hyperparameter optimization. A dataset containing 250 samples from five operating conditions was constructed. Vibration features were extracted to characterize mechanical impacts and transient dynamic responses, whereas acoustic features were derived to describe spectral-envelope and time-frequency texture variations during switching. In the proposed framework, PKO is used to jointly optimize the feature-selection mask and the SVM hyperparameters C and γ, thereby reducing empirical parameter dependence and balancing recognition performance and feature compactness through a unified fitness function based on mean Macro-F1 and a feature-count penalty term. Repeated experiments with an independent test set were conducted for evaluation. The PKO-SVM model using the fused vibration-acoustic feature set achieved an accuracy of 92.53% ± 2.98% and a Macro-F1 of 0.9252 ± 0.0299. Compared with acoustic-feature-only and vibration-feature-only inputs, the fused vibration-acoustic feature set improved the average accuracy by 8.43 and 2.96% points, respectively. Comparisons with MLP/BPNN, TabNet, Random Forest, GA-SVM, and XGBoost, together with feature-contribution analysis, further supported the effectiveness and interpretability of the proposed multimodal PKO-SVM framework. These results indicate that the multimodal PKO-SVM framework has the potential to provide a reliable and compact diagnostic model for online condition assessment of vacuum OLTCs.