Bearing fault diagnosis encounters limitations including insufficient accuracy, elevated model complexity, and demanding hyperparameter optimization. This research introduces a diagnostic framework combining variational mode decomposition (VMD) and fast Fourier transform (FFT) for extracting comprehensive temporal–spectral characteristics from vibration data. The methodology employs a hybrid deep learning architecture integrating convolutional neural networks (CNNs) with Transformers, where CNNs identify local features while Transformers capture extended dependencies. Meta-learning-enhanced Bayesian optimization and HyperBand (Meta-BOHB) is utilized for efficient hyperparameter selection. Evaluation on the Case Western Reserve University (CWRU) dataset using 5-fold cross-validation demonstrates a mean classification accuracy of 99.91% with exceptional stability (±0.08%). Comparative analysis reveals superior performance regarding precision, convergence rate, and loss metrics compared to existing approaches. Cross-dataset validation using Mechanical Fault Prevention Technology (MFPT) and Paderborn University (PU) datasets confirms robust generalization capabilities, achieving 100% and 98.75% accuracy within 5 and 7 iterations, respectively. Ablation studies validate the contribution of each component. Results demonstrate consistent performance across diverse experimental conditions, indicating significant potential for enhancing reliability and reducing operational costs in industrial fault diagnosis applications. The proposed method effectively addresses key challenges in bearing fault detection through advanced signal processing and optimized deep learning techniques.

To further improve the economic benefits of operators and the low-carbon performance within the system, this paper proposes a hierarchical distributed low-carbon economic dispatch strategy for regional integrated energy systems (RIESs) based on the Alternating Direction Method of Multipliers (ADMM). First, the energy coupling relationships among conversion devices in RIESs are analyzed, and a structural model of RIES incorporating an energy generation operator (EGO) and multiple load aggregators (LAs) is established. Second, considering the stepwise carbon trading mechanism (SCTM) and the average thermal comfort of residents, economic optimization models for operators are developed. To ensure optimal energy trading strategies between conflicting stakeholders, the EGO and LAs are embedded into a master–slave game trading framework, and the existence of the game equilibrium solution is rigorously proven. Furthermore, considering the processing speed of the optimization problem by the operators and the operators’ data privacy requirement, the optimization problem is solved in a hierarchical distributed manner using ADMM. To ensure the convergence of the algorithm, the non-convex feasible domain of the subproblem bilinear term is transformed into a convex polyhedron defined by its convex envelope so that the problem can be solved by a convex optimization algorithm. Finally, an example analysis shows that the scheduling strategy proposed in this paper improves the economic efficiency of energy trading participants by 3% and 3.26%, respectively, and reduces the system carbon emissions by 10.5%.