Rapid and accurate multi-class fault diagnosis is essential for high-end equipment because different fault categories require different maintenance responses. This study aims to develop a lightweight and discriminative diagnostic framework that can identify multiple fault categories from non-stationary vibration signals while reducing redundant computation. High-frequency vibration signals provide direct condition information, but long sequences, noise, nonlinear dynamics, and non-stationary behavior make raw-signal classification unreliable. From an entropy-based information-processing perspective, the key issue is to separate informative fault modes from redundant fluctuations and enlarge inter-class distinctions in the probabilistic decision space. This study proposes Fastformer, an integrated framework for vibration-based fault identification. Empirical Mode Decomposition first converts each signal into Intrinsic Mode Functions to reduce modal mixing and preserve fault-related oscillatory components. The resulting components are processed by an encoder-oriented Q/K/V dot-product scoring mechanism, which constructs compact spatiotemporal embeddings without adopting a complete Transformer architecture. Validation-guided pruning removes low-contribution attention responses, while a Margin-Enhanced Fault Softmax classifier optimized with a cross-entropy-based objective strengthens category separation. By combining stable decomposition, lightweight attention scoring, pruning, and probabilistic margin learning, Fastformer achieves faster and more stable convergence. On the XJTU-SpurGear dataset, Fastformer obtains precision, recall, F1-score, and AUC values of 1.000. Additional validation on the HUST bearing dataset further shows that Fastformer achieves the best overall performance among the compared methods, with an AUC value of 0.9596.

Reliable hourly forecasts of fine particulate matter (PM_2.5) can help cities anticipate deteriorating air quality and prepare measures to limit exposure. A central modeling challenge is to combine rapid pollution fluctuations with meteorological and ecological observations that are updated less frequently. This study develops an adaptive frequency gated network (AFGN) that integrates hourly pollution histories, daily meteorological records, and satellite ecological indicators. Parallel temporal convolutions and recurrent encoders represent concentration changes at multiple resolutions, while attention and signed gating incorporate environmental conditions into the forecast. The framework is evaluated using observations from Beijing, Shanghai, Chengdu, and Wuhan during 2023 and 2024. AFGN achieves lower mean prediction error than the gated recurrent unit (GRU) baseline at 1, 6, and 12 h. At 6 h, mean root mean square error (RMSE) decreases from 13.498 to 12.526 μg/m³, corresponding to an absolute reduction of 0.971 μg/m³ and a relative reduction of 7.20%. These results demonstrate the value of combining multiresolution pollution representations with environmental context for short-range forecasting. The approach provides concentration estimates that could inform the timing of pollution surveillance and exposure advisories as part of sustainable urban air quality management.