Tongbo Zhu

Strings (cables) are basic structural elements in many engineering systems, including cranes, maritime vessels, and bridge structures, where dynamic loads can induce large-amplitude transverse vibrations. Such nonlinear vibrations may cause fatigue damage and eventually lead to cable or structural failure. Therefore, the nonlinear large-amplitude vibration of taut strings is crucial for engineering design and safety assessment. This technical note derives explicit and highly accurate analytical expressions for the period of transverse vibration of flexible strings. The proposed method consists of two main steps: (i) expressing the exact period in integral form, and (ii) applying a variable transformation along with the two-node and three-node Gaussian–Legendre quadrature rules. The obtained period expression is explicit and maintains high accuracy over the entire amplitude range from small to large. As the amplitude tends to infinity, the approximate period shows an error of only 0.00081% relative to the exact period. The results presented in this study will provide theoretical support and useful guidance for string design.

Accurate remaining useful life (RUL) prediction of proton exchange membrane fuel cells (PEMFCs) is essential for reliability-oriented operation and predictive maintenance of hydrogen energy storage systems. However, PEMFC degradation under dynamic operating conditions is often non-stationary and non-Gaussian, exhibiting long-range dependence, heavy-tailed fluctuations, and abrupt jump behaviors. To address these challenges, this paper proposes a mechanism-constrained fractional Lévy–Poisson (fLP) degradation model for probabilistic RUL prediction and uncertainty quantification. In the proposed framework, fractional Lévy stable motion is employed to characterize continuous degradation dynamics with long memory and heavy-tailed stochastic fluctuations, while a Poisson jump process is introduced to capture abrupt degradation events induced by operating-condition variations. Moreover, a composite degradation factor is embedded into the drift term to impose mechanism-related constraints and enhance physical consistency. Based on adaptive parameter estimation and Monte Carlo simulation, the proposed model enables probabilistic RUL prediction under both steady-state and dynamic operating conditions. Experimental results show that the proposed method outperforms representative benchmark and ablation models, achieving MAE, MAPE, RMSE, and R² values of 0.5833, 1.6826%, 0.7642, and 0.9847, respectively. These results indicate that the proposed fLP model provides an interpretable and reliable prognostic framework for uncertainty-informed maintenance and lifetime management of PEMFCs in hydrogen energy storage systems.

To address the challenges of high feature similarity and severe noise interference in the open-circuit fault diagnosis of IGBT inverter modules under harsh marine conditions, this paper proposes an improved artificial bee colony-optimized one-dimensional convolutional neural network (IABC-1D-CNN) for robust fault diagnosis in marine ranching power systems. This study provides a MATLAB R2024a/Simulink-based feasibility validation rather than hardware or field verification. First, a photovoltaic grid-connected inverter simulation model is established to generate three-phase current signals under different operating conditions and fault states, and a sliding-window segmentation method combined with data augmentation is employed to improve sample diversity. Then, the improved artificial bee colony algorithm, incorporating differential evolution and genetic strategies, is used to globally optimize the key hyperparameters of the 1D-CNN, thereby improving convergence efficiency and model stability. Based on the optimized architecture, the proposed model enables automatic feature extraction and accurate identification of IGBT open-circuit faults under complex marine environments. Experimental results show that the proposed method achieves high diagnostic accuracy under both noise-free and noisy conditions. Under signal-to-noise ratios (SNRs) of 20 dB, 15 dB, 10 dB, and 0 dB, the diagnostic accuracies reach 99.55%, 98.86%, 97.27%, and 89.25%, respectively, consistently outperforming Baseline 1D-CNN, CNN-LSTM, and ELM. These results demonstrate that the proposed method provides a simulation-validated diagnostic framework with strong classification accuracy and noise robustness, while practical deployment requires further HIL and field-data validation.

Accurate prediction of the remaining useful life (RUL) of proton exchange membrane fuel cells (PEMFCs) remains challenging due to strong stochasticity, non-Gaussian characteristics, and complex degradation behaviors under dynamic operating conditions. To address these challenges, this paper proposes a mechanism-informed fractional Lévy–Poisson (fLP) degradation model for probabilistic RUL prediction and uncertainty quantification.Statistical analysis of experimental voltage data demonstrates that PEMFC degradation exhibits pronounced non-stationary features, including long-range dependence, heavy-tailed fluctuations, and abrupt jump behaviors. To capture these characteristics, fractional Lévy stable motion is employed to model continuous degradation dynamics with long memory and heavy-tailed distributions, while a Poisson jump process is introduced to characterize sudden degradation events induced by operating condition perturbations. Furthermore, a composite degradation factor is incorporated into the drift term to impose physical constraints, enabling the integration of degradation mechanisms and stochastic properties within a unified modeling framework.Based on adaptive parameter estimation and Monte Carlo simulation, probabilistic RUL prediction is achieved under both steady-state and dynamic operating conditions. Experimental results demonstrate that, compared with conventional models such as fractional Lévy stable motion (fLsm), fractional Brownian motion (fBm), and CNN–LSTM, the proposed fLP model achieves superior prediction accuracy and uncertainty control. Specifically, the model yields MAE, MAPE, and RMSE values of 0.5833, 1.6826%, and 0.7642, respectively, with a coefficient of determination (R²) of 0.9847. These results confirm the effectiveness and robustness of the proposed approach for PEMFC lifetime prediction under complex operating conditions.

Under dynamic loading conditions, the output voltage of proton exchange membrane fuel cells (PEMFCs) exhibits nonlinear degradation characterized by non-Gaussian fluctuations, abrupt changes, and long-range temporal dependence, which are difficult to model using conventional short-correlation or remaining useful life (RUL) prediction approaches. To capture both historical dependency and stochastic jump behavior, this study proposes a SHAP-driven mechanism–data fusion fractional stochastic degradation model based on fractional Brownian motion (fBm) and fractional Poisson process (fPp) for degradation trend forecasting. A terminal voltage mechanism model considering activation, ohmic, and concentration polarization losses is first established, and SHapley Additive exPlanations (SHAP) analysis is employed to quantify the contributions of multi-source operational variables and enhance interpretability. The Hurst exponent is then used to verify long-range dependence and jump characteristics in the voltage sequence. Subsequently, fBm is integrated with a fPp to construct a unified stochastic degradation framework capable of jointly describing continuous decay and discrete abrupt variations, enabling multi-step probabilistic prediction with confidence intervals. Validation on the publicly available FCLAB FC1 and FC2 datasets shows that the proposed model achieves superior overall performance under both steady and dynamic conditions, with MAPE/RMSE/R² of 0.027%/0.00178/0.9895 and 0.056%/0.00259/0.9896, respectively, outperforming fBm, Wiener, WTD-RS-LSTM, and CNN-LSTM methods. The proposed approach provides accurate and interpretable degradation forecasting for PEMFC health management and maintenance decision support.

With the increasing penetration of offshore wind power, extreme marine conditions pose significant challenges to forecasting accuracy and grid stability. To address this issue, this study proposes a robust offshore wind power forecasting framework based on multi-source feature fusion and a hybrid TCN–BiLSTM–KAN architecture. Specifically, a Temporal Convolutional Network (TCN) is employed to extract local multi-scale temporal features and suppress high-frequency disturbances, followed by a Bidirectional Long Short-Term Memory (BiLSTM) network to capture long-term temporal dependencies. A Kolmogorov–Arnold Network (KAN) is further integrated as a nonlinear mapping module to approximate complex dynamics under extreme marine conditions. The model is validated using a real-world offshore wind power dataset with a 15 min forecasting horizon, where balanced samples are constructed across different operating conditions. Experimental results demonstrate that, under extreme conditions, the proposed model achieves an RMSE of 3.58 MW and an R² of 97.84%, with RMSE reductions of 56.8% and 42.3% compared to CNN-BiLSTM and Transformer-KAN, respectively. Furthermore, cross-site validation confirms that the model maintains stable predictive performance, indicating its preliminary spatial generalization capability. Overall, the proposed framework provides an effective solution for enhancing forecasting reliability and supporting secure grid integration of offshore wind power under extreme marine environments.

With the rapid development of renewable energy, accurately forecasting wind power is crucial for the stable operation of power systems and effective energy management. This paper proposes a short-term wind power forecasting method based on the Orthogonalized Maximal Information Coefficient (OMNIC) combined with an Adaptive fractional Generalized Pareto motion (fGPm) model. The method quantifies the influence of meteorological factors on wind power prediction and identifies the optimal set and number of influencing factors. The model accounts for long-range dependence (LRD) in time series data and constructs an uncertainty model using the properties and parameters of the fractional generalized Pareto distribution (GPD), significantly improving prediction accuracy under nonlinear conditions. The proposed approach was validated using a real dataset from a wind farm in northwest China and compared with other models such as Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) and Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU). Results show that the adaptive fGPm model reduces RMSE by 0.448 MW and 0.466 MW, MAPE by 6.936% and 9.702%, and achieves an average R² of 0.9826 compared to CNN-GRU and CNN-LSTM. The improvement is due to the dynamic adjustment to data trends and effective use of LRD features. This method provides practical value in improving wind power prediction accuracy and addressing grid integration and regulation challenges.

With the rapid development of renewable energy, accurately forecasting wind power is crucial for the stable operation of power systems and effective energy management. This paper proposes a short-term wind power forecasting method based on the Orthogonalized Maximal Information Coefficient (OMNIC) combined with an Adaptive Fractional Generalized Pareto Motion (fGPm) model. The method quantifies the influence of meteorological factors on wind power prediction and identifies the optimal set and number of influencing factors. The model accounts for long-range dependence (LRD) in time series data and constructs an uncertainty model using the properties and parameters of the fractional generalized Pareto distribution (GPD), significantly improving prediction accuracy under nonlinear conditions. The proposed approach was validated using a real dataset from a wind farm in northwest China and compared with other models such as Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) and Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU). Results demonstrate that the adaptive fGPm model significantly reduces wind power forecasting errors, offering high accuracy and robustness. This method provides practical value in alleviating peak voltage and frequency regulation challenges in power systems and in promoting the integration of wind power into the grid.

To enhance the economic viability of wind energy in cold regions and ensure the safe operational management of wind farms, this paper proposes a short-term wind turbine blade icing wind power prediction method that combines principal component analysis (PCA) and fractional Lévy stable motion (fLsm). By applying supervisory control and data acquisition (SCADA) data from wind turbines experiencing icing in a mountainous area of Yunnan Province, China, the model comprehensively considers long-range dependence (LRD) and self-similar features. Adopting a combined pattern of previous-day predictions and actual measurement data, the model predicts the power under near-icing conditions, thereby enhancing the credibility and accuracy of icing forecasts. After validation and comparison with other prediction models (fBm, CNN-Attention-GRU, XGBoost), the model demonstrates a remarkable advantage in accuracy, achieving an accuracy rate and F1 score of 96.86% and 97.13%, respectively. This study proves the feasibility and wide applicability of the proposed model, providing robust data support for reducing wind turbine efficiency losses and minimizing operational risks.