The precise forecast of solar radiation is exceptionally imperative for the steady operation and logical administration of a photovoltaic control plant. This study proposes a hybrid framework (CBP) based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), an enhanced Gaussian process regression with a newly designed physical-based combined kernel function (PGPR), and the backtracking search optimization algorithm (BSA) for solar radiation forecasting. In the CEEMDAN-BSA-PGPR (CBP) model, (1) the CEEMDAN is executed to divide the raw solar radiation into a few sub-modes; (2) PACF (partial autocorrelation coefficient function) is carried out to pick the appropriate input variables; (3) PGPR is constructed to predict each subcomponent, respectively, with hyperparameters optimized by BSA; (4) the final forecasting result is produced by combining the forecasted sub-modes. Four hourly solar radiation datasets of Australia are introduced for comprehensive analysis and several models available in the literature are established for multi-step ahead prediction to demonstrate the superiority of the CBP model. Comprehensive comparisons with the other nine models reveal the efficacy of the CBP model and the superb impact of CEEMDAN blended with the BSA, respectively. The CBP model can produce more precise results compared with the involved models for all cases using different datasets and prediction horizons. Moreover, the CBP model is less complicated to set up and affords extra decision-making information regarding forecasting uncertainty.

Fatigue crack propagation in friction stir welded joints significantly affects aircraft structural integrity. This study investigates the influence of welding speed, rotational speed, specimen thickness, loading frequency, and stress ratio on the fatigue crack growth rate. Four classical machine learning models with different structures—Deep Back-Propagation Network, Random Forest, Support Vector Regression, and K-Nearest Neighbors—were employed to predict fatigue crack growth behavior. The results show that all models achieve strong predictive performance. For FSWed joints, Deep BP and KNN exhibit comparable performance (R² > 0.98) on the training data, indicating similar learning capabilities with sufficient data coverage. Notably, KNN achieves the fastest training time (<0.3 s), while all models require less than 5 s of computation time. These results demonstrate that machine learning-based models provide an efficient and reliable alternative for rapid fatigue crack growth evaluation, supporting damage-tolerant design and structural integrity assessment in aircraft engineering.