A series of CFD RANS simulations are presented for Wigley hulls of two freeboard heights progressing with forward speed in waves. Free surface effects are captured using the Volume of Fluid (VOF) method embedded in open source software OpenFOAM. Comparisons of heave, pitch motions and added resistance of the first Wigley model against the experiments of Kashiwagi (2013) confirm the numerical validity of the hydrodynamic modelling approach. Further simulations for the lower-freeboard Wigley model reveal that the highest green water impact on decks appears in way of $\lambda /L=1.3$ and at the highest instantaneous pitch amplitude where the water propagates far downstream and across the deck. The simulations also demonstrate that the green water events are associated with air bubble entrapment.

To address the challenge of fatigue life prediction caused by multiple-crack interactions in ship and offshore structures, this study proposes a dynamic Bayesian network (DBN)-based method for predicting the fatigue life of structures with multiple cracks, which is systematically validated through physical experiments. First, a numerical model of a representative structure containing a central hole and multiple initial cracks was established based on the coupled simulation platform of ABAQUS and Franc3D. The nonlinear interaction behavior among multiple cracks under different geometric configurations was systematically investigated. Subsequently, a neural network surrogate model was developed, in which geometric features and crack lengths were employed as inputs and key fracture mechanics parameters were taken as outputs, enabling efficient prediction of complex stress intensity factor (SIF) fields. On this basis, fatigue crack growth experiments were conducted on DH36 high-strength steel specimens containing multiple cracks, and crack evolution data under realistic cyclic loading conditions were obtained. Finally, by coupling the surrogate model with the Paris law as the state transition equation and incorporating sparse experimental observations as dynamic updating information, a dynamic Bayesian network framework based on the particle filtering algorithm was established. This framework enables posterior probability tracking of multiple-crack fatigue states and rolling prediction of the remaining fatigue life. The results demonstrate that the proposed method can effectively mitigate the error accumulation associated with deterministic simulation models during long-term open-loop prediction while relying only on a limited number of discrete observation anchors. Consequently, the prediction accuracy of the fatigue life of multiple-crack systems is significantly improved. Furthermore, under crack co-propagation conditions, the proposed framework exhibits a strong capability to capture the propagation retardation of secondary cracks induced by shielding effects. The proposed method provides a theoretical foundation and technical support for the dynamic assessment of fatigue damage and the development of digital twins for complex structures containing multiple cracks.

The integration of active learning methods and multi-fidelity (MF) Kriging models has been demonstrated to effectively reduce the number of high-fidelity (HF) samples required for reliability analysis. However, there is a lack of comparative research on different MF Kriging models in this context. In this work, the performances of the hierarchical Kriging model, dis-Kriging model, and Co-Kriging model are compared within one-stage and two-stage active learning frameworks through five numerical examples. The total cost, the number of HF samples required, and the stability of estimated failure probability are utilized to facilitate a comparative analysis of different MF Kriging models. The results from the five examples indicate the following: the hierarchical Kriging model demonstrates a satisfactory performance in both one-stage and two-stage frameworks; the dis-Kriging model is not adequately equipped to handle complex, highly nonlinear problems; and the Co-Kriging model exhibits a lack of robustness, though it performs well in certain cases.