Research on Hybrid Deep Learning Prediction Method for Midship Vertical Bending Moments

Rapid and accurate prediction of the midship vertical bending moment is critical for ensuring the ship safety in severe sea conditions. However, conventional prediction methods encounter significant challenges in achieving both high precision and reliable uncertainty quantification. This is primarily attributed to the strong nonlinearity and chaotic nature of marine load signals, which is further complicated by the high-frequency disturbances such as wave-induced vibration and slamming events. To overcome these limitations, this study proposes a hybrid deep learning prediction method that integrates Variational Mode Decomposition (VMD), Bidirectional Gated Recurrent Unit (BiGRU), and Quantile Regression Neural Network (QRNN). This method proceeds in three key stages: Firstly, the original bending moment signal is decomposed into a set of low-complexity subsequences to mitigate the interference induced by its inherent nonlinearity. Then, the BiGRU network is used to capture the temporal dependencies of the subsequences for deterministic prediction. Finally, the prediction uncertainty is quantified based on QRNN conjunction and confidence intervals. The hybrid model is validated using the ship model tests that involved wave-induced vibration and slamming events, and its satisfactory performance is achieved with an average coefficient of determination of 0.9533 and a coverage rate of 94.22% for the 95% confidence level. These results confirm its capability to provide both accurate deterministic predictions and effective uncertainty quantification for the midship vertical bending moment, offering a practical support for ship design and real-time operational decisions.