An enhanced model based on deep operator network for very short-term forecasting of ship motion

Abstract

Very short-term forecasting of ship motion involves forecasting future ship movements based on learned characteristics from historical motion data. However, ship motion exhibits not only temporal features but also features in the frequency domain, which are often overlooked. This paper introduces a novel method called Fourier Transform and Multilayer Perceptron-net enhancement based on Deep Operator Network (DeepONet), abbreviated as FMD. This approach effectively captures and learns ship motion patterns in both the temporal and frequency domains. Specifically, the branch net of DeepONet learns temporal features, while the trunk net performs Fourier filtering to capture the underlying ship motion patterns. In addition, the learning effectiveness of Fourier filtering is complemented by using MPL-net to enhance the extraction of detailed features in motion data. To evaluate the prediction performance of FMD, this study explores the optimal filtering frequency of the FMD model using experimental ship model motion data. Comparative testing with the DeepONet model includes multi-step prediction, coupled data forecasting, and generalization studies. Testing results demonstrate that the proposed FMD model improves prediction accuracy from 11.78% to 33.10% under Mean Squared Error (MSE) compared to the DeepONet model. Even under sea conditions ranging from mild to intense, the FMD model maintains high accuracy, with an improvement of over 30% in accuracy compared to DeepONet at longer step lengths under MSE conditions. Testing results indicate the superiority and advancement of FMD in prediction accuracy, generalization, and versatility, showcasing significant advantages in very short-term forecasting of ship motion.