Objective Ship motions in real marine environments are inherently random and uncertain due to the combined effects of wind, waves, and currents, which pose significant challenges to offshore operations such as ocean engineering construction, port berthing, and navigation in confined waterways. Accurate and real-time prediction of ship motion states in advance is crucial for optimizing operational decision-making, enhancing safety, and improving work efficiency. Conventional ship motion prediction approaches based on mechanical models are constrained by high computational complexity and difficulties in parameter tuning, which limit their applicability in real-time scenarios, particularly for extreme short-term prediction. With the rapid development of artificial intelligence, data-driven approaches represented by neural networks have emerged as effective alternatives, promoting the integration of intelligent technologies with marine equipment as a key development trend in ocean engineering. This study aims to develop a high-precision and real-time extreme short-term prediction model for ship motions, focusing on the three degrees of freedom most critical to operational safety and performance: roll, pitch, and heave.

Methods To address the nonlinear and non-stationary characteristics of real-ship motion time series, a prediction network model combining variational mode decomposition (VMD) with Long short-term memory (LSTM) neural network (named VMD−LSTM) is proposed. First, raw ship motion data (including speed, heave, roll, pitch, and yaw) measured in the Qingdao Maidao sea area are preprocessed. The heave, roll, and pitch time series, which are the core prediction targets, are decomposed into multiple variational mode functions (VMFs) using VMD, a technique that overcomes the mode mixing and end-effect limitations commonly encountered in empirical mode decomposition (EMD). These VMFs, together with the speed and yaw data, form the input feature set of the model. The dataset is then divided into training and testing subsets, followed by normalization to accelerate model convergence and improve stability. The LSTM neural network is employed as the core predictor to capture the temporal dependencies in the decomposed data. To enhance the model's learning capability for complex data, the network structure is designed with two LSTM layers and two Dropout layers (for overfitting prevention). The particle swarm optimization (PSO) algorithm is employed to optimize key hyperparameters, including the number of hidden units, Dropout rates, initial learning rate, and learning rate drop factor, with the mean squared error (MSE) as the objective function. Both simulated data (generated using a 6-DOF ship motion unified model) and real-ship measured data are used for model training and validation. Four real-ship test conditions (navigation to test area, head sea navigation, zero speed, and following sea navigation) and two simulated conditions are considered to cover diverse ocean scenarios. Four metrics (SAE, MAE, MSE, RMSE) are used to quantitatively evaluate the prediction accuracy. Additionally, power spectrum analysis based on the Fourier transform is performed to verify the consistency between predicted and measured ship motion characteristics. The proposed VMD−LSTM model is compared with a classical time series prediction approach (ARMA model) and a mainstream deep learning model (CNN) to demonstrate its superiority. For real-time prediction simulation, the model reads data at a sampling rate of 2 Hz and updates prediction results every 0.5 s. A real-time inverse normalization correction method, based on the statistical characteristics of pre-prediction actual data, is applied to mitigate the lag effect of training set features.

Results The results indicate that the optimal prediction lead time of the VMD−LSTM model is approximately one motion cycle, achieving an effective balance between prediction accuracy and engineering applicability. For the three target motions (roll, pitch, heave), the overall prediction accuracy ranges from 75% to 90% under real-ship conditions. Specifically, the heave and pitch motions achieve lower average errors, while the roll motion, despite relatively higher errors, still effectively captures the periodic characteristics. Power spectral analysis confirms that the predicted results are consistent with the measured data in terms of frequency distribution. Compared with the model without VMD decomposition, the VMD−LSTM model exhibits significantly reduced prediction errors, highlighting the effectiveness of VMD in mitigating the impact of nonlinearity and non-stationarity. In the comparison with ARMA and CNN models, the VMD-LSTM model outperforms the others, especially in roll and pitch predictions. The real-time prediction simulations show that the proposed model has strong real-time performance, with an average computation time of less than 0.05 s per prediction step, meeting the requirements of practical offshore operations.

Conclusions Compared with complex theoretical mechanical models and conventional data-driven methods, the proposed VMD−LSTM model achieves a substantial improvement in prediction efficiency while maintaining high accuracy, thereby providing reliable technical support for real-time extreme short-term ship motion prediction in practical engineering applications. The integration of VMD and LSTM effectively addresses the challenges associated with the nonlinear and non-stationary nature of ship motion time series, while PSO-based hyperparameter optimization further enhances the model's adaptability under diverse marine conditions. The real-time inverse normalization correction method improves the model's robustness in dynamically varying ocean environments. This study expands the application of hybrid neural network models in ocean engineering and lays a foundation for the intelligent development of ship motion control systems and the enhancement of offshore operation safety.