Objectives 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 narrow waterway navigation. Accurate and real-time prediction of ship motion states in advance is crucial for optimizing operational decisions, enhancing safety, and improving work efficiency. Traditional ship motion prediction methods based on mechanical models are limited by high computational complexity and difficulties in parameter tuning, making them inadequate for real-time applications, especially in extreme short-term prediction scenarios. With the rapid development of artificial intelligence, data-driven approaches represented by neural networks have emerged as promising 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 most operationally critical degrees of freedom: 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) and Long Short-Term Memory (LSTM) neural network (named VMD-LSTM) is proposed. First, the original 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 issues of empirical mode decomposition (EMD). These VMFs, together with the speed and yaw data, form the input feature set of the model. The input data are then divided into training and test sets, followed by normalization to accelerate model convergence and improve stability. The LSTM neural network is employed as the base 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 utilized to optimize key hyperparameters, including the number of hidden units, Dropout rates, InitialLearningRate, and LearnRateDropFactor, with the Mean Squared Error (MSE) as the objective function. Both simulated data (generated by 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 evaluation metrics (SAE, MAE, MSE, RMSE)are used to quantify the prediction accuracy. Additionally, power spectrum analysis via Fourier transform is performed to verify the consistency between predicted and measured motion characteristics. The proposed VMD-LSTM model is compared with classical time series prediction methods (ARMA model) and mainstream deep learning models (CNN) to demonstrate its superiority. For real-time prediction simulation, the model reads data at a sampling rate of 2 Hz, updates prediction results every 0.5 s, and adopts a real-time inverse normalization correction method using the statistical characteristics of pre-prediction actual data 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, balancing prediction accuracy and engineering applicability. For the three target motions (roll, pitch, heave), the overall prediction accuracy reaches 75%–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 spectrum analysis confirms that the predicted results are consistent with the frequency distribution of measured data. 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 simulation shows that the model has strong real-time performance, with each prediction step taking less than 0.05 s on average, meeting the requirements of practical offshore operations.

Conclusions Compared with complex theoretical mechanical models and traditional data-driven methods, the proposed VMD-LSTM model significantly improves prediction efficiency while maintaining high accuracy, 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 posed by nonlinear and non-stationary ship motion data, and the PSO-based hyperparameter optimization further enhances the model's adaptability to diverse marine conditions. The real-time inverse normalization correction method ensures the model's robustness in dynamic ocean environments. This study enriches the application of hybrid neural network models in ocean engineering and lays a foundation for the intelligent development of ship motion control and offshore operation safety.