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In order to solve the problem of control performance degradation caused by time delay in wave compensation control system, predicting vessel heave motion can be the input vector of the control system to alleviate time delay problem. The vessel heave motion belongs to the problem of time series, this paper proposes an improved Long Short-Term Memory (LSTM) model with a random deactivation layer (dropout), which can deal with the time series problem very well. In order to obtain the vessel heave motion, this paper establishes a wave model suitable for marine operation, and solves the vessel heave motion through the mathematical model of vessel motion. Finally, the paper predicts the vessel heave motion in a short predicted time series. In the process of obtaining the prediction effect of vessel heave motion, the Back Propagation (BP) neural network and the standard LSTM neural network are used to compare with the improved LSTM neural network. While the predicted time series is 0.1 s at sea state 3, the mean absolute percentage (MAPE) errors of BP neural network in the prediction of vessel heave motion is 1.06 × 10 −2 %, the standard LSTM in the prediction of heave motion is 1.43×10 −4 %, the improved LSTM in the prediction of heave motion is 7.51 × 10 −6 %. The improved LSTM improves MAPE by 1.05 × 10 −2 % compared with the BP and 1.42 × 10 −4 % compared with the standard LSTM. The prediction results show that the improved LSTM has a strong prediction capability with not easily overfitted in vessel heave motion prediction. The results show that the improved LSTM provides a new idea for vessel motion prediction and solves the problem of time delay, which is useful for the study of stability in marine operations.INDEX TERMS Short-term prediction, improved long short-term memory (LSTM), vessel heave motion, time delay.

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The accurate prediction of significant wave height (SWH) offers major safety improvements for coastal and ocean engineering applications. However, the significant wave height phenomenon is nonlinear and nonstationary, which makes any prediction work a non-straightforward task. The aim of the research presented in this paper is to improve the predicted significant wave height via a hybrid algorithm. Firstly, an empirical mode decomposition (EMD) is used to preprocess nonlinear data, which are decomposed into several elementary signals. Then, a least squares support vector machine (LSSVM) with nonlinear learning ability is adopted to predict the SWH, and a particle swarm optimization (PSO) automatically performs the parameter selection of the LSSVM modeling. The results show that the EMD–PSO–LSSVM model can compensate for the lag in the prediction timing of the prediction models. Furthermore, the prediction performance of the hybrid model has been greatly improved in the deep-sea area; the prediction accuracy of the coefficient of determination (R2) increases from 0.991, 0.982, and 0.959 to 0.993, 0.987, and 0.965, respectively. The prediction performance results show that the proposed EMD–PSO–LSSVM performs better than the EMD–LSSVM and LSSVM models. Therefore, the EMD–PSO–LSSVM model provides a valuable solution for the prediction of SWH.