A hybrid VMD-LSTM/GRU model to predict non-stationary and irregular waves on the east coast of China

Accurate wave forecasting is essential for the safety of port and offshore structure operations and ship navigation. Computational fluid dynamics (CFD) and traditional time series models are ineffective in dealing with nonlinearities and non-smoothness. However, long short-term memory (LSTM) and gate recurrent units (GRU) have strong non-linear handling capabilities but are deficient in non-stationary situations. Variational mode decomposition (VMD) can effectively separate the non-linearity and non-smoothness in data. In this report, a VMD-LSTM/GRU model is proposed by combining the advantages of the LSTM model, the GRU model, and the VMD technique. Based on the one-tenth maximum wave height at three locations on the east coast of China, the error of the VMD-LSTM/GRU model is shown to be lower than that of the LSTM/GRU model, and significantly lower than that of the single LSTM and single GRU models. By analyzing different forecast durations, it was found that the correlation of the VMD-LSTM/GRU model improved from 10.75% to 20.99% compared to the corresponding LSTM/GRU model. The RMSE and relative errors of the VMD-LSTM/GRU model were reduced by 96.77% and 95.52%, respectively, for the most difficult forecast result 10 h ahead. Thus, this model has proved to be superior in predicting non-linear and non-stationary waves.