Short-term significant wave height prediction using adaptive variational mode decomposition and error-compensation model

• An adaptive VMD method called GAVMD is designed. • An error-compensation model based on GRU and ELM is constructed. • A novel hybrid model GAVMD-GRU-ELM is proposed to improve forecast accuracy. • Comprehensive tests on various scenarios are performed for model verification. Significant wave height (Hs) is a critical parameter for the design of offshore structures and marine construction planning. Recently, pre-processing techniques have been extensively employed to enhance the performance of Hs predictions. Although variational mode decomposition (VMD) has been proven as an effective tool, it is not parameter-adaptive, and manual parameter selection introduces significant uncertainty. To address this issue, an adaptive VMD method, termed GAVMD, is developed, integrating the grey wolf optimizer (GWO), attention entropy (AE), and VMD. Furthermore, the gated recurrent unit (GRU) and extreme learning machine (ELM) are combined into an error-compensation model (GRU-ELM) to perform prediction tasks. By integrating GAVMD with the error-compensation model, a novel hybrid model, GAVMD-GRU-ELM, is proposed for Hs prediction. To validate the proposed model, two single models, ELM and GRU, as well as two hybrid models, VMD-GRU and GAVMD-GRU, are adopted as baselines. The experimental results demonstrate that while single models perform adequately for 3-h predictions, they fall short for 6-h forecasts. In contrast, hybrid models consistently achieve accurate predictions, benefiting from VMD or GAVMD, with GAVMD showing superior improvement compared to VMD. In all prediction scenarios, GAVMD-GRU-ELM outperforms the other models, indicating that the error-compensation model effectively enhances forecast accuracy.