In this paper, we have developed a series of wave hybrid models for significant wave height prediction. Our developed hybrid models uses a triplet of signal decomposition method, regression model and meta-heuristic algorithm. We have used the ϵ-Support Vector Regression (ϵ-SVR) , Least Squares Support Vector Regression (LS-SVR) , Long Short-Term Memory (LSTM) and Large-margin Distribution Machine based Regression (LDMR) model for the regression task. For signal decomposition methods, we have considered theWavelet Decomposition (WD), Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) method. Apart from this, we have also used the Particle Swarm Optimization (PSO) method to tune the parameters of the used regression model in our wave hybrid models. Till now, the VMD method and LDMR model have not been used in any wave hybrid model. We have evaluated the performance of our developed wave hybrid models on time-series significant wave heights, collected from four different buoys using the different evaluation criteria. After the detailed statistical analysis of the obtained numerical results, we conclude that the VMD-PSO-LDMR based wave hybrid model obtain best performance on six datasets out of seven considered datasets. Also, the VMD based wave hybrid models can obtain better performance than other decomposition based hybrid models. Further, we also conclude from our numerical results that the LSTM model outperforms the SVR, LS-SVR and LDMR based hybrid models if we do not decompose the significant wave height signals apriori. But, when we decompose the SWH time-series signals using a particular decomposition method, then SVR, LS-SVR and LDMR based hybrid models tend to improve their prediction ability significantly.

Ocean buoy sensors stand out as the most reliable means of recording Significant Wave Height (SWH). However, accurate forecasting of SWH is still challenging in energy production. To circumvent such a challenge, this work introduces a Huber Support Vector Regression (SVR) based wave hybrid model for short-term Significant Wave Height (SWH) forecasting using data collected from the buoy sensors. The model employs three distinct signal techniques, including wavelet decomposition, empirical mode decomposition, and variational mode decomposition, along with particle swarm optimization to fine-tune the parameters of the Huber SVR model. Our extensive experimental analysis encompassed six cases from buoys located at four different geographical regions. We compared the Huber SVR-based wave hybrid models with twelve alternative models incorporating $\epsilon$ -SVR, LS-SVR, or LSTM models with different decomposition methods. The results of our numerical experiments demonstrate that the Huber SVR-based wave hybrid models yield superior SWH predictions compared to the other existing models.

The Pin-SVM model (Huang et al., [1]) has gained popularity among researchers in recent days. Bi and Bennett [2] have developed a geometrical framework, in which they have derived the optimization problem of the SVR model from a related SVM model. In this paper, we have used the result of Bi and Bennett in the Pin-SVM model to obtain its corresponding SVR model. We have termed the resulting model with ‘Pinball loss Support Vector machine-based Regression’ (Pin-SVR) model and briefly described its different properties. Further, we have compared the prediction of the proposed Pin-SVR model with the existing standard $\epsilon$-SVR model and its L 1 -norm variant on several artificial and real-world benchmark datasets. Our numerical results conclude that the proposed Pin-SVR model can obtain the better generalization ability than the existing $\epsilon$-SVR model and its variant.