A wavelet - Particle swarm optimization - Extreme learning machine hybrid modeling for significant wave height prediction

Predictions of Significant wave height (Hs) of oceans is highly required in advance for coastal and ocean engineering applications. Therefore, this study aims to precisely predict the ocean wave height via developing a novel hybrid algorithm. Wavelet, Particle Swarm Optimization (PSO), and Extreme Learning Machine (ELM) methods were used and integrated to design the wavelet-PSO-ELM (WPSO-ELM) model for estimating the wave height belongs to coastal and deep-sea stations. A comparative analysis among the ELM, Kernel ELM (KELM), and PSO-ELM models were performed with and without wavelet integration. In addition, wave height prediction time leads up to 72 h were assessed. The meteorological data, including wave height for one year, have been utilized and evaluated to design and validate the proposed model; the data obtained from buoys situated off the southeast coast of the US. The results demonstrated that the WPSO-ELM outperforms other models to predict the wave height in both hourly and daily lead times; in addition, the wavelet increased the accuracy of the prediction models, with the goal that coefficient of determination (R-2), willmott's index of agreement (d), root mean square error (RMSE), and mean absolute error (MAE) were obtained for the lead time 12 h equivalent 0.794, 0.784, 0.374 m, and 0.297 m, respectively for the WPSO-ELM, and 0.643, 0.736, 0.495 m and 0.363 m, respectively for the PSO-ELM. Comparing the obtained results revealed the better performance of the WPSO-ELM model in predicting wave height for coastal and deep-sea regions up to 36 h' lead times.