Significant Wave Height Prediction with the CRBM-DBN Model

In recent years, deep learning technology has been gradually used for time series data prediction in various fields. In this paper, the restricted Boltzmann machine (RBM) in the classical deep belief network (DBN) is substituted with the conditional restricted Boltzmann machine (CRBM) containing temporal information, and the CRBM-DBN model is constructed. Key model parameters, which are determined by the particle swarm optimization (PSO) algorithm, are used to predict the significant wave height. Observed data in 2016, which are from nearshore and offshore buoys (i.e., 42020 and 42001) belonging to the National Data Buoy Center (NDBC), are taken to train the model, and the corresponding data in 2017 are used for testing with lead times of 1-24 h. In addition, we trained the data of 42040 in 2003 and tested the data in 2004 in order to investigate the prediction ability of the CRBM-DBN model for the extreme event. The prediction ability of the model is evaluated by the Nash-Sutcliffe coefficient of efficiency (CE) and root-mean-square error (RMSE). Experiments demonstrate that for the short-term (<= 9 h) prediction, the RMSE and CE for the significant wave height prediction are 0.98, respectively. Moreover, the relative error of the short-term prediction for the maximum wave height is less than 26%. The excellent short-term and extreme events forecasting ability of the CRBM-DBN model is vital to ocean engineering applications, especially for designs of ocean structures and vessels.