In this paper, we propose a least square support vector machine (LSSVM) model to predict ocean wave elevations in a random sea state. The frequency and time domain characteristics of historical wave data are both considered in the proposed model. The wave data following a JONSWAP spectrum measured through an indoor wave tank experiment are used for the study. The measured time series were transformed to frequency domain by the fast Fourier transform and divided into five bands by filtering method. With the time series corresponding to each band, the LSSVM model is trained separately and used to predict future time series. The proposed model is shown to greatly extend the prediction time length, making it more effective to the application of the short-term real-time wave prediction.


The real ocean waves are irregular, random and highly nonlinear. Though theoretical and numerical models have been developed for long to understand the behavior of ocean waves, it remains a challenge to make real-time predictions. A variety of prediction methods have been developed. For computational models, wave parameters are simulated and predicted by solving equations based on theoretical models, such as the wave model (WAM) proposed by Group (1988). This method could make good prediction for waves in deep-sea areas, but it has certain limitations of application for nearshore areas with complex terrain. In recent years, artificial intelligent (AI) methods such as machine learning techniques have attracted much attention of researchers in various fields because its emergence effectively makes up the shortcomings of conventional prediction methods. Machine learning (ML) method could make statistical prediction based on historical data, which has been widely applied in the prediction of energy consumption, traffic flow, rainfall, stock price and other fields, and has great potential in marine engineering applications (Gopinath, 2015).

ML technique becomes an alternative to predict the time history of surface wave elevations as in many other fields. Although the wave propagation in the time domain is nonlinear, they are not completely ‘random’ and can be predicted within a certain range of accuracy error. Artificial neural network (ANN) is widely used in early studies for wave prediction. Deo and Chaudhari (1998) utilized ANN technology to predict tides at three different locations on the east coast and west coast of India. Makarynskyy et al. (2005) used ANN to predict wave heights and periods 3, 6, 12 and 24 hours in advance on the west coast of Portugal. Kalra and Deo (2007) estimated the effective wave height, average wave period and wind speed in coastal areas through ANN based on the values collected from 19 offshore sites. In order to deal with the problem that simple feedforward neural networks cannot consider the long-term dependence on time series, Recurrent Neural Networks (RNNs) have been developed, which store the information of past values (Williams and Zipser, 1989).

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