Periodogram estimation based on LSSVR-CCPSO compensation for forecasting ship motion

A ship motion time series (SMTS) exhibits obvious periodicity under the effects of periodic wave and strong nonlinearity owing to wind, ocean currents, and the load of ship itself, which make accurate forecasting difficult. To improve forecasting accuracy, this investigation divides the SMTS into a periodic term and a nonlinear term and forecasts each term separately. First, the periodogram estimation method (PEM) is implemented to forecast the periodic term. Then, owing to the strong nonlinearity of SMTS, the LSSVR model is used to forecast the nonlinear residual term that is generated by the PEM. On account of parameters that determine the predictive accuracy of the LSSVR model, the chaotic cloud particle swarm optimization (CCPSO) algorithm is introduced to optimize the parameters of the LSSVR model. Finally, combining the PEM, LSSVR model, and CCPSO algorithm, a hybrid forecasting method for SMTS, PEM&LSSVR-CCPSO, is developed. Subsequently, SMTS data for two ships that are sailing on the ocean are used as a numerical example, and thus, the forecasting performance of the presented method is evaluated. The results of the analysis demonstrate that the proposed hybrid SMTS forecasting scheme has better forecasting performance than classical forecasting models that are considered herein.