Probabilistic time series prediction of ship structural response using Volterra series

Abstract

This study targets to develop a computational procedure to predict the structural response of a ship voyaging through irregular seaways taking into account the relevant uncertainties from probability perspective. To achieve the goal, ship structural response under random wave excitation was assumed to be linear one and represented by linear Volterra series, which is expanded by linear combination of Laguerre polynomials. Then the unknown Laguerre coefficients were treated as random variables, the probability of which was sought by solving Bayesian linear regression model using prepared data sets. For the validation of the proposed methodology, a single DOF linear oscillator model with artificial damping uncertainties was introduced and time series of the system response was predicted probabilistically. For more practical and realistic application, 400,000 DWT VLOC model ship experimental data was analyzed and vertical bending moment time series were probabilistically predicted using the proposed method. On top of probabilistic time series prediction of model ship, the fatigue damage was also estimated based on the stochastic time series obtained using predicted probabilistic time series data.