Comparative Study of Statistical Analysis Methods for Nonlinear Hydrodynamic Responses of Offshore Structures

Abstract

The present study compares the statistical analysis methods for nonlinear hydrodynamic responses in offshore engineering. In particular, the Kac–Siegert and Hermite-moment methods were compared for estimating the probability distribution of the second-order responses represented via the two-term Volterra series. The Kac–Siegert method analytically formulates the probability density function (PDF) of the second-order Volterra series using an eigenvalue problem constructed with the frequency-domain transfer functions and the wave spectrum, whereas the Hermite-moment method utilizes the statistical moments to determine the coefficients of the fitting function. In addition, the probability distribution of the peak values in the second-order Volterra series with high spectral bandwidth was derived explicitly. The fatigue damage rate and the extreme response were estimated analytically. The accuracy and applicability of each method were investigated by comparing the methods with the results of the direct sampling obtained from the time series.