Response statistics of non-linearly moored vessels under the action of first and second order wave forces

Abstract

Various techniques are used to predict the response probability density function (pdf) and mean up-crossing rate of a non-linearly moored vessel subject to combined first and second order wave forces. The main approach used is based on the assumption that the response can be expressed as a combined first and second order Volterra/Wiener series; the advantage of doing this is that the response pdf and mean up-crossing rate may be calculated using previously developed techniques. The methods used to express the response in this form are the Volterra series method, the Statistical Linearisation technique, the method of Statistical Quadratization and the Wiener-Hermite functional approach. The accuracy of these techniques to predict the response pdf and mean up-crossing rate of a catenary moored vessel subject to wave forces is investigated by comparison with numerical simulation. In addition to the aforementioned techniques, a semi-empirical method for calculating the response pdf and mean up-crossing rate is presented. This method is based on a known analytic solution to the Fokker-Planck equation and uses the values of mean and rms response calculated using the Gaussian version of the Statistical Linearisation technique. For the examples considered, it is found that the Wiener method is capable of predicting a good estimate of the response statistics if the first order wave forces significantly affect the response, while the Wiener method, the Gaussian version of the Statistical Linearisation technique and the Fokker-Planck based solution may be used to obtain an indication of the response statistics if the second order wave forces dominate the response.