Long-Term Non-Linear Bending Moment Prediction
Authors: Derbanne Quentin , Leguen Jean-Franc¸ois , Dupau Thierry , Hamel Etienne 
Published: July 2009

Long-term analysis is more and more used to establish the design loads by performing direct loads evaluation. The long-term distribution of wave loads acting on a ship depends on the short-term contributions of the response in all the wave conditions the ship encounters in her life: sea state, relative heading, speed, load case... For each short-term condition the statistical parameters that describe the response are considered to be constant. Therefore a long-term analysis needs a correct evaluation of the short-term parameters that characterise the short-term response. The Weibull distribution is often used to model the extreme response on a given sea state. The precision of the long-term analysis depends directly on the precision of the Weibull parameters. The first part of this paper is a study of the influence of the simulations parameters (number of wave components, simulation time) and of the different methods used to fit a Weibull distribution on the bending moment extremes, on the precision of the Weibull parameters and on the extreme values. Every choice of parameter used for the final calculations will be justified. The conclusion is that by using a correct fitting method, and provided that there are at least 128 wave components, the overall precision is only dependent on the simulation time: the precision on the 10−5 extreme value is only ±6.4% with 400 extremes, and ±1.9% with 3200 extremes! In order to increase the precision of the evaluation of the Weibull parameters over the entire scatter diagram, without increasing the simulation time, a smoothing method is proposed, based on a polynomial smoothing of the A1/3 and A1/10 values obtained from linear and non linear calculations on the same wave signal, and on the method of moments. This method leads to an increase of precision of about 3 times, that is equivalent to increase the simulation time by 8 or 9! The second part of this paper presents the results of the long-term analysis carried out on 14 ships (ferries, container vessel, naval ships,...), using a non-linear sea-keeping time-domain software. Calculations have been done without forward speed in head waves and for all the sea states of the IACS scatter diagram (more than 200 sea states). The smoothing method has been used to compute all the Weibull coefficients. Results show that it is possible to model the non-linear effects by applying a non-linear coefficient on the linear bending moment for one speed, one scatter diagram and one extreme value probability. But this coefficient can’t be applied, and must be recalculated, if other cases are needed (other speed, other scatter diagram, relative heading distribution or other extreme value probabilities). Every ships will be compared in the same graph in order to evaluated the influence of the design hull form (as overall length and bow flare) on the non linear long term bending moments value (in hogging and in sagging). The calculations were focused on the case of a particular frigate where more parameters were studied as forward speed, operational profile (in speed and relative headings) and scatter diagram choice. In the third part results from model test performed on a height segmented model of the frigate will be compared to the short term results computed by the sea-keeping software. This frigate has been monitored for three years, and the strain measurements at sea will be compared to the numerical long-term analysis.