Estimation of nonlinear long-term extremes of hull girder loads in ships

This paper deals with a estimation of long-term extreme value for a given return period, say D=100 yr. In principle, this response is obtained by combining the response in all the sea states. The long-term response for a linear system can be effectively obtained by determining the response for each sea state, specified by the significant wave height, H_s, and the peak period, T_p, in the frequency domain. However, if the response is nonlinear, time domain simulation and a long time series would be required, to limit statistical uncertainty. Therefore, the long-term analysis becomes rather complicated and time consuming. For the long-term analysis, it is crucial to introduce ways to improve the efficiency in the calculation. In this work, it is shown that, the long-term extremes can be estimated by considering only a few short-term sea states. A long-term analysis based on identifying the most important sea state, defined by the coefficient of contribution, using linear analysis is applied. An iteration procedure is thereafter used to find the nonlinear long-term extreme values. It is concluded that only a limited number of sea states is necessary to get an acceptable estimate of the nonlinear D-year response as long as the most important sea states are included, i.e., the sea state with the maximum coefficient of contribution.