Efficient FORM-based extreme value prediction of nonlinear ship loads with an application of reduced-order model for coupled CFD and FEA

In this paper, a method for predicting the extreme value distribution of the vertical bending moment (VBM) in a ship under a given short-term sea state is presented. To predict the extreme value distribution of the VBM, the first-order reliability method (FORM), by which the most probable wave episodes (MPWEs) leading to given VBMs are identified, is introduced. The coupled computational fluid dynamics (CFD) and finite-element analysis (FEA) are used to provide the high-fidelity numerical solutions for the wave-induced and whipping components of the VBM. Then, a Reduced-Order Model (ROM) which can yield the predictions equivalent to the coupled CFD-FEA results in a relatively short time is developed. The ROM is incorporated into FORM to identify the MPWEs, in lieu of the coupled CFD-FEA. The accuracy of the ROM is verified by comparing with the coupled CFD-FEA results under identified MPWEs, in terms of both the wave-induced and whipping VBM. Then, a series of tank tests using a scaled container ship is conducted. In the first series of the tests, the VBM measurements under the MPWEs identified from the FORM-based approach using the ROM are made, to validate the accuracy of the ROM. The extreme value distribution of the combined wave-induced and whipping VBM is also measured by performing the second series of the tests, in random waves. The validity of the FORM-based extreme value prediction using the ROM is investigated by comparing with the second series of the tests.