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

Abstract

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.

Extreme value prediction of nonlinear ship loads by FORM using Prolate Spheroidal Wave Functions

“…In this study, the extreme value problem of the hull girder VBM is addressed by FORM introducing the PSWF. A series of numerical demonstrations are carried out using a Reduced Order Model (ROM) of the VBM which was developed in our previous studies [11,12]. Two short-term sea states are selected to make a comparisons between the two FORM based approach, using the trigonometric components and PSWF.…”

“…In general, to predict extreme values of wave-induced responses using FORM, the wave elevation has been represented based on the superposition of the trigonometric components (see e.g. [5,11,18]).…”

“…u u u u = via an optimization process, e.g. the Response Surface Method (RSM) [11]. Then, the most probable wave episode (MPWE) leading to the given extreme response level is eventually predicted by assigning the design point * * , i i u u to Eq.…”

“…Then, the most probable wave episode (MPWE) leading to the given extreme response level is eventually predicted by assigning the design point * * , i i u u to Eq. (11). It is well known that a substantial number of estimations under various combination of , i i u u is needed, e.g.…”

“…It is well known that a substantial number of estimations under various combination of , i i u u is needed, e.g. at least 4M+2 estimations in the case of RSM [11]. Obviously, a large number of M results in the increase of computational efforts.…”