Stochastic analysis of the non-Gaussian airgap response of a semi-submersible using frequency domain analysis

Abstract

Airgap is a crucial design parameter for semi-submersibles. The analysis of the extreme airgap statistics is challenging due to nonlinearities in the wave elevation and platform motions, as well as their interactions and phase relationships. In this paper, an efficient frequency domain approach is developed for airgap analysis, using second-order diffraction analysis to model the wave loads. The wave amplification effect is predicted using second-order random wave theory together with linear diffraction/radiation analysis, and the drag forces are linearized. The linear and quadratic transfer functions (sum- and difference frequencies) of the airgap response are derived, preserving all the phase relationships. The crossing rate is a key quantity for characterizing the extreme of a stochastic process. Using the transfer functions, the crossing rate of the non-Gaussian airgap process is derived via a statistical method that preserves the statistical dependency between the linear, sum- and difference-frequency components. In the case studies, the spectral density of the airgap obtained from frequency domain analysis are compared to time domain simulations (which are performed as a benchmark), and the results are found to be in excellent agreement. Moreover, the proposed approach generally provides good estimation of the crossing rate. The results also reveal insights into the airgap behavior; for example, the airgap at the platform center is nearly Gaussian, whereas the off-center locations are significantly non-Gaussian. Finally, the influence of various nonlinearities on the airgap statistics are systematically investigated.