Control variates for efficient long-term extreme analysis of mooring lines

Predicting the long-term extreme response is a major challenge for compliant offshore structures such as mooring lines. The structure is exposed to long-term uncertainties from varying environmental conditions and short-term uncertainties from random waves. The "all sea states approach" is rigorous but computationally prohibitive, since each sea state necessitates time domain simulations to capture the nonlinearities and non-Gaussian characteristics of the dynamic system. This paper presents a new approach for accurate long-term extreme analysis of mooring lines. The short-term conditional failure probability is estimated based on extrapolation of crossing rates. Monte Carlo simulation (MCS) is used to perform the integration over the long-term variables, which include the significant wave height, average period, and the speed/direction of wind and current. The classical control variates technique is invoked to reduce the variance of the MCS estimator. The difficulty of obtaining a good control function for complex problems is resolved through a new auto-control variates scheme, wherein the control is formulated as a surrogate model constructed from existing MCS scatter. Since variance reduction is effected by post-processing, multiple stress locations can be evaluated from the same dynamic simulations. The proposed method is implemented on a turret-moored vessel, and the predicted failure probability is compared against subset simulation, in which all the short- and long-term uncertainties are incorporated as random variables and no arbitrary assumptions are made. The proposed method is found to be in excellent agreement with subset simulation, and the variance reduction is considerable, resulting in a speedup of roughly an order of magnitude or more.