Long-term fatigue analysis of mooring lines considering wind-sea and swell waves using the Univariate Dimension-Reduction Method

Abstract

In offshore structures analysis, one of the greatest challenges is the high computational cost of evaluating long-term waves-induced fatigue damage. Complication lies on the large number of required numerical stochastic simulations to compute the long-term multi-dimensional integral associated to the problem. In addition, when effects of wind-sea and swell waves are simultaneously considered as independent phenomena, the order of the damage integral increases, which leads to an even greater amount of numerical simulations. Aiming at reducing the number of short-term stochastic simulations needed in order to evaluate the multi-dimensional fatigue damage integral, this work investigates the Univariate Dimension-Reduction Method (UDRM) as an efficient numerical approach. In this method the original random variables, which represent the environmental conditions parameters, are transformed into standard Gaussian variables and, in this reduced space, an additive decomposition to represent the short-term fatigue damage by a simpler function is employed. Due to this transformation, the problem of simultaneous independent wind and swell waves that previously could only be solved by one four-dimensional integral can now be solved by four one-dimensional integrals. These one-dimensional integrals can be solved by appropriate quadrature techniques, such as the one based on the Gauss-Hermite quadrature. Final result is a significantly reduced number of numerical analyses required for a good estimation of the long-term fatigue damage, allowing its use for practical cases. To evaluate the methodology performance, two case studies involving mooring systems of FPSOs (a spread-moored and another turret-moored) located offshore Brazil in approximately 1800 m (∼6000 ft) water depth are presented. Fatigue damages of the mooring lines are individually calculated by UDRM and results are compared to those obtained by the traditional approach of estimation of fatigue damage considering environmental data of a large enough number of short-term conditions. It is shown that, even with less than 2% of the total short-term numerical simulations required by the traditional approach, UDRM leads to very suitable fatigue damages results, i.e., with differences lower than 9% in the first case study and 24% in the second one. The accuracy of UDRM due to statistical modeling of environmental parameters is also investigated.