A major challenge in the design of a mooring line or riser is the evaluation of the fatigue damage accumulated over the lifetime of the structure. The long-term environmental condition is usually represented by a scatter diagram, or a joint probability density of the significant waveheight and a characteristic wave period. Since it is computationally impractical to consider a large number of sea states, a common practice is to condense the sea states into a small number of blocks, but this procedure inevitably introduces significant errors owing to the coarse discretization. In view of the need for efficient but accurate approaches, this paper investigates the application of an asymptotic approximation, which is an established technique for estimating probability integrals, but it has so far not been applied to the fatigue design of moorings and risers. In addition, a classical method known as the perturbation approach is examined. The above approximate methods are implemented on an FPSO floating system, and direct numerical integration is carried out to ascertain the accuracy of the approximate solutions.

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