Accurate prediction of roll motions is important for the design of vessels of various types, especially ship-shaped floating production, storage and offloading (FPSO) systems for the oil and gas industry. For frequency domain analysis with sea spectrum, the viscous roll damping is usually linearised following a known procedure of stochastic linearization. This involves replacing damping terms that are non-linear with roll velocity with an equivalent linear term such that the error between certain statistical properties of the non-linear and linearised roll responses is minimized. An iterative procedure is used for this calculation where repetitive computations of Response Amplitude Operators (RAO) are undertaken by solving equations of motions until convergence is obtained. If the sea state changes the analysis must be repeated. For motions analysis in multidirectional seas or with fully directional (carpet) spectrum such computations must be carried out for several wave directions, and the numerical burden becomes an issue. This is especially the case for vessel operability or response based analyses, when the number of sea states considered is measured in thousands. The paper presents a method for an approximate stochastic linearization, which is intended to adjust the viscous roll damping without re-computing complete motion RAOs. On the basis of a single degree of freedom roll model, a pair of correction functions are introduced, which describe the effect of change in the viscous damping on the roll amplitude and phase via a single parameter. Assuming that the effect of viscous roll damping is qualitatively similar for any wave direction, the problem is reduced to solving a single non-linear equation about the unknown parameter. The procedure is numerically efficient; it requires the knowledge of some “reference” RAO and phase functions, but does not involve solving equations of motions and the knowledge of all hydrodynamic coefficients of the vessel. Comparison between the proposed method and the exact stochastic linearization demonstrates that the method is sufficiently accurate in predicting stochastic roll amplitudes, as well as in generating both the RAO and the phase functions of roll motion. It is also demonstrated that the impact of changing the equivalent roll damping on other vessel motions, which are weakly coupled with roll, is small and may be ignored.

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