A hybrid Rayleigh and Weibull distribution model for the short-term motion response prediction of moored floating structures

Abstract Nonlinearities inherent in the dynamic system lead the motion response of moored floating structure to be non-Gaussian processes, and the short-term motion response prediction based on Rayleigh distribution therefore becomes inaccurate. This paper proposes a probability density function (PDF), termed as the hybrid Rayleigh and Weibull distribution (HRW), to accurately characterize the probability distribution of motion amplitude of moored floating structures. In the HRW model, the Rayleigh distribution is adopted to depict wave frequency (WF) motion amplitude, and the Weibull distribution is employed to describe low frequency (LF) motion amplitude. Since the probability contribution of WF and LF motion amplitude in total motion amplitude depends on the occurrence frequency of WF and LF motion amplitude, a weighting factor related to the mean up-crossing rate of WF and LF motion response is introduced in the HRW model to combine the Rayleigh and Weibull distribution. The proposed HRW model can consider the statistical interference effects of WF and LF motion, and has an advantage of characterizing WF and LF motion amplitude simultaneously. To verify the effectiveness of the proposed HRW model, a case study for a moored semi-submersible was conducted. Numerical calculation results indicate that the proposed HRW model not only yields accurate short-term motion response prediction but also has robustness under severe sea states.