Abstract: Accurate modelling of the characteristics of the distribution tail (high ice force area) of the ice force of polar ships has a decisive impact on structural safety, and the existing distribution model has insufficient accuracy in fitting the tail data, which limits the reliability of the safety design of ships. In order to overcome the limitations of the standard distribution model, this paper proposes a high-precision tail fitting method to provide theoretical support for the reliability design of polar ships. In this paper, based on the measured ice force, the Rayleigh separator is used to extract the peak data, and a nonlinear mixed index distribution model is proposed to improve the fitting adaptability of the tail. Combined with the quantile-quantile plot and the coefficient of determination, the goodness of fitting of exponential distribution, Weibull distribution, exponential Weibull distribution, linear mixed exponential distribution and nonlinear mixed exponential distribution were comprehensively compared. The results show that the tail coefficient of determination of the distribution model proposed in this paper is greater than 0.85 on all ice force datasets, and the goodness of fitting is the best among all the compared distributions, which can accurately characterize the tail characteristics of ice force and provide a reliable basis for the design and risk assessment of ship ice-resistant structures.

Key words: ice force peaks, probability distribution fitting, nonlinear mixed exponential distribution, exponential Weibull distribution