## 1 Introduction  
A ship is one main way of the transportation of goods in international trade. However, during the transportation process, ships may encounter various adverse sea conditions that endanger their safety. Freak waves, also known as rogue waves, which are rare and unpredictable waves characterized by an unusual high amplitude, sharp crest, and concentrated energy [1, 2, 3], are one of the most dangerous. The interaction between ships and freak waves can result in complex nonlinear phenomena including slamming and green water on deck, which may lead to severe damages on the ship structures, e.g., the 'World Glory' accident [4], the 'SS El Faro' accident [5] and many other destructions [6, 7]. Therefore, investigation on the impact loads and structural response of the ship structures is crucial for ship safety. In recent decades, many studies have been conducted to investigate the effects of freak waves on marine structures in order to understand the damage mechanisms caused by these waves. Some scholars have studied the wave force induced by freak waves. For example, [PERSON] et al. [8] examined the impact of freak waves on cylinders in a large-scale physical model test and studied the influence of tilt angles. They found that the maximum impact pressure of freak waves on cylinders occurred when the incoming wave direction was opposite to the cylinder's tilt direction. [PERSON] and [PERSON] [9] utilizeda wave superposition model to simulate freak waves and investigated the impact loads of freak waves on vertical rigid cylindrical piles. [PERSON] et al. (2010) investigated the impact pressure of Draupner freak waves and fifth-order Stokes waves on cylinders and found that the impact load of the freak wave was 2.8 times that of regular waves of the same scale. [PERSON] et al. (2011) used an energy-focusing model in the laboratory to simulate freak waves and studied the influence of wave parameters such as amplitude, period, and spectral width on the impact load of freak waves on cylinders. [PERSON] et al. (2012) conducted numerical simulations of fixed offshore platforms subjected to freak-wave impacts using a numerical wave tank. They predicted the impact loads on offshore platforms caused by freak waves and designed model experiments based on simulated conditions. The experimental results were in good agreement with those of the numerical simulations. In the academic circle, focused wave groups are frequently used to generate the freak waves, and as such, some scholars have researched the interaction between focused wave groups and marine/coastal structures. [PERSON] et al. (2013) utilized OpenFOAM to examine the transient fluid resonance phenomenon occurring in a narrow gap between two adjacent boxes that were excited by incident focused waves with varying spectral peak periods and focused wave amplitudes. [PERSON] et al. (2014) investigated the transient fluid motion within a narrow gap formed by two fixed boxes under the action of an incident focused wave group, using a two-dimensional viscous flow numerical wave flume. In the study of [PERSON] et al. (2015), based on the Morlet wavelet transform and discrete Fourier transform techniques, the capability of focused transient wave groups to trigger the harbor resonance phenomenon was revealed for the first time. Some scholars have investigated the motion response and longitudinal strength of marine structures under freak waves. For example, [PERSON] et al. (2016) described how to evaluate the strength of a ship based on its nonlinear vertical bending moment (VBM), and investigated the influence of freak-wave height and speed on VBMs and deformation. [PERSON] et al. (2017) investigated the VBM in the midship induced by freak waves and explored the influence of the position in space where the freak waves were generated on the variation of the maximum bending moment. [PERSON] et al.