### 1. Introduction

### 2. Measurement of Ice Load in an Ice Tank Test and Post-processing of the Data

### 2.1 Experimental Setup and Conditions

### 2.2 Post Processing of the Measured Data

*F*,

_{x}*F*, and

_{y}*M*, each dataset was divided into 292 intervals using its minimum and maximum values as the reference. A histogram was drawn based on the ratio of each interval. Fig. 4 shows the measurement data for the heading angle of 0°. For comparison, the kernel density estimation, which estimates the density of the histogram, is represented by a red line, and a blue line represents the normal distribution graph based on the mean and standard deviation of the measured data.

_{z}*F*. When the QQplot graph is viewed from the x-axis perspective, the two distributions seem to align between 0 and ±2.5, but the data and the red line show a discrepancy beyond this range. The histogram appears to follow the normal distribution, but there is a small difference between the data and the normal distribution curve as it gets closer to the extreme values. For

_{x}*F*, the data and the red line agree reasonably well between 0 and ±3, so it can be considered that the data possess normality. However, the

_{y}*M*graph shows some discrepancies.

_{z}*F*,

_{x}*F*, and

_{y}*M*component data. The normal distribution utilizing the mean value and the standard deviation of each set of data was used as the assumed distribution. The normality test was performed based on the 5% p-value, and the results have been marked by P (pass) and F (fail), as shown in Table 3.

_{z}*F*. Even when the log-normal distribution and other distributions were applied to the measured data, as was done by Zvyagin and Sazonov (2014), the results showed that the assumed distribution was not satisfied. This result shows the difficulty of applying statistical methods to ice load generation and the differences in methods measuring the ice resistance. It was determined that

_{y}*F*tends to deviate from the normal distribution at either extreme value of the QQ plot graph because of outliers measured at certain intervals (260–270 s). Here,

_{x}*F*shows a tendency to form a normal distribution based on the incident angle, and

_{y}*M*seems to be affected by the characteristics of the sensor, which performs calculations based on the measured values of

_{z}*F*and

_{x}*F*. However, there is still a need to develop an ice load generation module. This module is required for running simulations in the time domain. The statistical processing method can be developed at a later time. Furthermore, meaningful results can be achieved in determining the design parameters if the simulation is run repeatedly. Ice load generation logic that assumes a normal distribution using the mean and standard deviation of the measured values was applied in this study.

_{y}### 3. Ice Load Generation in Time Domain Simulation

### 3.1 Process to Generate Random Value to an Arbitrary Heading Angle

*F*,

_{x}*F*, and

_{y}*M*for arbitrary head angles (

_{z}*ψ*) are shown in Eq. (1).

*F*is expressed in a linear function,

_{x}*F*and

_{y}*M*and are expressed in a cubic function. When used in simulations, the Froude number is applied according to the full-scale vessel, the average value of

_{z}*F*and

_{x}*F*is multiplied by

_{y}*λ*

^{3}, and the standard deviation function of

*M*is multiplied by.

_{z}*F*,

_{x}*F*, and

_{y}*M*each has interpolation functions for two standard deviations, with 0° being the reference point. The results are shown in Eq. (2). The values of the interpolation function for the standard deviation were also derived based on the measured values from the model test. In the full-scale vessel simulation, the horizontal force (

_{z}*F*,

_{x}*F*) and moment (

_{y}*M*) are multiplied by the third power and the fourth power of the scale ratio, respectively.

_{z}### 3.2 Module for Ice Load Generation

*μ*(

*ψ*)) and standard deviation (

*σ*(

*ψ*)) of the

*F*,

_{x}*F*, and

_{y}*M*component measurement data are calculated for the input heading angle. The interpolation formula described in Eqs. (1) and (2) of Section 3.1 are used for this calculation.

_{z}*μ*(

*ψ*)) and standard deviation (

*σ*(

*ψ*)) values for the corresponding heading angle, and a random number (

*X*∼

*N*(

*μ*(

*ψ*),

*σ*(

*φ*)

^{2})) is generated from the probability density function as an output.

### 4. Simulation Results

### 4.1 Setup for Simulation

### 4.2 Validation Test for the Ice Load Generated by the Developed Module

*F*graph has the highest qualitative similarity between the values generated by the module and the experimental measurement values. (b) The

_{x}*F*graph shows slight differences, but the generated values and the measured values lie within the maximum measurement values from the 10° towing experiment. (c) The

_{y}*M*comparison graph has the largest difference from a normal distribution, and the generated values and the measured values are slightly different. However, the random values are still generated normally within the maximum values.

_{z}### 4.3 Derivation of Limit Status of DP Heading Control

### 4.4 Evaluation of Stationkeeping Performance

### 5. Conclusions

Although the simulated ice loads lacked statistical consistency with the experimental data, their validity was verified by creating ice loads that share some of the statistical characteristics and applying them to the simulation in the time domain. Although random variables were generated by assuming a normal distribution in this study, other distributions, such as a log-normal distribution, can be easily applied. Because the direction angle of the structure kept changing in the simulation, it is difficult to make a direct comparison between the simulation data and the values measured in the experiment while maintaining a particular angle. However, the analysis of the mean and maximum values, one of the main factors that characterize the ice load, is deemed acceptable.

Using the relative magnitude of the ice load and the DPS, it was found that the limit for maintaining the heading angle is approximately 4°. For the floating structure applied in the simulation, there were limitations in maintaining the position and controlling the heading angle simultaneously because the difference in thrust value between the thrusters installed at the bow and stern was significant.

Efforts were made to control the heading angle so it would match the ice load. As a result, the heading angle and the ice load could be matched, even when the contained angle was at 17°. The overall load acting on the structure is reduced by rotating the heading angle in the direction where the load is exerting the greatest force. As a result, it is possible to control the station keeping. This result, along with the previous simulation results, can be used as a reference for setting the acceptable heading angle in the DP-assisted mooring system.

Simulations were performed under a collinear condition, as well as under two different noncollinear conditions where the direction in which the ice load acts was different. The results showed that the station-keeping systems satisfied the performance requirements of the design phase. Because the mooring system is designed rather conservatively, the DPS did not seem to contribute to the station-keeping function. However, in a noncollinear condition, the difference in maximum tension between the stand-alone mooring system and the DP-assisted mooring system was 5,375 kN. Hence, the tension reduction effect of the DPS was shown. This result could be the basic data for redesigning a mooring system.