## 3 Data Analysis Methodology  
### Method of Analysis of the Whipping Factor  
To quantitatively evaluate the whipping response generated on the hull, the whipping factor \(\gamma\) is calculated for every one-hourly stress time-series data point. The whipping factor is given by Equation (1), and is defined as the ratio of the maximum expected value of the raw stress time-series data, including the whipping response component, to the maximum expected value of the wave response component, excluding the whipping response component [10]. \[\gamma=\frac{\sigma_{r,1/1000}}{\sigma_{w,1/1000}} \tag{1}\]  
where \begin{table}
\begin{tabular}{c c} \hline \hline LOA & 334.5 m \\ \hline Breadth & 45.6 m \\ \hline Depth & 24.4 m \\ \hline Design Draft & 14.0 m \\ \hline Gross Tonnage & 97,000 ton \\ \hline Max. service speed & 24.5 knot \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main specifications of the container ship used in this study. \begin{table}
\begin{tabular}{c c} \hline \hline
**DFP/DFS** & Deck at fore port/starboard \\ \hline
**BFP/BFS** & Lower longitudinal bulkhead at fore port/starboard \\ \hline
**DMP/DMS** & Deck at midship port/starboard \\ \hline
**BMP/BMS** & Lower longitudinal bulkhead at midship port/starboard \\ \hline
**DAP/DAS** & Deck at aft port/starboard \\ \hline
**BAP/BAS** & Lower longitudinal bulkhead at aft port/starboard \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Location details of each strain sensor. Figure 1: Stress measurement points (orange and blue circles are measurement points). (**a**) Top view and side view, (**b**) sectional view of the starboard side at the midship. \(\sigma_{r,1/1000}\): 1/1000 maximum expected value of raw data of the stress time series \(\sigma_{w,1/1000}\): 1/1000 maximum expected value of the wave response component \(\sigma_{r,1/1000}\) and \(\sigma_{w,1/1000}\) are calculated in accordance with the flow chart shown in Figure 2. Each step of the flowchart is explained as follows:  
1. Time-series stress data measured at the four corners of the midship are prepared. An example of the time-series data is shown at the top of Figure 2.
2. The time-series data is decomposed into four components: vertical bending, horizontal bending, torsion, and axial force. An example of the decomposed time-series data is shown in Figure 3.
3. From the four time-series stress data obtained, a low-frequency component, less than 0.01 Hz, and a high-frequency component, greater than 2.0 Hz, are removed by a band-path filter to remove the mean value drift and noise. The obtained time-series stress data, including the frequency range of 0.01-2.0 Hz, are used as the raw data. Then, a low-pass filter is applied to the raw data with a cutoff frequency of 0.3 Hz to obtain the wave response component. An example time series of the raw data and the extracted wave component are included in Figure 4 to show how the low-frequency component is decomposed from the raw data. 4. For the obtained wave response component, the zero up-crossing period is determined using the zero up-cross method, and the peak value, \(\sigma_{w,i}\), in hogging is determined for each period \(i\). The peak value of the raw data, \(\sigma_{r,i}\), is also determined for the same period obtained from the zero up-crossing of the wave response component. This procedure is illustrated in Figure 4.
5. These single-amplitude extrema, both for the wave response component and for the raw data, are statistically represented in the frequency distribution, and are approximated by the Weibull distribution. Weibull fitting is performed using the least squares method on the data of the top 20% of the single-amplitude extrema. Each curve shown in Figure 5 was obtained using the Weibull approximation. 6.