## 2 Materials and Methods
### Single Factor Influence Analysis of Ship Resistance  
Ship resistance is one of the main factors affecting the marine navigation state, which has a great impact on the ship's power type selection, the overall hull design, route adjustment, ship attitude correction, and cargo loading, so it is very necessary to study the ship's navigation resistance. Based on this, the resistance test of the ship model under four working conditions was carried out to analyze the law of the change in ship resistance by means of experimental research in this paper. Figure 2 shows the relationship between ship resistance and speed under four working conditions, respectively. According to the preliminary analysis of the data, the change rule of the data is in accordance with the exponential function. The data fitting method based on exponential function is as follows:  
\[y=ae^{bx} \tag{5}\]  
where \(y\) is the dependent variable, \(x\) is the independent variable, and a and b are the coefficients. Taking the logarithm of both sides, Equation (6) becomes as follows:  
\[\ln y=\ln a+bx \tag{6}\]  
Equation (7) is transformed into the following:  
\[Y=A+bx \tag{7}\]  
Equation (8) is calculated as follows:  
\[\left\{\begin{aligned} b=\frac{\sum xY-n\overline{i}\overline{Y}}{ \sum t^{2}-n\overline{t}^{2}}\\ A=\overline{Y}-b\overline{t}\end{aligned}\right. \tag{8}\]  
Figure 2: The variation trend between speed and ship resistance under four working conditions.  
The fitting coefficients \(R^{2}\) are calculated as follows  
\[R^{2}=\frac{\sum\left(\hat{y}_{i}-\overline{y}_{i}\right)^{2}}{\sum\left(y_{i}- \overline{y}_{i}\right)^{2}} \tag{9}\]  
where \(\hat{y}_{i}\) is the predicted value of the fitted function and \(y_{i}\) is the experimental true value. According to the results of the resistance test, there is an obvious positive correlation between the ship resistance and its speed. With the increase in speed, the resistance of the ship increases continuously, which conforms to the change law of the exponential equation. According to the change trend of resistance, it can be seen that the increase degree in ship resistance also gradually increases with the increase in speed, which indicates that the speed has a great influence on the ship's resistance. The data analysis results also show that the ship resistance corresponding to the condition of being fully loaded is the greatest and the ship resistance corresponding to the condition of being lightly loaded is the lowest when the speed is constant.  
In the process of this experimental test, the maximum resistances corresponding to the four working conditions of lightly loaded without appendages, lightly loaded with appendages, fully loaded without appendages, and fully loaded with appendages are 65.72 N, 66.87 N, 69.59 N, and 70.14 N, respectively, when the ship model speed is at its maximum (2.06 m/s). As shown in Figure 3, the resistance of ships increases by 0.8% from fully loaded without appendages to fully loaded with appendages, and it increases by 1.8% from lightly loaded without appendages to lightly loaded with appendages. Therefore, it can be inferred that the influence of appendages on the resistance of ships under the condition of being fully loaded is less than that under the condition of being lightly loaded. According to the above analysis results, it can be seen that the ship speed, displacement, and appendages can all have an impact on the ship's resistance, among which speed is the most important factor, and the displacement has a greater impact than the ship appendages.