## 5 Simulation Analysis  
### Method Validation  
To validate the proposed speed-varying collision avoidance method for super-large vessels, a simulator was selected to conduct single-vessel collision avoidance experiments in this work. Speed-varying collision avoidance and steering collision avoidance were used for simulations. The data were compared and analyzed from the perspectives of CR, and changes in \(d_{CPA}\) and \(t_{CPA}\) values. According to rule 8 of COLREGS, the vessel needs to undertake substantial collision avoidance operations. After several simulator experiments, it was decided to set the steering collision avoidance angle to 30\({}^{\circ}\) in the  
Figure 4: Optimization steps of CIPSO algorithm.  
steering collision avoidance experiment, and to decelerate the ship to half of the original speed in the speed-varying collision avoidance experiment.  
Simulation parameter settings: The vessel (OS) is 290.5 m in length \(L\), 50 m in breadth \(B\), 202,000 t deadweight tonnage (DWT), heading \(C_{0}\) = 330\({}^{\circ}\), speed \(v_{0}\) = 8 knots; the target vessel (TG) is 230 m in length \(L\), 36.7 m in breadth \(B\), 83,752 t DWT, heading \(C_{1}\) = 257\({}^{\circ}\), speed \(v_{1}\) = 10 knots; TG is 3 n miles away from OS, and TG's true bearing \(T_{B}\) is 31.6\({}^{\circ}\).  
Figure 5 shows the simulation results of the speed-varying collision avoidance operation and the steering collision avoidance operation in the simulator. The green trajectory is OS decelerating to avoid TG, and the red trajectory is OS steering to avoid TG. The numbers in the figure represent different time points, where 1 is the start time, and the time interval is 2 min. In the deceleration collision avoidance operation, OS reduces from 8 knots to 4 knots at the 2 nd moment and maintains smooth sailing, and TG passes through the bow of OS at the 10 th moment and maintains a safe distance of 1 n miles. During the steering collision avoidance operation, OS starts to steer at the position of 2 n miles away from TG at the 5 th moment. Due to channel constraints, the vessel is unable to steer in narrow channels, so steering operations can only be carried out at the intersection of two channels. After several simulations, it was concluded that the steering collision avoidance operation takes 15 min, and there is a risk of touching the channel buoys. Through an analysis of the results, it was concluded that it is feasible for the super-large vessel to vary its speed to avoid collision when it faces the intersection of the vessels in the port, which can ensure the super-large vessel's safe navigation.  
Figure 6 presents the variation curve of CRI derived from the calculation. The speed-varying collision avoidance operation reduces the risk degree to 0.3 within 5 min, while the steering collision avoidance operation maintains a high-risk degree within 20 min, and OS navigation is riskier. Figure 7 shows the graphs of \(d_{CPA}\) value and \(t_{CPA}\) value changes during the two collision avoidance operations. The comparison shows that the \(d_{CPA}\) value of TG in the speed-varying collision avoidance, relative to OS, stays above 1 n miles within 20 min. In conclusion, considering the unique characteristics of port waters and the constraints of navigational channels, the findings from the simulation experiments and data analysis suggest that employing speed-varying collision avoidance holds a certain degree of rationale. This approach can serve as a valuable reference for ship navigators when operating within port environments.  
Figure 5: Simulation of the trajectory of each vessel in the experiment.