## 5 Analysis and Discussion  
### Results and Discussion  
The core algorithm for avoiding collisions, which combines the improved MMG and VO algorithms, was proposed in the preceding section. Two groups of case studies are offered to demonstrate the effectiveness of the basic algorithm in various encounter circumstances in this paper. The results and discussion are as follows.  
In the situation of a multi-vessel encounter, the ship's avoidance action should not only evaluate the vessels with whom the ship is at risk of collision with, but should also take into account whether this action will generate a new danger of collision with other TS. In Scenario 1, the action taken by OS to avoid collision with TS\({}_{1}\), TS\({}_{2}\), and TS\({}_{3}\), will impede the safe movement of TS\({}_{4}\); In Scenario 2, when taking measures to present the TS in danger, the ships must take into account the TS\({}_{3}\), although the risk of collision does not exist.  
In some circumstances, changing speed can successfully lessen the amplitude of the alternation of course, which is highly advantageous for confined seas. In Scenario 1, only three decisions by altering course to the starboard side to avoid collision for all the TSs, and the minimum degree (41\({}^{\circ}\)) in the manner of only altering course are greater than the minimum degree (37\({}^{\circ}\)) in the manner of both alterations of course and speed. However, in Scenario 2, only altering course is the optimal decision for collision avoidance. Thus, alternation of speed is a benefit for collision avoidance in some special circumstances.  
The dynamic feasible manoeuvring interval is shown in Figure 12 The outcome demonstrates that decision-making at distinct telegraphs may be used to avoid collision in common scenarios. The evaluation function is used to determine the optimal decision based on timeliness and economy. From Figures 13b and 15b, the relative distance between OS and TS shows that TS is not invaded its ship domain.  
In all case investigations, the minimum distance between OS and TS at various decision-making points is more than \(2(L_{1}+L_{2})\), indicating that TS does not invade OSship domain. Furthermore, the resulting DCPA is significantly bigger than the safety threshold. In light of the aforementioned case studies, it is apparent that the presented collision avoidance algorithm is highly adaptable and credible in dealing with ship collision risk in a variety of typical encounter situations. Moreover, changing the speed of the telegraph can be suitable for the most complicated situation. As a result, the fundamental algorithm is very advantageous for the ship in confined waters.  
The main contributions of this paper are drawn in two aspects based on simulation results: On the one hand, the improved MMG is more feasible and valuable when considering the influence of ship manoeuvrability by changing speed. On the other hand, an intelligent collision avoidance model for ships is provided based on the IVO algorithm and improved MMG. In this paper, the decision-making including altering course and changing  
Figure 15: Simulation results of scenario 2: (**a**) Trajectory of OS and TSs; (**b**) Distance between OS and different TSs; (**c**) DCPA between OS and different TSs; (**d**) Speed of OS.  
speed takes into account COLREGs, ship manoeuvrability, and sea practice, which are reliable and useful for collision avoidance in multi-ship collision.