## 5 Results
### The Effect of Directions of Waves on the Salvage System
#### 5.2.1 The Effect of Directions of Waves on the Ship's Motion Response
Figure 13 displays each DOF's safety scores under waves from different directions, while Figure 14 represents the total safety score of the 6 DOFs under waves from different directions. The numerical simulations in this paper investigate wave behavior from 90\({}^{\circ}\) to 180\({}^{\circ}\). Drawing upon the research conducted by [PERSON] [33], the arrangement of the salvage system exhibits a symmetrical configuration. As a result, the analysis encompassing the quadrant ranging from 90\({}^{\circ}\) to 180\({}^{\circ}\) can be extrapolated to the remaining three quadrants, considering both the symmetry inherent in the salvage system and the optimization of computational resources. Different score thresholds are set for the scores of various DOFs and the total score of the 6 DOFs. These thresholds are depicted in Figures 12 and 13. For each degree of freedom (DOF), the Safety and Stability scores of the thresholds are set at 11 points, referring to the sum of \(SA_{a}\), \(SA_{b}\), \(SA_{c}\), \(ST_{a}\), \(ST_{b}\), and \(ST_{c}\) in Formula (11). In Formula (11), \(RAN_{i}\) refers to the ranking score. Under different working conditions, the highest-ranking score receives 5 points, the lowest-ranking score receives 1 point, and the middlemost-ranking score is 3 points. The value of 3 points corresponds to the threshold of \(RAN_{i}\) in Formula (11). Each \(RAN_{i}\) has a threshold of 3 points, which means that \(RAN_{i}/6\) is also 3 points. Therefore, the score threshold for a single DOF, without considering weight multiplication, is 33 points. In Table 5, the weights assigned to the 6 DOFs are 1.5, 1.25, 1.25, 1, 1, and 1. After accounting for these weights, the score thresholds for the 6 DOFs become 49.5, 41.25, 41.25, 33, 33, and 33 points. Figure 13: _Cont._  
Figure 14: Total scores of Safety and Stability of 6 DOFs under the action of waves in different directions. Figure 13: Scores of SDOF under the action of waves in different directions: (**a**) Roll; (**b**) Pitch; (**c**) Yaw; (**d**) Surge; (**e**) Sway; (**f**) Heave. Consequently, based on the Formula (12) information, the total score threshold for the 6 DOFs is 231 points. All the thresholds are indicated by red dotted lines in the figures. In Figure 12, areas exceeding the thresholds are depicted in gray, while light green represents areas within the thresholds. In Figure 13, areas surpassing the thresholds are displayed in red, while dark green indicates areas within the thresholds. An examination of Figure 13 indicates that the roll response achieves its highest score under waves from the 90\({}^{\circ}\) and 270\({}^{\circ}\) directions and reaches 97.5 points, which significantly surpasses the score threshold. In contrast, the lowest score occurs under waves from the 180\({}^{\circ}\) and 0\({}^{\circ}\) directions, registering only 18 points, which is well below the score threshold. However, the situation differs for the pitch responses. The lowest score is recorded under waves from the 90\({}^{\circ}\) and 270\({}^{\circ}\) directions, totaling only 16.88 points, which is significantly below the score threshold. Conversely, the highest score is observed under waves from the 180\({}^{\circ}\) and 0\({}^{\circ}\) directions, amounting to 67.71 points, which is well above the score threshold. Although the results for roll and pitch responses under varying wave directions differ substantially, the yaw response remains safe in almost all directions. Regarding the surge response, safety is demonstrated for wave intervals of (45\({}^{\circ}\), 135\({}^{\circ}\)) and (225\({}^{\circ}\), 315\({}^{\circ}\)). The adjacent regions of 0\({}^{\circ}\) and 180\({}^{\circ}\) also show safety for the sway response, though within a narrow range. Regarding the heave response, apart from the adjacent 90\({}^{\circ}\) and 180\({}^{\circ}\) areas, waves in other intervals mostly satisfy safety criteria.