# Research on Collision Warning Method for Ship-Bridge Based on Safety Potential Field
## 3 Establishment of Safety Potential Field Model in Bridge Area
### Channel Boundary Potential Field  
In inland waterway navigation, the boundary limits imposed by the bank and navigational marking facilities have a higher restraining effect on passing ships compared with the static potential energy field and are intended to warn passing ships of deviations from their normal travelling position and to prevent them from running aground or touching the bank wall. A threshold range for the boundary potential energy field is set to ensure that the ship can navigate within a safe distance. To simplify the representation, the channel can be abstracted as a uniformly extended straight line, with the coordinate axis x direction aligned with the travelling direction of the ship in the channel and the coordinate axis y direction perpendicular to it. Let the target ship A be located at \((x_{i},y_{i})\), \(E_{R1}\) denotes the field strength from the bank wall of the channel and \(E_{R2}\) denotes the field strength from the navigational beacon. The boundary field \(E_{R}\), considering the bank wall on both sides of the channel, is thus defined as follows:  
\[E_{R}=E_{R1}+E_{R2} \tag{7}\]  
Of these, the safety potential field effect of the channel bank wall on the ship is as follows:  
\[E_{R1}=\sum_{j=1}^{2}\mu_{1}exp\left[\left(\frac{1}{|r_{aj}|}\right)^{b}\right] \tag{8}\]  
Of these, the influence of the navigational markers on the safety potential field of the ship is as follows:  
\[E_{R2}=\sum_{i=1}^{2}\mu_{2}exp\left[\left(\frac{1}{|r_{bi}|}\right)^{b}\right] \tag{9}\]  
In the formula, \(\mu_{1}\) and \(\mu_{2}\) are the coefficients of determination for the boundary field of the channel and the navigational marker, respectively; \(r_{aj}\) indicates the vector distance of the target ship A from the shore wall on both sides of the channel, and the lengths are \(r_{a1}\) and \(r_{a2}\); \(r_{bj}\) indicates the vector distance of the target ship \(A\) from the navigational mark on both sides, and the lengths are \(r_{b1}\) and \(r_{b2}\), with the different distances causing a change in the strength of the boundary field; \(b\) is the trend of the gradient of the negative correlation of the distance. That is, the closer the ship is to the shore wall and the navigational markers on both sides of the channel, the larger the boundary field is, and the higher the degree of danger; the specific values of \(r_{aj}\) and \(r_{bj}\) can be obtained from the respective and following provisions of the _Navigation Standard of Inland Waterway:  
Figure 3: Schematic diagram of the kinetic energy field strength of the dynamic object marker.  
1. The safety distance from the outboard side of the cargo ship to the edge of the fairway may be taken as 0.34-0.40 times the width of the track zone, and the safety distance between the outboard side of the ship and the embankment of the fairway, as follows: \[r_{aj}=\gamma_{1}\times(B_{s}+L\cdot\sin\alpha)(0.34<\gamma_{1}<0.40)\] (10)
2. Safe distance between the ship's outboard side and the navigational markers, as follows: \[r_{bj}=1.0\times B_{s}\] (11)
3. The boundary field schematic, which is shown in Figure 4.