# Research on Collision Warning Method for Ship-Bridge Based on Safety Potential Field
## 3 Establishment of Safety Potential Field Model in Bridge Area
### Dynamic Ship Kinetic Energy Field  
In navigating in the bridge area, vessels must maintain the correct vessel position and safe speed to avoid collision with static elements, such as bridge piers. The range and size of the kinetic energy field mainly depend on the motion state of the ship, including the ship speed and turning rate, as well as the nature and distance of the ship. In order to accurately assess the potential hazards of a moving ship, a Gaussian function is used to simulate the kinetic energy field in this study. The kinetic energy field includes not only the kinetic energy of the ship, but also takes into account the effects of its position and speed changes on the environment. The energy field formed by these factors may pose a potential collision threat to the surrounding static structures. Specifically, the mathematical expression for the strength of the kinetic energy field is as follows:  
\[E_{Di}=\begin{cases}\tau\cdot\exp(\frac{(v_{balance}-\mu)^{2}}{2\sigma^{2}}) \cdot g(\theta,d_{1},d_{2})\cdot v_{kalman}&v_{kalman}\in\mu\\ K&v_{kalman}\
otin\mu\end{cases} \tag{5}\]  
where \(E_{Di}\) denotes the strength of the kinetic energy vector field at the angle \(\theta\) relative to the bridge axis that is normal for the velocity, \(v_{kalman}\), predicted by the Kalman filter after considering the effect of the wind flow; \(\tau\) is a coefficient to be determined for adjusting the overall strength of the kinetic energy field; and \(\mu\) denotes the restricted ship speed in bridge-area waters, which is based on the AIS data of the ships in the vicinity of the Baijusi Bridge after the analysis, which is set to 6-15 knots in this study; \(\sigma\) denotes the standard deviation of the velocity distribution; \(v_{kalman}\) is the predicted vessel velocity in the bridge area; K is a large constant used to denote the sudden increase in field strength when the velocity exceeds the safe range; the \(g(\theta,d_{1},d_{2})\) term reflects the effect of the relative angle between the vessel and the direction normal to the axis of the bridge abutment as well as the vessel's distance from the abutment, which are explained in the following Equation (6):  
\[g(\theta,d_{1},d_{2})=\begin{cases}0.5\cdot(1+\cos(\theta))&\theta=0\ and\ d_{1},d_{2}>\Delta\\ 2\cdot(1+\cos(\theta))&\theta=0\ and\ \min(d_{1},d_{2})<\Delta\\ 1+\cos(\theta)&\text{else}\end{cases} \tag{6}\]  
where \(d_{1},d_{2}\) denote the distance of the ship from the two bridge abutments and \(\Delta\) is the threshold value of the ship's distance from the bridge abutments set according to the _Navigation Standard of Inland Waterway_.  
By quantifying the potential collision hazard to the static elements in the bridge area when the ship changes its speed and direction due to wind currents and other factors, the hazard can be assessed more accurately. The kinetic energy field of a dynamic ship, for example, is shown in Figure 2(a), which displays the effect of speed and angle on the kinetic  
Figure 2: Example of static element potential energy field intensity.  
energy field, and Figure 3b, which displays the strength of the potential field of the ship in a certain area.