# Research on Collision Warning Method for Ship-Bridge Based on Safety Potential Field
## 3 Establishment of Safety Potential Field Model in Bridge Area  
### Static Elemental Potential Energy Field  
According to the _Navigation Standard of Inland Waterway_, vessels are required to maintain a certain safety distance when passing through bridge areas in order to avoid a collision with bridge piers and other structures. Therefore, a certain range around bridge piers and other static objects is regarded as an inaccessible area for ships. In order to effectively manage this distance and dynamically assess the interactions between ships and static elements, the concept of the potential energy field is introduced to predict and avoid collision hazards by simulating the distance changes between ships and static objects. Due to the importance of bridge piers for ship-bridge collision avoidance, this section takes bridge piers as an example by which to introduce the potential energy field. Bridge piers are important structures in the navigation channel, and their physical properties naturally form a fixed static potential energy field. The strength and magnitude of a bridge abutment's potential energy field depends on its properties, including size, structural strength, and location in the water. The potential energy field of each abutment can be considered an independently existing virtual force field with specific spatial distribution properties. The centre of these potential energy fields is usually located at the geometric centre of the bridge abutment and their influence decreases with increasing distance from the centre. The safety of the waters in the bridge area is jointly determined by a variety of static elements in the channel, among which the bridge piers play a central role in ensuring safety. In addition, other static elements in the bridge area, such as bridge abutments and stationary ships, generate their own potential energy fields. The potential energy fields of these elements, together with those of the bridge abutments, form an integrated safety zone network, providing multiple guarantees for navigation safety. To quantitatively  
Figure 1: Safety potential field model-based ship-bridge collision warning framework. describe the potential energy fields of the static elements in the bridge area, the following mathematical model can be used:  
\[E_{Si}(x,y)=k_{i}\cdot\left(\frac{d_{i}}{\left|\overrightarrow{r_{d}}\right|} \right)^{n} \tag{1}\]  
where \(E_{Si}(x,y)\) denotes the magnitude of the field strength of static element \(i\) at any coordinate position \((x_{i},y_{i})\) in the channel area, with the direction of the field strength coinciding with the direction of the vector, as denoted by \(r_{d}\); \(d_{i}\) is the reference size of static element \(i\); \(n\) is a positive integer denoting the variation of the potential field strength with distance power; and \(k_{i}\) is a constant related to the properties of the static element \(i\) (e.g., size, type, etc.). The specific determination is shown in the following equation:  
\[k_{i}=S\cdot S_{i}^{\alpha}\cdot T_{i}^{\beta}\cdot I_{i}^{\gamma} \tag{2}\]  
where \(S\) is a normalization constant used to ensure that the dimensions and range of values of \(k_{i}\) are appropriate, \(S_{i}^{\alpha}\) denotes the dimensions of static element \(i\), such as radius or cross-sectional area; \(T_{i}^{\beta}\) denotes the type of static element i, which can be expressed as a categorical variable, with different types of static elements having different values of \(T_{i}\); \(I_{i}^{\gamma}\) denotes the structural strength of static element \(i\), or an indicator of the potential impact of the static element; and \(\alpha\), \(\beta\) and \(\gamma\) are indices which are used to indicate the relative importance of each attribute in terms of its impact on \(k_{i}\).