A Method for Estimating Dynamic Collision Risk of Vessels Considering Spatial-temporal Adjacency
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摘要: 为解决传统船舶碰撞风险计算方法在繁忙受限水域的应用局限性问题，运用突变理论提出了1种考虑时空紧迫度的船舶碰撞风险计算方法。根据2船实际船舶领域叠加区域数值和2船同方位发生碰撞时的船舶领域叠加区域数值，建立船舶碰撞空间紧迫度计算模型；基于2船相对位置和相对速度的矢量关系，建立船舶碰撞时间紧迫度计算模型。在此基础上，运用突变理论建立了考虑时空紧迫度的船舶碰撞风险计算模型。通过模拟仿真实验，将该模型与最小会遇距离（DCPA）和最小会遇时间（TCPA）及基于时空距离的碰撞风险评估模型进行了对比分析。实验结果表明：提出的船舶动态风险计算模型在复杂受限水域中能反映船舶碰撞风险变化量，且碰撞风险变化幅度较小，克服了DCPA、TCPA以及基于时空距离的碰撞风险评估模型在复杂受限水域中非线性描述风险变化的不足，可为船舶避碰决策提供参考。Abstract: The catastrophe theory is used to propose a vessel collision risk calculation method considering spatial- temporal urgency to solve the limited applications of traditional risk-calculation methods in terms of ship collision in busy restricted waters. A model to calculate spatial urgency of vessel collision is proposed based on the numerical calculation of the superimposed area of the vessel domain. Then a model to calculate temporal urgency of vessel collision is also proposed considering vector relationships between relative position and relative speed of ships. Moreover, based on the catastrophe theory, a model to calculate collision risk of vessels is proposed, reflecting spatial-temporal urgency. The proposed models are validated by simulations, and compared with the models considering distance to the closest point of approach(DCPA), time to the closest point of approach(TCPA), and spatio- temporal distance-based collision risk assessment. The results show that the proposed vessel dynamic risk model in this work is more accurate in judging the collision risk, associated with the reflection of decreased changes in collision risk. This improvement avoids the drawback of a lacking description of nonlinear risk changes by other methods. The proposed model provides mariners with an accurate means to make decisions of vessel collision avoidance.
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Key words:
- traffic safety /
- vessels /
- collision risk /
- catastrophe theory /
- vessel domain /
- spatial-temporal urgency
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图 1 船舶碰撞风险计算建模流程
Figure 1. Modeling process on the calculation of vessel collision risk
图 5 船A与船B，C，D的多船碰撞风险
Figure 5. Multi-vessel collision risk among vessel A and vessels B, C, and D
图 6 船A与船B，C，D的基于时空距离的碰撞风险
Figure 6. Spatio-temporal distance-based collision risk among vessel A and vessels B, C, and D
表 1 船舶领域层级边界尺度及权重赋值
Table 1. Boundary scale and weight assignment of vessel level domain
船舶领域层级 船舶领域层级边界尺度 权重赋值μi 长轴/m 短轴/m Ⅰ 2L 0.32L+0.8B 16 Ⅱ 3L 0.64L+0.6B 8 Ⅲ 4L 0.96L+0.4B 4 Ⅳ 5L 1.28L+0.2B 2 Ⅴ 6L 1.6L 1 注：L为船长（m），B为船宽（m）。 
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表 2 船舶领域叠加层级权重赋值
Table 2. Weight assignment on overlap of vessel level domain
船舶领域叠加层级 船舶领域叠加层级权重赋值μij Ⅰ-Ⅰ 32 Ⅰ-Ⅱ/Ⅱ-Ⅰ 24 Ⅰ-Ⅲ/Ⅲ-Ⅰ 20 Ⅰ-Ⅳ/Ⅳ-Ⅰ 18 Ⅰ-Ⅴ/Ⅴ-Ⅰ 17 Ⅱ-Ⅱ 16 Ⅱ-Ⅲ/Ⅲ-Ⅱ 12 Ⅱ-Ⅳ/Ⅳ-Ⅱ 10 Ⅱ-Ⅴ/Ⅴ-Ⅱ 9 Ⅲ-Ⅲ 8 Ⅲ-Ⅳ/Ⅳ-Ⅲ 6 Ⅲ-Ⅴ/Ⅴ-Ⅲ 5 Ⅳ-Ⅳ 4 Ⅳ-Ⅴ/Ⅴ-Ⅳ 3 Ⅴ-Ⅴ 2
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表 3 实验船舶数据表
Table 3. Experimental data of vessels
船舶 船长/m 船宽/m 航速/kn 航向/（°） 船首向/（°） 纬度距离/m 经度距离/m 船A 189 28 8 090 090 船B 250 34 12 090 093 200 1 000 船C 250 34 12 270 267 200 2 000 船D 250 34 12 000 002 2 639.445 2 000
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表 4 3种风险计算方法结果对比
Table 4. Comparison of the results of three risk-calculation methods
实验方法 风险要素 船A-B 船A-C 船A-D 碰撞动态风险计算模型 最大风险时刻T/s 425 190 440 最大风险值Rmax 0.755 0.781 0.968 基于CPA的碰撞风险判断法 TCPA为零时刻/s 485.96 194.37 445.50 DCPA /m 200 200 200 基于时空距离的碰撞风险评估模型 最大风险时刻T'/s 485.00 195.00 445.00 最大风险值rmax 0.52 0.52 0.89
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