To reduce the occurrence of ship collisions, immediate danger, and close-quarters situations in narrow inland waterways, a step-by-step early warning system for ship collision-avoidance actions was developed, along with an early warning method and model of collision risk based on coordinated collision-avoidance actions. This study first analyzed the importance of coordinated collision-avoidance actions in inland waterways, and the process and key components of coordinated collision-avoidance actions were studied. Then, the early warning method of inland ship collision risk based on coordinated collision-avoidance actions was introduced; the effectiveness of the early warning method was comparatively analyzed via experimental observations. A framework of early warning model of inland ship collision risk was created based on the early warning method; a collision risk early warning model for inland ships based on coordinated collision-avoidance actions was proposed according to the relationship between the distance/time to the closest point of approach (DCPA, TCPA), coordination degree of collision-avoidance actions of the two considered ships and collision risk; moreover, the early warning model of inland ship collision risk was further considered for quantitative calculation. Finally, the application of the early warning method and model was demonstrated using a case study. The results indicate that the early warning method of inland ship collision risk based on coordinated collision-avoidance actions could effectively reduce the emergence of close-quarters situations and immediate danger, and the early warning model could quantitatively show the evolution of collision risk of two ships along with the process of coordinated collision-avoidance actions.
Some studies have estimated that 80% of maritime accidents and 86–95% of ship collisions are due to human error; thus, the quantification of the impact of human error is of great importance to shipping safety [
Statistical data show that ship collisions account for the most traffic accidents in inland waterways [
Guodao [
Wang and Fan [
Montewka et al. [
In ship collision risk early warning systems, the most commonly used methods of risk estimation are the DCPA and TCPA. When DCPA > MinDCPA and TCPA > MinTCPA, there is no risk of collision. When DCPA ≤ MinDCPA and TCPA > MinTCPA, there is a nonimminent risk of collision. Finally, when DCPA ≤ MinDCPA and 0 < TCPA ≤ MinTCPA, there is an imminent risk of collision.
Kearon [
Zhang [
Based on the literature review, the relative studies mainly focus on uncoordinated collision-avoidance actions of two ships and evaluation of ship collision risk; minimal work has been reported on early warning of inland ship collision risk based on coordinated ship-ship action.
Regarding anti-collision early warning systems for inland ships, the use of only DCPA and TCPA is not suitable for representing the conditions of inland ship navigation. Therefore, this study developed an early warning method and model of inland ship collision risk based on DCPA, TCPA, and the coordination degree of collision-avoidance actions of two ships.
Inland waterways are usually relatively narrow, with a high ship density and limited maneuvering space. For two ships to pass each other at a safe distance, collision-avoidance actions of a single ship are often insufficient. Instead, both vessels should implement coordinated anticollision actions to prevent a close-quarters situation, an imminent danger, or a collision. If the movements of the two ships are not mutually clear and their intended avoidance strategies and maneuvers are not harmonized, the ship operators might perform conflicting or counteractive avoidance actions. According to Guodao [
The number of inland ship collision accidents caused by the uncoordinated actions of two ships accounted for more than 90% of the total number of inland ship collision accidents from 2009 to 2015 in the waterway, administrated by the Changjiang Maritime Safety Administration Bureau (Figure
Statistics of inland ship collision accidents from 2009 to 2015.
With regard to the input and output factors of a coordinated collision-avoidance process, coordinated collision-avoidance requires that both ships understand each other’s movements, unify their collision-avoidance strategies, and take coordinated maneuvering actions throughout the process to ensure safe passage for both ships.
In the present study, 20 sets of avoidance actions were observed on-board inland ships in the Yangtze River of China, which were operated by skilled ship officers with Very High Frequency (VHF), radar and Automatic Identification System (AIS). The observation ships are cargo ships; their ship lengths range from 60 to 90 meters, their ship breadths range from 14 to 18 meters, and their ship tonnage ranges from 2000 to 5000 deadweight tons. The target ships are also cargo ships, and their ship lengths range from 50 to 100 meters, their ship breadths range from 14 to 20 meters, and their ship tonnage ranges from 1500 to 6000 tons. The observation process was divided into the following four stages: free navigation, collision risk, close-quarters situation, and immediate danger [
The observation data showed that during the free navigation stage, the vessel operators took actions in three sets that reflected an understanding of the other vessel’s movements. During the collision risk stage, the vessel operators took actions in 15 sets, which reflected an understanding of the other vessel’s movements; in 12 sets, the operators took actions showing that their collision-avoidance strategies were uniform; in 10 sets, the operators undertook coordinated maneuvering actions. During the close-quarters situation stage, the operators took actions in two sets, which reflected an understanding of the other vessel’s movements; in six sets, the operators took actions showing that their collision-avoidance strategies were uniform, and, in four sets, the operators took coordinated maneuvering actions. During the immediate danger stage, there was one set in which the operators were able to avoid collision through coordinated maneuvering actions.
This means that among the 20 sets of observations, the vessel operators in all sets took actions, which reflected an understanding of the other vessel’s movements. In 18 sets, the operators took actions that reflected uniform collision-avoidance strategies, and in 15 sets they took coordinated maneuvering actions (Figure
Distribution of observed coordinated collision-avoidance actions that two ships typically take in an inland waterway.
The above-mentioned observation and Figure
According to the above-mentioned observation analysis and common practice for seafarers, the entire process of coordinated collision-avoidance actions includes five elements, namely, the ships being not in sight of one another, understanding each other’s movements, unifying their collision-avoidance strategies, taking coordinated maneuvering actions, and safe passage, as well as four stages, namely, not yet understanding each other’s movements, not yet unifying collision-avoidance strategies, not yet taking coordinated maneuvering actions, and verifying the effect of their avoidance actions (Figure
Coordinated avoidance process for two ships approaching each other in an inland waterway. A: understanding each other’s movements. B: unifying collision-avoidance strategies. C: taking coordinated maneuvering actions. S1: not yet understanding each other’s movements. S2: not yet unifying collision-avoidance strategies. S3: not yet taking coordinated maneuvering actions. S4: verifying collision-avoidance effectiveness.
Coordination degree of collision-avoidance actions of two ships.
When 0 ≤ DCPA ≤ MinDCPA (the DCPA safety limit), the sooner two vessels coordinate their collision-avoidance actions, the more the collision imminence can be reduced and the more effective the early warning will be.
Figure
Coordinated avoidance actions of two ships with early warning. A: understanding each other’s movements. B: unifying collision-avoidance strategies. C: taking coordinated maneuvering actions. S1: not yet understanding each other’s movements. S2: not yet unifying collision-avoidance strategies. S3: not yet taking coordinated maneuver’s actions. S4: verifying collision-avoidance effectiveness. TCPA: time to the closest point of approach.
It is evident from Figure
The ships being not in sight of one another and safe passage, namely, the beginning and end of the entire process of coordinated collision-avoidance actions, had no effect on early warning of inland ship collision risk.
Therefore, the early warning method of the inland ship collision risk based on coordinated collision-avoidance actions was a step-by-step early warning method for ship collision-avoidance actions, along with understanding each other’s movements, unifying collision-avoidance strategies, and taking coordinated maneuvering actions. Additionally, when TCPA > MinTCPA and the two vessels have understood each other’s movements and unified their collision-avoidance strategies, alerting both ships to prepare for the coordinated maneuvering action had the greatest early warning effect and provided the best chance of avoiding a collision (Figure
Demonstration of early warning method of inland ship collision risk based on coordinated collision-avoidance actions. A: understanding each other’s movements. B: unifying collision-avoidance strategies. C: taking coordinated maneuvering actions. S1: not yet understanding each other’s movements. S2: not yet unifying collision-avoidance strategies. S3: not yet taking coordinated maneuver’s actions. S4: verifying collision-avoidance effectiveness. TCPA: time to the closest point of approach.
Process of early warning method of inland ship collision risk based on coordinated collision-avoidance actions.
Distance to the closest point of approach (DCPA) | Time to the closest point of approach (TCPA) | Coordination degree for collision-avoidance actions of two ships ( | Early warning conclusion |
---|---|---|---|
DCPA > MinDCPA | TCPA > MinTCPA | Any value | When |
DCPA ≤ MinDCPA | TCPA > MinTCPA | A collision risk exists, but it is not yet imminent; an alert is issued that the two ships have not yet understood each other’s movements | |
A collision risk exists, but it is not yet imminent; the vessels have understood each other’s movements; an alert is issued that the vessels have not unified their collision-avoidance strategies | |||
A collision risk exists, but it is not yet imminent; the vessels have understood each other’s movements and unified their collision-avoidance strategies; an alert is issued that the vessels have not yet taken coordinated maneuvering actions | |||
0 < TCPA ≤ MinTCPA | The collision risk is imminent; the vessels have understood each other’s movements, unified their collision-avoidance strategies, and taken coordinated maneuvering actions; an alert is issued that the vessels have to verify the effectiveness of their collision-avoidance actions |
In this study, a comparative experiment was designed to evaluate the effectiveness of collision risk early warning methods using DCPA, TCPA, and
Simulation experiment scenario.
A total of 30 effective simulation experiments were carried out, with each experiment divided into two groups, namely, Groups A and B. Group A used DCPA and TCPA to evaluate collision risk, whereas Group B used three parameters, namely, DCPA, TCPA, and
Comparison of two types of early warning methods.
Early stage | Early warning conclusion | Later stage | Early warning conclusion | Early warning effectiveness | |
---|---|---|---|---|---|
Group A | DCPA ≤ MinDCPA and TCPA > MinTCPA | A collision risk exists, but is not imminent | DCPA ≤ MinDCPA and 0 < TCPA ≤ MinTCPA | Imminent risk of collision exists | Ultimately, seven groups encountered close-quarters situations, and one was almost in immediate danger. |
Group B | DCPA ≤ MinDCPA TCPA > MinTCPA, | A collision risk exists, but is not imminent; an alert is issued that the two ships have not yet understood each other’s movements | Through step-by-step early warning alerts, when TCPA > MinTCPA, the vessels have understood each other’s movements and unified their avoidance strategies. Ultimately one group was almost in a close-quarters situation, but none encountered immediate danger | ||
DCPA ≤ MinDCPA TCPA > MinTCPA, | A collision risk exists, but is not imminent; the vessels have understood each other’s movements; an alert is issued that the vessels have not unified their collision-avoidance strategies | ||||
DCPA ≤ MinDCPA TCPA > MinTCPA, | A collision risk exists, but it is not imminent; the vessels have unified their collision-avoidance strategies; an alert is issued that the vessels have not yet taken coordinated maneuvering actions | ||||
DCPA ≤ MinDCPA 0 < TCPA ≤ MinTCPA, | The collision risk is imminent; the vessels have taken coordinated maneuvering actions; an alert is issued that the vessels have to verify the effectiveness of collision-avoidance actions |
Comparison of the early warning process for two ships in an inland waterway proposed in this study. A: understanding each other’s movements. B: unifying collision-avoidance strategies. C: taking coordinated maneuvering actions. S1: not yet understanding each other’s movements. S2: not yet unifying collision-avoidance strategies. S3: not yet taking coordinated maneuvering actions. S4: verifying collision-avoidance effectiveness.
Comparison of the effectiveness of an early warning system for two ships in an inland waterway proposed in this study.
The analysis shows that the use of DCPA, TCPA, and
Based on traditional collision risk estimation via DCPA and TCPA, combined with the important effect of the coordination degree of collision-avoidance actions on inland ship collision avoidance, a framework of the early warning model of inland ship collision risk based on coordinated collision-avoidance actions was established (Figure
Early warning model framework proposed for inland-waterway ships.
This study established the model using elementary functions as a result of the complexity of the research question and limited experimental conditions.
Based on the framework of early warning model of inland ship collision risk, the function format of the early warning model was proposed as follows:
Relationship between DCPA and collision risk.
Based on the above analysis, the elementary functions
Relationship between TCPA and collision risk.
Based on the above analysis, the elementary functions
Relationship between coordination degree and collision risk of two ships.
Based on the above analysis, the elementary functions
Functions of relationships between DCPA, TCPA,
Relationship | Proposed function 1 | Proposed function 2 |
---|---|---|
Relationship between DCPA and collision risk | ||
Relationship between TCPA and collision risk | ||
Relationship between |
When DCPA reaches a certain value, especially when 0 ≤ DCPA ≤ MinDCPA, the smaller the TCPA value is, the more imminent ship-ship collision becomes, the higher is the probability of ship-ship collision. So, the TCPA has the direct impact on the occurrence probability of ship-ship collision. When TCPA reaches a certain value, especially when 0 < TCPA ≤ MinTCPA, the smaller the DCPA value is, the higher the hazardous consequence of ship-ship passage is. So, the DCPA has the direct impact on the hazardous consequence of ship-ship passage. According to the general definition of risk, the risk of a dangerous event is the function of the occurrence probability of a dangerous event and the hazardous consequences of the dangerous event [
Based on the above analysis, the closest to expressing the relationships between DCPA, TCPA,
The impact of TCPA change on the risk of ship-ship collision is faster than the impact of DCPA change, so function (
Function (
Function (
Function (
The Niukou waterway of the upper Yangtze River with high vessel density was selected as a case study. The visibility and water state are good. Ship A’s length was 106 meters, and its breadth was 16 meters, navigated along the narrow waterway; ship B’s length was 92 meters, and its breadth was 16 meters, crossed the waterway so that the two ships were at a collision risk, and DCPA = 0.1 nmile (Figure
Stages of collision-avoidance in a narrow waterway of the Yangtze River. Stage one: the two vessels have not yet understood each other’s movements. Stage two: the vessels have not yet unified their collision-avoidance strategies. Stage three: the vessels have not yet taken coordinated maneuvering actions. Stage four: the vessels have to verify collision-avoidance effectiveness.
According to the actual environment and professional experiences, it was assumed that MinDCPA = 0.3 nmile, MinTCPA = 12 min,
In stage one (S1), TCPA >18 min and DCPA = 0.1 nmile, the collision risk is detected but is not imminent, and the two vessels have not yet understood each other’s movements,
On the first key point of coordinated collision-avoidance actions (A), TCPA = 18 min and DCPA = 0.1 nmile; the two vessels begin to understand each other’s movements,
In stage two (S2), 15 min < TCPA<18 min and DCPA = 0.1 nmile, the collision risk is detected but is not imminent, and the two vessels have understood each other’s movements but have not unified their collision-avoidance strategies,
On the second key point of coordinated collision-avoidance actions (B), TCPA = 15 min and DCPA = 0.1 nmile; the two vessels begin to unify their collision-avoidance strategies,
In stage three (S3), 12 min < TCPA<15 min and DCPA = 0.1 nmile, the collision risk is detected but is not imminent, and the two vessels have unified their collision-avoidance strategies, but have not taken coordinated maneuvering actions,
On the third key point of coordinated collision-avoidance actions (C), TCPA = 12 min, the two vessels begin to take coordinated maneuvering actions, and the DCPA becomes 0.3 nmile,
In stage four (S4), 0 min < TCPA<12 min, the two vessels have taken coordinated maneuvering actions, and the DCPA becomes 0.3 nmile (actually DCPA ≥ 0.3 nmile),
Through these stepwise early warning alerts based on the proposed method and model, ships A and B achieved coordinated collision avoidance, with ample time to take appropriate actions (Figure
Distribution of early warning and risk estimation of ship-ship collision. A: understanding each other’s movements. B: unifying collision-avoidance strategies. C: taking coordinated maneuvering actions. S1: not yet understanding each other’s movements. S2: not yet unifying collision-avoidance strategies. S3: not yet taking coordinated maneuvering actions. S4: verifying collision-avoidance effectiveness. TCPA: time to the closest point of approach.
Compared with traditional collision risk evaluation methods based on DCPA and TCPA, the proposed early warning method and model of ship collision risk based on coordinated collision-avoidance actions serve as a step-by-step early warning system that allows ample time for taking appropriate collision-avoidance actions. However, this early warning method and model of ship-ship collision risk for inland waterways based on coordinated collision-avoidance actions has the following shortcomings: (a) the early warning method could not be used without effective communication between two ships; (b) the early warning model only uses elementary functions to model the ship-ship collision risk, the prediction accuracy of the model is insufficient, and the prediction accuracy of the model could be enhanced using senior functions; (c) the simplification from function (
Modeling DCPA, TCPA, and
The data used in this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
This work was supported by the China Postdoctoral Science Foundation (Grant no. 2016M592889XB), the Science and Technology Research Program of the Chongqing Education Commission (Grant no. KJ1500519), and the Hubei Provincial Key Laboratory of Inland Navigation Technology (Grant no. NHHY2015001).