Article(id=1240656101541203998, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240656096998773667, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1000-4653.2025.01.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1701100800000, receivedDateStr=2023-11-28, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773725064882, onlineDateStr=2026-03-17, pubDate=1742832000000, pubDateStr=2025-03-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773725064882, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773725064882, creator=13701087609, updateTime=1773725064882, updator=13701087609, issue=Issue{id=1240656096998773667, tenantId=1146029695717560320, journalId=1240618002186551303, year='2025', volume='48', issue='1', pageStart='1', pageEnd='198', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773725063800, creator=13701087609, updateTime=1773725118083, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240656324749480238, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240656096998773667, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240656324749480239, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240656096998773667, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=60, endPage=68, ext={EN=ArticleExt(id=1240656101750919208, articleId=1240656101541203998, tenantId=1146029695717560320, journalId=1240618002186551303, language=EN, title=A study of mathematical modeling of close-quarter situation distance and collision distance in altering course collision avoidance, columnId=1240655017900823355, journalTitle=Navigation of China, columnName=Marine Traffic Safety, runingTitle=null, highlight=null, articleAbstract=

In order to solve the key problem of collision avoidance action of close ships, the steering avoidance process during collision encounter is studied, combining with the ship's maneuvering performance, the time characteristics of the ship's initial turning semicircle elements and turning angle are analyzed; through the decomposition of the relative motion diagram and the inverse approximation algorithm, the mathematical model of the close-quarter situation distance and collision distance is obtained when the ship is steering avoidance. The application of the model is also given; the results of the model application are verified by arithmetic examples and simulation tests. The results show that the proposed two distance models can be used to guide the collision avoidance actions of ships at close range, and provide a theoretical basis for the study of collision risk and the establishment of an automatic collision avoidance decision-making system for ships. At the same time, according to the model, the collision avoidance actions that should be taken by the ship at different stages of the encounter are analyzed for the target ships with different speed ratios and different bearings when there is a collision danger, and the close-range ship collision avoidance action mode is also given. It also gives the model of close-range ship collision avoidance action. It provides the ship deck officers with the support of close-range ship collision danger prediction and ship collision avoidance decision-making. The research results are of great significance to ship navigation safety and navigation intelligence.

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为解决近距离船舶避碰行动的关键问题，研究船舶碰撞会遇过程中转向避让过程，结合船舶的操纵性能，对船舶初始旋回半圆要素以及旋回角度的时间特性进行分析；通过相对运动图的分解和逆向逼近算法，得到船舶转向避让时紧迫局面距离和碰撞距离的数学模型，并且给出该模型的应用；模型应用的结果通过算例和模拟试验得到验证。研究结果表明：提出的两个距离模型可用来指导近距离时船舶避碰行动，为研究船舶碰撞危险度和建立船舶自动避碰决策系统提供理论依据。同时，根据该模型，分析对于不同船速比和不同方位的目标船，存在碰撞危险时，本船在不同的会遇阶段应该采取相应的避碰行动，也给出了近距离船舶避碰行动模式。为船舶驾驶员提供近距离船舶碰撞危险预测和船舶避碰决策支持。研究成果对船舶航行安全和航行智能化具有重要意义。

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毕修颖（1965—），男，船长，教授，博士，研究方向为航海技术、船舶安全。E-mail: 122020827534@qq.com

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毕修颖（1965—），男，船长，教授，博士，研究方向为航海技术、船舶安全。E-mail: 122020827534@qq.com

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