论文总字数：20678字

摘 要

在非航海类专业人员眼中看来，在船舶会遇局面中，最直观的表现为两船相对距离和相对速度的改变。本文考虑的核心即如何实现基于相对速度和相对距离的船舶碰撞风险建模。同理，对于值班驾驶员来说其值班监控的初始视觉感知亦为相对速度、相对距离的变化，其次才能考虑诸如DCPA 、TCPA等的船舶驾驶专业领域计算术语的分析。因此如何基于人体视觉感知对船舶间相对距离和相对速度进行准确描述，将直接与碰撞风险紧密连接。相对于欧几里得空间直角坐标系而言，非欧几里得空间黎曼球面的视觉投影更符合人类视网膜投影成像，因此本文的重点为借助非欧空间黎曼球面对船舶间会遇局面下相对距离和相对速度进行投影研究，并构建基于非欧空间投影变换的船舶会遇视觉风险感知模型。

本文首先研究了传统二维平面上的船舶会遇过程中的主要风险要素的选取和分步求取过程，并借此构建出平面视觉风险模型；其次通过对非欧空间黎曼球面的引入，将原本基于二维平面上来船的运动轨迹点投影变换到所引入的黎曼球面上，转变为在其上的曲线运动，并对其投影点做具体的分析以求出与平面中相对应的风险要素并同样借此构建出球面视觉风险模型；最后可视化分析并比较这两个模型的风险评价表现。

研究结果表明：在船舶会遇过程中，若船舶间保速保向运动，基于非欧空间船舶会遇视觉风险模型的船舶间相对距离持续降低，其倒数不断增大；相对速度在船舶侵入各自碰撞领域前不断增大。其相对速度变化过程与欧几里得空间三维直角坐标下船舶间相对速度变化趋势存在显著差异。因此对非欧空间投影变换的相对距离和相对速度进行量化，以此来构建船舶会遇视觉风险感知模型更符合人类视觉感知。

关键词：非欧空间 投影变换 避碰模型 风险感知

Abstract

In the eyes of non navigational professionals, the most intuitive performance in the situation of ship encounter is the change of the relative distance and speed of the two ships. The core of this paper is how to realize the risk modeling of ship collision based on relative velocity and relative distance. In the same way, the initial visual perception of on duty monitoring is also the change of relative speed and relative distance, and then the analysis of calculation terms in ship driving field such as DCPA and TCPA can be considered. Therefore, how to accurately describe the relative distance and speed between ships based on human visual perception will be directly connected with the collision risk. Compared with Euclidean space rectangular coordinate system, the vision projection of non Euclidean space Riemannian sphere is more in line with the human retinal projection imaging. Therefore, the focus of this paper is to use the non Euclidean space Riemannian sphere to study the relative distance and relative speed of ships in the encounter situation, and to build a visual risk perception model based on non Euclidean space projection transformation.

Firstly, this paper studies the selection and step-by-step process of the main risk factors in the process of ship encounter in the traditional two-dimensional plane, and then constructs the plane visual risk model; secondly, by introducing the Riemannian sphere in the non European space, the projection of the motion locus points of the ship based on the two-dimensional plane is transformed to the Riemannian sphere, and the curve motion on it is transformed And make a concrete analysis of its projection points to find out the corresponding risk elements in the plane and build a spherical visual risk model; finally, visual analysis and comparison of the performance of risk evaluation of these two models.

The results show that: in the process of ship encounter, if the ships move in the same speed and direction, the relative distance between the ships based on the visual risk model of non European space ships encounter will continue to decrease, and its reciprocal will continue to increase; the relative speed will continue to increase before the ships invade their respective collision fields. There is a significant difference between the change process of relative velocity and the change trend of relative velocity between ships in Euclidean space. Therefore, it is more suitable for human visual perception to quantify the relative distance and relative speed of non Euclidean space projection transformation, so as to build a visual risk perception model of ship encounter.

Key Words：Non-Euclidean Space Projective transformation Collision avoidance model Risk Perception

目 录

摘 要 I

Abstract II

第一章 绪论 1

1.1 航运业务的发展现状与船舶避碰的客观需求 1

1.2 其他研究的缺陷与不足 2

1.3 基于非欧空间的投影变换如何解决问题 2

1.3.1 研究的技术路线 3

第二章 基于欧式几何的船舶会遇分析 4

2.1 欧式空间中船舶会遇的模型 4

2.1.1 船舶会遇模型的理论基础 4

2.1.2 传统模式下对船舶会遇情况的构建 4

2.2 两船舶间的相对距离S 5

2.2.1 两会遇船舶间相对距离S的定义 5

2.2.2 相对距离S的计算求取过程 6

2.2.3 MATLAB对S相关的函数可视化绘图分析 6

2.3 两会遇船舶间的相对速度 7

2.3.1 本研究中对两会遇船舶间相对速度的定义 7

2.3.2 相对速度的计算求取过程 7

2.3.3 MATLAB对相关的函数可视化绘图 9

2.4 试建立碰撞风险模型 9

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