空间曲线不变量约束下的公路几何线形三维设计理论与方法

发布时间：2018-03-23 03:32

本文选题：公路三维线形设计　切入点：道路安全性　出处：《华南理工大学》2015年博士论文　论文类型：学位论文

【摘要】：公路线形设计作为公路建设的重要环节,其设计合理与否不仅关系到公路建设项目的质量好坏、投资成本,更直接影响到公路运行安全和行车舒适。受计算机技术发展的限制和公路线形三维解析模型复杂性的影响,现行线形设计方法通常将公路中心线投影到二维平面上分别进行设计,然后通过平、纵线形组合得到三维线形。这种人为拆分和组合式的设计方法忽略了平、纵设计要素之间的交互和耦合作用,使得线形设计的质量很大程度上取决于设计人员的相关经验,使得一些设计缺陷和疏漏被直接带到后期运营中,易引发交通事故。为了明确传统公路平、纵分离设计思想存在的不足并改善线形设计质量和安全性水平,本文从公路三维线形本质出发,依据微分几何曲线论,采用曲率和挠率这两个指标对空间曲线的几何特性进行描述,曲率、挠率作为空间曲线的内在几何不变量,可以完全确定曲线的几何形状。并建立了现行二维设计指标与新的三维线形指标曲率、挠率之间的关系模型以便从三维角度对现行平纵组合线形的空间几何特性进行分析。在上述研究的基础上,提出以弧长为参数、曲率和挠率为线形的控制指标,以几何连续性、车辆稳定性和行车舒适性为基本的工程约束条件,建立了新的公路三维线形设计方法和设计框架。本文就公路三维线形控制指标的约束条件和三维线形模型的构建等问题进行了详细的研究,主要研究内容和创新性成果如下:(1)线形连续性是曲线光滑程度的描述,也是线形设计的一项基本要求。本文提出采用几何连续性方法对组合曲线的连续性进行客观描述和分析,空间曲线在连接点处的几何连续性主要由曲线的切矢量、曲率、挠率和Frenet标架的连续性来决定。采用相邻路段曲率差和挠率差这两个指标来量化组合线形曲率和挠率的突变量大小,利用SPSS分别建立了高速公路和双车道公路相邻路段曲率差、挠率差与事故率之间的关系模型以及连续性评价标准。研究结果表明:公路线形设计时平纵线形的叠加并不能保证组合线形在三维空间中的连续性,当二维线形要素变化时,空间曲线的几何连续性会存在不同程度地衰减;空间曲率和挠率的突变量大小与行车安全强相关,其中曲率的连续对行车安全起主导作用,挠率影响相对较小;与现有的运行速度一致性评价方法相比,新的三维线形指标连续性评价方法和标准可以很好地识别平纵组合设计不当和事故多发位置。(2)在车辆坐标系(即Frenet活动标架)的基础上,将汽车视为刚体,对汽车空间运动进行了研究分析,从微观角度建立了以三维线形指标曲率、挠率为控制量的汽车空间运动模型。为保证车辆行驶的稳定性和舒适性,三维线形设计时需对曲率和挠率进行合理控制和约束。综合线形几何连续性、车辆稳定性、行车舒适性等要求,建立了公路三维线形设计指标的工程约束模型。在借鉴现有设计规范和经验的基础上,结合已建立的约束模型,最终确定了不同设计速度下三维线形指标应满足的设计约束值。研究发现曲率的设置对汽车空间运动起主导作用,挠率仅与竖向加加速度变化有关;为保证行车安全和舒适,设计的公路三维线形应至少保证二阶几何连续。(3)本文对不同平纵线形组合得到的空间曲线的类型和相应地曲率、挠率形式进行了详细地分析,发现组合线形主要表现为空间直线段、螺旋线和近似螺旋线三种形式,而组合线形的空间曲线不统一是造成线形整体连续性衰退的主要原因。从线形本身的几何特性、计算需求和信息传递三个方面对3-D样条曲线、组合曲线和PH曲线进行了综合对比,确定采用五次PH曲线进行公路三维几何线形设计和构造。采用五阶Bezier多项式形式表示PH曲线,可将三维PH曲线求解问题转换为确定多项式系数问题,此时曲线的路径长度、曲率和挠率均可用多项式表达式表示,可精确计算而不是估计值。本文给出了详细的PH曲线模型的求解过程。(4)公路三维线形设计时,首先在设计起、终点间选定一系列主控制点,并确定起、终点和这些主控制点处的切矢量方向,通过在主控制点切矢量方向上进行插值以确定从控制点,根据PH曲线算法即可确定初始曲线形状、对应的曲率和挠率大小;为了使设计线形满足工程约束条件,即曲率连续、最大曲率、曲率变化率和挠率约束,可通过不断调整主、从控制点间距进行迭代计算,直至曲率和挠率满足设计要求为止,可调控制点间距的引入为设计人员提供了实现曲线形状和设计指标控制的方便手段。这将保证最终所设计的三维PH曲线是一条曲率连续且能保证行车安全的可行驶路径,且该曲线具有统一的数学表达形式。本文取得的主要研究成果为改善传统道路平纵分离式线形设计方法、提高道路线形设计的安全性提供了新的理论支撑,为后续公路真三维线形设计系统的研发奠定了坚实的理论基础。
[Abstract]:Highway alignment design is an important part of highway construction, its design is reasonable or not is not only related to the quality of highway construction project investment cost, but also directly affect the traffic safety and driving comfort. Affected by the complexity of a 3D analytical model of the development of computer technology and highway alignment, the alignment design method will usually be the center line of highway two-dimensional projection of the plane are designed respectively, and then through the flat, vertical line shape combination of three-dimensional linear. The design method of artificial split and combination of ignoring the interaction and coupling between the flat, vertical design elements, related experience makes the alignment design quality depends largely on the design of personnel, and makes some design flaws oversight was sent directly to the post operation, easily lead to traffic accidents. In order to clear the traditional highway plane, longitudinal separation design and existence To improve the alignment design quality and safety level, this article from the essence of highway 3D alignment, based on differential geometry curve theory, the geometric characteristics of the curvature and the torsion of the two indicators for the space curve described by the curvature, torsion as the intrinsic geometric invariants of space curve, can be completely determined by the geometry of the curve and the establishment of the current. The two-dimensional design index and a new three-dimensional alignment index of curvature, torsion between the relational model in order to analyze the geometric properties on the plane and vertical alignment from the three-dimensional perspective. On the basis of the above research, the arc length parameter, curvature and torsion as control index to linear, geometric continuity, vehicle the stability and driving comfort for the engineering constraints of the basic conditions for the establishment of a new three-dimensional highway alignment design method and design framework. The highway 3D linear control index about A detailed study on construction of beam condition and three-dimensional linear model, the main research contents and innovations are as follows: (1) linear continuous smooth curve is a description of the level, but also the basic requirements of alignment design. This paper adopts the method of geometric continuity of the objective description and analysis of continuous composite curve the space curve in geometric continuity at the connection point is mainly composed of a tangent vector, curvature, torsion and Frenet frame to determine the continuity of adjacent sections. The curvature and torsion of the two indicators to quantify the linear combination of curvature and torsion of variable size are established and highway the two lane highway adjacent section curvature using SPSS torsion relation model between the difference and the accident rate and the continuity of the evaluation criteria. The results show that: the superposition is not flat and vertical alignment of highway alignment design. To ensure the continuity of the linear combination in the three-dimensional space, when 2D alignment elements change, geometric space curve continuous attenuation will exist to varying degrees; the size of the space of variable curvature and torsion and traffic security, including the continuous curvature on the traffic safety play a dominant role, the torsion effect is relatively small; compared with the existing speed consistency evaluation method, three-dimensional linear index new continuous evaluation method and standard can well identify improper design of flat and longitudinal combination and accident prone position. (2) in the vehicle coordinate system (i.e. Frenet movable frame) on the basis of the vehicle as rigid body, to vehicle space motion is studied and analyzed, from the microscopic point of view to establish a three-dimensional linear index of curvature, torsion of vehicle space motion model control. In order to ensure the vehicle driving stability and comfort, the line of 3D shape design Reasonable control and constraint of curvature and torsion. Linear geometric continuity, vehicle stability, driving comfort requirements, and established the engineering constraint model design index of highway 3D linear. Based on present design specification and experience, combined with the constraints of the model, and ultimately determine the design constraints under different design speed the three-dimensional alignment index should satisfy the value. The study found that the leading role of the curvature of the set on the vehicle space motion, only torsion and vertical jerk changes; in order to ensure traffic safety and comfort, the design of the highway three dimensional linear should ensure that at least two order geometric continuity. (3) the space curve of different horizontal and vertical linear combination the types and the corresponding curvature, torsion form in detail, found mainly for the space combination form of line segments, helix helix and approximate three forms, and The space curve is not uniform linear combination is the main cause of linear continuity decline. From the geometric characteristics of linear itself, the computing and information transfer in three aspects of 3-D spline curve, combined curve and PH curve were determined using five PH curve of highway 3D geometric design and construction. The five order Bezier polynomial representation of PH curve, which can convert 3D PH curve to solve problems in order to determine the coefficients of the polynomial, the path length curve, curvature and torsion are available polynomial expression said, can accurately calculate instead of estimated value. This paper gives a detailed model of the solving process of PH curve (4). Design of highway alignment design in 3D, first of all, between the end point selected a series of main control points, and determining the end point and the direction of the tangent vector, the main control points, through the main control point cut The vector direction interpolation to determine from a control point, according to the PH curve algorithm to determine the initial shape of the curve corresponding to the curvature and torsion of linear size; in order to make the design meet the engineering constraints, namely the maximum curvature, curvature continuity, constraint change rate of curvature and torsion, may adjust, iterate from a control point until the distance calculation, curvature and torsion can meet the design requirements, adjustable spacing is introduced into the control design provides a convenient means of curve shape and design control index. This will ensure that the final design of the three dimensional PH curve is a curvature and ensure the safety of the traveling path can continuously, and the expression of the curve has a unified mathematical form. The main achievements of this dissertation is to improve the traditional road horizontal and vertical separation type linear design method, to improve the safety of the road alignment design provides a new The theoretical support has laid a solid theoretical foundation for the research and development of the follow-up Road real 3D linear design system.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U412.3

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