本文選題：公路三維線形設(shè)計(jì)　切入點(diǎn)：道路安全性　出處：《華南理工大學(xué)》2015年博士論文　論文類型：學(xué)位論文

【摘要】：公路線形設(shè)計(jì)作為公路建設(shè)的重要環(huán)節(jié),其設(shè)計(jì)合理與否不僅關(guān)系到公路建設(shè)項(xiàng)目的質(zhì)量好壞、投資成本,更直接影響到公路運(yùn)行安全和行車舒適。受計(jì)算機(jī)技術(shù)發(fā)展的限制和公路線形三維解析模型復(fù)雜性的影響,現(xiàn)行線形設(shè)計(jì)方法通常將公路中心線投影到二維平面上分別進(jìn)行設(shè)計(jì),然后通過平、縱線形組合得到三維線形。這種人為拆分和組合式的設(shè)計(jì)方法忽略了平、縱設(shè)計(jì)要素之間的交互和耦合作用,使得線形設(shè)計(jì)的質(zhì)量很大程度上取決于設(shè)計(jì)人員的相關(guān)經(jīng)驗(yàn),使得一些設(shè)計(jì)缺陷和疏漏被直接帶到后期運(yùn)營中,易引發(fā)交通事故。為了明確傳統(tǒng)公路平、縱分離設(shè)計(jì)思想存在的不足并改善線形設(shè)計(jì)質(zhì)量和安全性水平,本文從公路三維線形本質(zhì)出發(fā),依據(jù)微分幾何曲線論,采用曲率和撓率這兩個(gè)指標(biāo)對(duì)空間曲線的幾何特性進(jìn)行描述,曲率、撓率作為空間曲線的內(nèi)在幾何不變量,可以完全確定曲線的幾何形狀。并建立了現(xiàn)行二維設(shè)計(jì)指標(biāo)與新的三維線形指標(biāo)曲率、撓率之間的關(guān)系模型以便從三維角度對(duì)現(xiàn)行平縱組合線形的空間幾何特性進(jìn)行分析。在上述研究的基礎(chǔ)上,提出以弧長為參數(shù)、曲率和撓率為線形的控制指標(biāo),以幾何連續(xù)性、車輛穩(wěn)定性和行車舒適性為基本的工程約束條件,建立了新的公路三維線形設(shè)計(jì)方法和設(shè)計(jì)框架。本文就公路三維線形控制指標(biāo)的約束條件和三維線形模型的構(gòu)建等問題進(jìn)行了詳細(xì)的研究,主要研究內(nèi)容和創(chuàng)新性成果如下:(1)線形連續(xù)性是曲線光滑程度的描述,也是線形設(shè)計(jì)的一項(xiàng)基本要求。本文提出采用幾何連續(xù)性方法對(duì)組合曲線的連續(xù)性進(jìn)行客觀描述和分析,空間曲線在連接點(diǎn)處的幾何連續(xù)性主要由曲線的切矢量、曲率、撓率和Frenet標(biāo)架的連續(xù)性來決定。采用相鄰路段曲率差和撓率差這兩個(gè)指標(biāo)來量化組合線形曲率和撓率的突變量大小,利用SPSS分別建立了高速公路和雙車道公路相鄰路段曲率差、撓率差與事故率之間的關(guān)系模型以及連續(xù)性評(píng)價(jià)標(biāo)準(zhǔn)。研究結(jié)果表明:公路線形設(shè)計(jì)時(shí)平縱線形的疊加并不能保證組合線形在三維空間中的連續(xù)性,當(dāng)二維線形要素變化時(shí),空間曲線的幾何連續(xù)性會(huì)存在不同程度地衰減;空間曲率和撓率的突變量大小與行車安全強(qiáng)相關(guān),其中曲率的連續(xù)對(duì)行車安全起主導(dǎo)作用,撓率影響相對(duì)較小;與現(xiàn)有的運(yùn)行速度一致性評(píng)價(jià)方法相比,新的三維線形指標(biāo)連續(xù)性評(píng)價(jià)方法和標(biāo)準(zhǔn)可以很好地識(shí)別平縱組合設(shè)計(jì)不當(dāng)和事故多發(fā)位置。(2)在車輛坐標(biāo)系(即Frenet活動(dòng)標(biāo)架)的基礎(chǔ)上,將汽車視為剛體,對(duì)汽車空間運(yùn)動(dòng)進(jìn)行了研究分析,從微觀角度建立了以三維線形指標(biāo)曲率、撓率為控制量的汽車空間運(yùn)動(dòng)模型。為保證車輛行駛的穩(wěn)定性和舒適性,三維線形設(shè)計(jì)時(shí)需對(duì)曲率和撓率進(jìn)行合理控制和約束。綜合線形幾何連續(xù)性、車輛穩(wěn)定性、行車舒適性等要求,建立了公路三維線形設(shè)計(jì)指標(biāo)的工程約束模型。在借鑒現(xiàn)有設(shè)計(jì)規(guī)范和經(jīng)驗(yàn)的基礎(chǔ)上,結(jié)合已建立的約束模型,最終確定了不同設(shè)計(jì)速度下三維線形指標(biāo)應(yīng)滿足的設(shè)計(jì)約束值。研究發(fā)現(xiàn)曲率的設(shè)置對(duì)汽車空間運(yùn)動(dòng)起主導(dǎo)作用,撓率僅與豎向加加速度變化有關(guān);為保證行車安全和舒適,設(shè)計(jì)的公路三維線形應(yīng)至少保證二階幾何連續(xù)。(3)本文對(duì)不同平縱線形組合得到的空間曲線的類型和相應(yīng)地曲率、撓率形式進(jìn)行了詳細(xì)地分析,發(fā)現(xiàn)組合線形主要表現(xiàn)為空間直線段、螺旋線和近似螺旋線三種形式,而組合線形的空間曲線不統(tǒng)一是造成線形整體連續(xù)性衰退的主要原因。從線形本身的幾何特性、計(jì)算需求和信息傳遞三個(gè)方面對(duì)3-D樣條曲線、組合曲線和PH曲線進(jìn)行了綜合對(duì)比,確定采用五次PH曲線進(jìn)行公路三維幾何線形設(shè)計(jì)和構(gòu)造。采用五階Bezier多項(xiàng)式形式表示PH曲線,可將三維PH曲線求解問題轉(zhuǎn)換為確定多項(xiàng)式系數(shù)問題,此時(shí)曲線的路徑長度、曲率和撓率均可用多項(xiàng)式表達(dá)式表示,可精確計(jì)算而不是估計(jì)值。本文給出了詳細(xì)的PH曲線模型的求解過程。(4)公路三維線形設(shè)計(jì)時(shí),首先在設(shè)計(jì)起、終點(diǎn)間選定一系列主控制點(diǎn),并確定起、終點(diǎn)和這些主控制點(diǎn)處的切矢量方向,通過在主控制點(diǎn)切矢量方向上進(jìn)行插值以確定從控制點(diǎn),根據(jù)PH曲線算法即可確定初始曲線形狀、對(duì)應(yīng)的曲率和撓率大小;為了使設(shè)計(jì)線形滿足工程約束條件,即曲率連續(xù)、最大曲率、曲率變化率和撓率約束,可通過不斷調(diào)整主、從控制點(diǎn)間距進(jìn)行迭代計(jì)算,直至曲率和撓率滿足設(shè)計(jì)要求為止,可調(diào)控制點(diǎn)間距的引入為設(shè)計(jì)人員提供了實(shí)現(xiàn)曲線形狀和設(shè)計(jì)指標(biāo)控制的方便手段。這將保證最終所設(shè)計(jì)的三維PH曲線是一條曲率連續(xù)且能保證行車安全的可行駛路徑,且該曲線具有統(tǒng)一的數(shù)學(xué)表達(dá)形式。本文取得的主要研究成果為改善傳統(tǒng)道路平縱分離式線形設(shè)計(jì)方法、提高道路線形設(shè)計(jì)的安全性提供了新的理論支撐,為后續(xù)公路真三維線形設(shè)計(jì)系統(tǒng)的研發(fā)奠定了堅(jiān)實(shí)的理論基礎(chǔ)。
[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.

【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：U412.3

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本文編號(hào)：1651725