【作者】 李昆；

【导师】 王卫华；

【作者基本信息】 武汉理工大学 ， 应用数学， 2005， 硕士

【摘要】 汽车后视镜是汽车上一个非常重要的部件,如果后视镜有盲区和图像变形,势必给安全行车带来隐患。研究出一种大视野低失真的后视镜对减少交通事故带来的损失有重要意义,而且现在汽车越来越普及,后视镜市场也有巨大潜力,在这种情况下出现了许多新型后视镜的设计,最具代表性的是渐变曲率后视镜,但这些新型后视镜都缺乏数学模型支持和可靠的理论分析,缺乏能够量化的评估方法。本文将通过分析某新型后视镜的特点,提出一种数学建模方法,建立该新型后视镜的数学模型,并通过该模型对这类后视镜进行理论分析和数值仿真,从而对这类后视镜的性能进行量化评估。 本文主要由理论研究和应用仿真两部分组成。第一部分是理论研究:在最小二乘法基础上引入了一种改进的算法——移动最小二乘法,并介绍了反求工程的应用方法。将移动最小二乘法应用于汽车后视镜拟合问题中,并与传统的最小二乘法的结果进行对照,展示该方法的优越性。第二部分是应用仿真:利用移动最小二乘法建立的数学模型,设计了相应的仿真算法,直观展现后视镜的视野范围。本文的具体研究内容如下: 第一章介绍了研究背景,指出本文研究要解决的关键技术问题及研究内容。 第二章介绍曲面拟合的传统方法——最小二乘法的理论,在此基础上,采用了一种改进的曲面拟合方法——移动最小二乘法。并对移动最小二乘法的权函数的选取、A矩阵的可逆性、影响域半径的确定以及插值函数的性质等关键性问题都进行了详细的分析。 第三章介绍了反求工程的基本理论,研究了基于特征的反求工程,并指出了其优势。提出了把反求技术应用于求汽车后视镜参数问题的思想方法。 第四章是将数学建模和仿真技术应用于后视镜问题中。首先利用反求技术得到后视镜上大量点的坐标。然后分别利用最小二乘法和改进的算法——移动最小二乘法对汽车后视镜进行曲面拟合,建立后视镜的数学模型。进而将仿真技术应用于后视镜中,设计相应的仿真算法,对前面建立的数学模型进行数值仿真分析,仿真结果直观展现后视镜的视野范围,为下一步工作打下基础。 最后总揽全文,得出结论。更多还原

【Abstract】 Rearview mirror is a quite important part of an automobile. If there are blind domains and distorted image on the rearview mirror of an automobile that may increase the probability of danger to driver. It is very significant to design a kind of rearview mirror with wide eyeshot and little distortion. Nowadays automobile is more and more popular, and the market of rearview mirror is quite large. So people have designed a lot of new rearview mirrors, of which the most typical type is gradual change curvature rearview mirror. However, these new types are short of the support of mathematical models and dependable theoretical analysis. In this paper we will present a new method and establish a mathematical model of new rearview mirror by analyzing its characteristic. Moreover, we will evaluate the quality of this rearview mirror by theoretical analysis and numerical simulation.The paper consists of two parts: in the first part we study the theory of rearviewmirror. On the basis of Least Squares, we present an improved algorithm ------Moving Least Squares. Moreover, we introduce the applied method of reverse engineer. We will apply Moving Least Squares to rearview mirror. Compared with the method of Least Squares, Moving Least Squares is more predominant. In the second part, we talk about the application of rearview mirror. And we establish the model of rearview mirror by Moving Least Squares and design corresponding algorithm. We apply simulation technique to mathematical model, which can display intuitionally field of vision of rearview mirror. The main research work is listed as follows:In the first chapter, we give research background. Then we point out the key problem and research content that may be solved in our research work.In the second chapter, we present the traditional way of surface fitting ------LeastSquares. We present a kind of amendatory algorithm------Moving Least Squaresbased on Least Squares. Moreover, we analyze explicitly selection of weighted function, reversibility of A matrix, confirm of radius of influencing domain and characteristic of interpolating function and so on.In the third chapter, we present the basis theory of reverse engineer and discussreverse engineering based on characteristic and point out its merit. Moreover, we present an ideology way that will apply reverse technology to seek the parameter of rearview mirror.In the fourth chapter, we apply mathematical model and simulation technique to rearview mirror. Firstly, we get a lot of coordinates of points of rearview mirror. Secondly, we apply surface fitting on rearview mirror by least squares and moving least squares and establish corresponding mathematical models. Finally, we apply simulation technique to rearview mirror and design corresponding simulation algorithm and make out numerical analysis to established mathematical model. The simulation result shows distinctly field of vision of rearview mirror.At last, the research work in the paper is summarized.更多还原