一种电子装备表面粗糙度的重构方法研究
发布时间：2019-02-10 20:11
【摘要】：随着电子装备向高频段、高增益、高密度、小型化方向发展,结构因素对其电性能的影响也愈发凸显,其中表面粗糙度因其存在的普遍性、分布的随机性及其对电性能影响机理的复杂性而备受关注。本学位论文在国家自然科学基金项目的支持下,以电子装备腔体结构内壁表面粗糙度为具体研究对象,针对表面粗糙度的重构问题,进行了深入的研究与探索,主要研究内容包括以下三部分:一是应用三种典型函数对一维表面粗糙度进行了建模;二是基于电磁散射理论对一维表面粗糙度形貌进行了重构;三是进行了二维表面粗糙度形貌的重构。1、表面粗糙度的建模分别建立了周期函数、随机函数和分形函数表面粗糙度模型。采用蒙特卡洛法建立表面粗糙度一维高斯随机粗糙度模型,验证了均方根高度、相关长度对粗糙表面形貌的影响关系;建立了周期函数粗糙度模型,简单讨论了其相关参数对粗糙表面形貌的影响关系;建立了一维W-M分形函数粗糙度模型,对其具有的自仿射性、自相似性等性质进行了验证,并讨论了分形函数的主要参数对粗糙表面形貌的影响。2、一维表面粗糙度形貌的重构采用矩量法对一维粗糙表面形貌的电场积分方程进行离散,将复杂的积分方程的求解转换成简单的线性方程组求解,从而得到散射数据;分别仿真验证了一维粗糙表面形貌的源项与入射角度、谱振幅与表面起伏高度之间的关系,验证了源项与入射场、谱振幅与散射场之间的等价关系;采用微扰法-矩量法混合算法对三种一维小尺度下的粗糙表面形貌进行了重构,包括周期函数、高斯函数和分形函数。由于分形函数具有处处连续且处处不可导的特性,使用现有理论出现了散射数据无法准确计算,重构过程无法进行的问题。本文通过引入分形几何领域内的分数阶微积分理论,解决了分形函数整数阶不可导问题,实现了分形粗糙表面形貌的准确重构。3、二维粗糙表面形貌的重构。针对二维高斯随机粗糙表面,采用蒙特卡洛法建立了二维高斯随机粗糙度模型,分析讨论了其均方根高度与相关长度对粗糙表面形貌的影响关系;采用离散化思想将二维高斯随机粗糙表面离散成大量可近似为一维粗糙表面形貌的条状模型,将二维高斯随机粗糙表面的电磁散射过程简化为若干一维高斯随机粗糙表面的电磁散射过程,实现了二维高斯随机粗糙表面形貌的准确重构。
[Abstract]:With the development of electronic equipment in the direction of high frequency band, high gain, high density and miniaturization, the influence of structural factors on its electrical performance is becoming more and more prominent. The randomness of distribution and the complexity of its influence mechanism on electrical properties have attracted much attention. Supported by the National Natural Science Foundation of China, this dissertation takes the surface roughness of the inner wall of the cavity structure of electronic equipment as the specific research object, aiming at the problem of surface roughness reconstruction, carries on the thorough research and the exploration. The main research contents include the following three parts: first, using three typical functions to model one-dimensional surface roughness; Secondly, based on the electromagnetic scattering theory, the one-dimensional surface roughness morphology is reconstructed. Firstly, the surface roughness models of periodic function, random function and fractal function are established. The one-dimensional Gao Si random roughness model of surface roughness was established by Monte Carlo method, and the effect of root mean square height and correlation length on rough surface morphology was verified. The periodic function roughness model is established, and the influence of the relative parameters on the rough surface morphology is briefly discussed. The roughness model of one-dimensional W-M fractal function is established and its properties of self-affine and self-similarity are verified. The influence of the main parameters of fractal function on the morphology of rough surface is discussed. The method of moment is used to discretize the electric field integral equation of one-dimensional rough surface topography, and the complex integral equation is transformed into a simple linear equation group to solve the scattering data. The relationship between source term and incident angle, spectral amplitude and surface fluctuation height of one-dimensional rough surface topography is verified by simulation, and the equivalent relationship between source term and incident field, spectral amplitude and scattering field is verified. In this paper, three kinds of rough surface topography at one dimension and small scale are reconstructed by the mixed algorithm of perturbation method and moment method, including periodic function, Gao Si function and fractal function. Because the fractal function is continuous everywhere and can not be differentiable everywhere, using the existing theory, the scattering data can not be accurately calculated, and the reconstruction process can not be carried out. By introducing the fractional calculus theory in the field of fractal geometry, this paper solves the problem of integral order nondifferentiability of fractal functions, and realizes the accurate reconstruction of fractal rough surface topography. 3. The reconstruction of two-dimensional rough surface topography. Aiming at the two-dimensional Gao Si random rough surface, the Monte Carlo method is used to establish the two-dimensional Gao Si random roughness model, and the relationship between the root mean square height and the correlation length on the rough surface morphology is analyzed and discussed. Using the idea of discretization, the two-dimensional Gao Si random rough surface is discretized into a large number of strip models which can be approximated to one-dimensional rough surface morphology. The electromagnetic scattering process of two dimensional Gao Si random rough surface is simplified as that of some one-dimensional Gao Si random rough surface, and the accurate reconstruction of the two-dimensional Gao Si random rough surface morphology is realized.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011
本文编号：2419504
[Abstract]:With the development of electronic equipment in the direction of high frequency band, high gain, high density and miniaturization, the influence of structural factors on its electrical performance is becoming more and more prominent. The randomness of distribution and the complexity of its influence mechanism on electrical properties have attracted much attention. Supported by the National Natural Science Foundation of China, this dissertation takes the surface roughness of the inner wall of the cavity structure of electronic equipment as the specific research object, aiming at the problem of surface roughness reconstruction, carries on the thorough research and the exploration. The main research contents include the following three parts: first, using three typical functions to model one-dimensional surface roughness; Secondly, based on the electromagnetic scattering theory, the one-dimensional surface roughness morphology is reconstructed. Firstly, the surface roughness models of periodic function, random function and fractal function are established. The one-dimensional Gao Si random roughness model of surface roughness was established by Monte Carlo method, and the effect of root mean square height and correlation length on rough surface morphology was verified. The periodic function roughness model is established, and the influence of the relative parameters on the rough surface morphology is briefly discussed. The roughness model of one-dimensional W-M fractal function is established and its properties of self-affine and self-similarity are verified. The influence of the main parameters of fractal function on the morphology of rough surface is discussed. The method of moment is used to discretize the electric field integral equation of one-dimensional rough surface topography, and the complex integral equation is transformed into a simple linear equation group to solve the scattering data. The relationship between source term and incident angle, spectral amplitude and surface fluctuation height of one-dimensional rough surface topography is verified by simulation, and the equivalent relationship between source term and incident field, spectral amplitude and scattering field is verified. In this paper, three kinds of rough surface topography at one dimension and small scale are reconstructed by the mixed algorithm of perturbation method and moment method, including periodic function, Gao Si function and fractal function. Because the fractal function is continuous everywhere and can not be differentiable everywhere, using the existing theory, the scattering data can not be accurately calculated, and the reconstruction process can not be carried out. By introducing the fractional calculus theory in the field of fractal geometry, this paper solves the problem of integral order nondifferentiability of fractal functions, and realizes the accurate reconstruction of fractal rough surface topography. 3. The reconstruction of two-dimensional rough surface topography. Aiming at the two-dimensional Gao Si random rough surface, the Monte Carlo method is used to establish the two-dimensional Gao Si random roughness model, and the relationship between the root mean square height and the correlation length on the rough surface morphology is analyzed and discussed. Using the idea of discretization, the two-dimensional Gao Si random rough surface is discretized into a large number of strip models which can be approximated to one-dimensional rough surface morphology. The electromagnetic scattering process of two dimensional Gao Si random rough surface is simplified as that of some one-dimensional Gao Si random rough surface, and the accurate reconstruction of the two-dimensional Gao Si random rough surface morphology is realized.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011
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