【作者】 徐遥远；

【导师】 董峰；

【作者基本信息】 天津大学 ， 检测技术与自动化装置， 2010， 博士

【摘要】 电阻层析成像技术作为电学层析成像技术的一种,是20世纪80年代后期逐渐发展起来的新型截面电导率参数检测技术。由于具有非扰动,响应速度快,成本低以及结构简单等优点,电阻层析成像技术在许多研究领域中备受关注。电阻层析成像重建问题是具有高度非线性和病态特性,图像的精确稳定重建很难实现。广泛接受的处理思想是:充分利用各种先验信息,选择尽可能少的未知参数量。本文利用被测介质常电导性质的先验信息,将电阻层析成像电导率重建转化为介质边界的重建问题,未知量数目可大幅减少。本文所研究的边界重建方法为定量算法,可从重建结果中方便地得到被测介质的几何分布信息。主要研究工作和结果如下:1.导出了全电极模型下的电阻层析成像敏感场边界积分方程,消去非独立变量,使获得的线性方程组阶数达到最小。与已有的研究相比,未知量数目降低了近50%(理论上极限值)。推导了二阶边界单元解析积分公式及其递推形式,保障了正问题计算的精确性。2.在解析边界单元积分的基础上,给出了Jacobian矩阵计算的直接线性化方法。系统方程的参数组织形式以及QR分解算法的应用保障了Jacobian计算的快速性,而解析公式又保证了其准确性。3.实现了基于Levenberg-Marquardt算法的电阻层析成像边界重建。考虑到重建算法对边界曲线的光滑性要求很高,引入其曲率半径限制条件作为调节阻尼参数的依据。对边界重建算法的稳定性和精确性进行了分析,当被测介质电导率与背景介质差异较大时,重建结果是稳定的,并且可对凸边界曲线进行准确重建;而当其电导率接近于背景介质时,重建稳定性变差。在先验信息不准确的情况下,对边界重建算法经修正逐渐逼近真实曲线的能力进行了讨论。4.针对被测介质为完全导电物体的情形,推导了新的积分方程公式,实现了电阻层析成像边界重建。5.在用边界测量数据直接估计液位的基础上,进行单步边界重建,实现对气液两相水平管流分离界面的更准确地估计。更多还原

【Abstract】 As a kind of electrical tomography techniques, electrical resistance tomography (ERT) is a novel technique to measure cross-sectional conductivity distribution, which has been developed since late 1980s. ERT has advantages in cost, speed and simplicity, and possesses a non-intrusive nature, thus it receives much concern in many research fields. However, the inverse conductivity problem is severely non-linear and ill-posed, which makes difficulties to get a precise and stable reconstruction. The widely acceptable idea to handle problems of this kind is to take full advantage of prior information and set least unknowns in the inverse problem solver. The conductivity reconstruction problem of ERT is transformed to determination of the boundary of inclusions in this paper, where the amount of unknowns is sharply decreased and the constant conductivity of objects is regarded as prior information.The presented boundary reconstruction method is quantitative, thus the geometric and distributional information of objects can be easily achieved from the result. Main efforts and results are as follows.Firstly, the boundary integral equations of ERT sensing field under complete electrode model are deduced, where the non-independent variables are eliminated and a set of linear equations with minimum variables is obtained. Compared to the existing studies, the amount of variables has been decreased at a theoretic maximum extent of 50% variables. The analytical integrations for quadratic elements are presented so that higher-order integrals are expressed by lower-order ones for rapid calculation, which ensures the precision of the ERT forward problem solver.Secondly, a direct linearizing method is presented to calculate the Jacobian matrix based on the analytic boundary integrations. The arrangement of the system matrix and the utilization of QR decomposition ensure rapid calculation of Jacobian matrix, and analytic integrations guarantee the precision.Thirdly, a boundary reconstruction algorithm is presented based on Levenberg-Marquardt method. Much importance is put on the smoothness of boundaries in the reconstruction, thus a restriction of the curve radius is introduced to adjust the damping parameter. Analysis results on the stability and precision of the boundary reconstruction are given. Stable results can be achieved when the conductivity of the objects differs much from that of background medium, and results for convex boundaries are precise. Reversely, the reconstructions for inclusions with similar conductivities to the background medium are not stable. The ability of the modified boundary reconstruction algorithm to approximate the true curve is discussed when the prior information is wrongly given.Fourthly, new integral equations are deduced for cases where complete conducting inclusions are encountered. Then the boundary reconstruction is also achieved.Finally, a one-step boundary reconstruction method is presented to obtain the separated interface of horizontal gas/liquid two phase flows, based on a rough estimation of the liquid level from the boundary measurements.更多还原