【作者】 朱学明；

【导师】 王化祥；

【作者基本信息】 天津大学 ， 检测技术与自动化装置， 2004， 博士

【摘要】 电容层析成像技术(ECT- Electrical Capacitance Tomography)是基于电容敏感原理的过程成像技术。它具有非侵入性、造价低、安装方便、实时性好等优点,可获取过程参数的二维/三维信息图像。目前的研究结果已显示出该项技术在工业过程检测与控制中的广阔应用前景。 本文主要探讨 ECT 的图像重建算法,研究工作如下:(1) 为深入了解 ECT 的‘软场’性质并优化电容传感器结构,作者利用 Ansys 软件对其电磁场特性进行系统仿真;(2) 正问题是图像重建算法的研究基础,作者编制了一套有限元仿真软 件,为正问题与图像重建算法的研究提供软件仿真平台;(3) 以最优化理论为基础,作者提出共轭梯度无约束优化算法,针对 ECT 灵敏度矩阵既非对称又非正定且为稠密阵的特点,重新设计了图像重 建算法,获得较好的图像重建效果;(4) 根据目前图像重建算法的研究现状,作者提出对不适定性问题进行正 则化的必要性;从第一类 Fredholm 积分方程出发,建立线性算子方程, 在度量空间详细讨论了 Hadamard 适定性三条件和有限秩算子的不适定 性;详细介绍了利用先验策略和后验策略确定正则参数的方法;(5) 作者针对 ECT 逆问题的不适定性,提出 L 曲线法、普通交叉校验法 和广义交叉校验法等三种确定正则参数的有效计算方法;并对三种方 法进行了相互验证;其中,对 L 曲线法进行了详细的理论推导,确定 滤波函数并设计运算步骤说明其理论上的合理性;(6) 作者利用获取的正则因子对无约束图像重建算法进行标准 Tikhonov 正 则化,并获得良好的成像效果。更多还原

【Abstract】 Electrical Capacitance Tomography (ECT), which is based on capacitance sensingprinciple, is a promising technique of process tomography. It has the advantage ofbeing non-intrusive, low cost, facilitated installment and fast response, which canacquire 2D/3D image information of process parameters. The latest reports havemanifested the technique has a broad application for the detection and control ofindustrial process. The paper mainly discussed the image reconstruction algorithm of ECT, Thecontributions of this dissertation are as follows:(1) For understanding the nature of ‘soft field’ deeply and optimizing the sensor structure, the author simulate the electromagnetic properties of the sensor by utilizing the ‘ANSYS’ software.(2) Because the forward problem is the foundation of the algorithm, the author programmed a FEM software specially for the research on the forward problem and the image reconstruction algorithm.(3) On the basis of the optimization theory, the unconstrained conjugate gradient method was introduced. When solving the inverse problem though, where the sensitivity matrix is asymmetric, non-definite and dense, the new algorithm was derived and the excellent image was obtained.(4) For the current research, it is necessary that regularization was employed for solving the ill-posed problems. Considering the Fredholm integral equations of the first kind and its linear operator equations, the three well-posed conditions and the ill-posed finite rank operator were discussed in the metric space. some methods determining the regularized parameter were discussed by utilizing prior and posterior strategy.(5) For solving the ill-posed problem of the ECT, three computational methods such as L-curve, ordinary cross validation and general cross validation were not only proposed which is introduced for determining the regularized parameter, but also II<WP=4>ABSTRACT they are testimonialised each other, otherwise, L-curve method was derived in terms of mathematical theory, its filter function was devised and the method was accounted for reasonably.(6) Employing the gained regularized parameter to unconstrained image reconstruction algorithm, which was standard Tikhonov regularization, some nice image were obtained.更多还原