Mathematical Sciences: RUI Inverse Problems in Thermal Imaging

数学科学：热成像中的 RUI 反问题

基本信息

批准号：
9623279
负责人：
Lester Caudill, Jr.
金额：
$ 8.54万
依托单位：
University of Richmond
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1996
资助国家：
美国
起止时间：
1996-07-15 至 1999-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623279&HistoricalAwards=false
关键词：
Mathematical Sciences RUI Inverse Problems

项目摘要

959623279 Caudill/Bryan This research project concerns the study of inverse problems which arise in using thermal methods for the nondestructive evaluation of materials. The focus is to investigate the mathematics involved in the use of techniques for imaging inaccessible portions of some object, e.g., an inaccessible part of the boundary, or the interior of the object. Such inverse problems arise when one uses thermal methods for corrosion detection. The program includes the study of uniqueness and continuous dependence questions, and explores the nature of the dependence of solutions on relevant model parameters. The results of this analysis serve as a foundation for designing inversion algorithms which are both theoretically sound and computationally efficient and reliable. The investigators also consider other thermal imaging problems, including the location of interior cracks, delaminations, or voids. %%% Inverse problems arise naturally when one mathematically models physical systems. Such systems almost always have certain unknown properties which one cannot easily measure directly. Instead, one gathers more readily available information and uses mathematical analysis to infer something about the unknown quantities. For example, by measuring the energy of an x-ray beam passed through a human body one can create images of the interior of the body, a process known as a CAT scan. Other important examples of inverse problems are medical imaging using MRI and PET scans, acoustic sonograms, and non-destructive evaluation of metal parts using electromagnetic methods, e.g., eddy currents. This project concerns the investigation of inverse problems which arise when one uses thermal methods to detect the presence and extent of corrosion in the interior of material objects such as aircraft wings and fuselages. ***

959623279 Caudill/Bryan这项研究项目涉及对使用热方法进行材料无损评估的反向问题的研究。重点是研究使用技术对某些对象的不访问部分的数学，例如边界的一个无法接近的部分或对象的内部。当人们使用热方法进行腐蚀检测时，就会出现这种反问题。该程序包括研究唯一性和持续依赖问题的研究，并探讨了解决方案对相关模型参数的依赖性的性质。该分析的结果是设计反转算法的基础，这些算法在理论上是合理的，而且在计算上有效且可靠。研究人员还考虑了其他热成像问题，包括内部裂缝的位置，分层或空隙。当一个数学对物理系统建模时，自然会出现%% %%逆问题。这样的系统几乎总是具有某些未知的属性，这些属性无法轻易直接测量。取而代之的是，一个人收集更容易获得的信息，并使用数学分析来推断未知数量的内容。例如，通过测量穿过人体的X射线束的能量，可以创建人体内部的图像，即一种称为猫扫描的过程。反问题的其他重要示例是使用MRI和PET扫描，声学超声图以及使用电磁方法（例如涡流电流）对金属零件进行非破坏性评估的医学成像。该项目涉及对使用热方法检测材料内部腐蚀的存在和程度（如飞机机翼和机身）中的存在和程度时的反向问题的研究。 ***