非均质生物体组织内复杂热源反演及温度场无损重构基础研究
发布时间：2018-12-16 14:22
【摘要】：以红外无损测温技术为基础的热源逆问题反演成像研究引发了越来越多的关注。本文主要探讨的方向为稳态多热源及分布式热源的反演成像技术,并希望尝试应用在定量化研究人体组织的稳态无损热源成像上。为研究红外无损探测稳态热源反演逆问题,首先建立不同形状的均质与非均质稳态热传导模型,其中内热源个数、位置、强度、面积均为未知项。基于数值算法中有限元算法对模型进行离散分析,根据对应的形状设计出不同的简单有效的有限元网格剖分方案。并分析化简有限元传热矩阵方程,最终转化为对Ax=b高度欠定方程的求解,求解未知量也变为内热源载荷场。通过对该欠定问题进行不适定性分析,并在探讨了几种相关的正则化方法的适用性后,确定了利用分段多项式谱截断奇异值分解法(PPTSVD)的正则化方法求解的思路。对于该方法在研究热源逆问题中存在的问题,我们对算法进行了改进。通过替换其中的微分算子矩阵及利用迭代排除方法对热源进行先分后合的过程,使得该算法可以求解热源逆问题并有效改善了该算法在处理多热源反演时存在的严重的热源叠加效应。最后根据反演出的内热源载荷场利用有限元算法计算重构出整个模型内所有节点的温度分布。运用数值仿真Comsol软件和具体实物实验对算法进行有效性和准确性评估,并验证算法在均质及非均质多热源热传导模型中的表现。结果表明,算法能够准确反演出多热源各参量信息,在非均质材料模型中仍能准确的反演出热源项并有效计算出模型内温度场,证实该算法可应用于材料无损检测及人体红外医学成像等领域。最终我们尝试了将算法应用于解决人体上臂组织截面内温度场重构问题。在处理人体内热源逆问题时,我们分析了人体内传热系统的复杂性,并采用了经刘静简化的Pennes生物传热公式反演人体内综合热源。在对算法进行小幅度改进后,使之可以求解对应生物体热场的分布式热源反演问题,并有了初步的成果。该方法目前仍处在起步阶段,为红外无损探测领域及人体医学红外成像领域提供了一种可行的方法。
[Abstract]:Inversion imaging of heat source based on infrared nondestructive temperature measurement technology has attracted more and more attention. This paper mainly discusses the inversion imaging technology of steady state multi-heat source and distributed heat source, and hopes to apply it to quantitative study of steady state non-destructive thermal source imaging of human tissue. In order to study the inverse problem of inversion of steady-state heat source in infrared nondestructive detection, a homogeneous and heterogeneous steady-state heat conduction model with different shapes is established, in which the number, position, strength and area of the internal heat source are unknown. Based on the finite element algorithm, the model is discretized and different simple and effective finite element mesh generation schemes are designed according to the corresponding shape. The finite element heat transfer matrix equation is analyzed and transformed into the solution of the Ax=b height underdetermined equation. The unknown solution is also transformed into the internal heat source load field. Based on the ill-posed analysis of the problem and the applicability of several related regularization methods, the idea of using the piecewise polynomial spectrum truncated singular value decomposition method (PPTSVD) to solve the regularization method is determined. In order to solve the problem of the inverse problem of heat source, we improve the algorithm. By replacing the differential operator matrix and using the iterative exclusion method, the heat source is separated and then closed. The algorithm can solve the inverse problem of heat source and effectively improve the serious heat source superposition effect in dealing with multiple heat source inversion. Finally, the temperature distribution of all nodes in the model is reconstructed by finite element method according to the internal heat source load field. The validity and accuracy of the algorithm are evaluated by numerical simulation Comsol software and physical experiments, and the performance of the algorithm in homogeneous and heterogeneous multi-heat source heat transfer models is verified. The results show that the algorithm can accurately invert the parameter information of multiple heat sources, and can also accurately reverse the heat source term in the heterogeneous material model and calculate the temperature field in the model effectively. It is proved that this algorithm can be used in material nondestructive testing and infrared medical imaging of human body. Finally, we try to apply the algorithm to the reconstruction of temperature field in the section of human upper arm. In dealing with the inverse problem of heat source in human body, we analyze the complexity of heat transfer system in human body, and use the Pennes's biological heat transfer formula simplified by Liu Jing to invert the comprehensive heat source in human body. After the small improvement of the algorithm, the distributed heat source inversion problem of the corresponding biological thermal field can be solved, and some preliminary results have been obtained. This method is still in its infancy and provides a feasible method for infrared nondestructive detection and infrared imaging of human body.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN219;Q-33
本文编号：2382499
[Abstract]:Inversion imaging of heat source based on infrared nondestructive temperature measurement technology has attracted more and more attention. This paper mainly discusses the inversion imaging technology of steady state multi-heat source and distributed heat source, and hopes to apply it to quantitative study of steady state non-destructive thermal source imaging of human tissue. In order to study the inverse problem of inversion of steady-state heat source in infrared nondestructive detection, a homogeneous and heterogeneous steady-state heat conduction model with different shapes is established, in which the number, position, strength and area of the internal heat source are unknown. Based on the finite element algorithm, the model is discretized and different simple and effective finite element mesh generation schemes are designed according to the corresponding shape. The finite element heat transfer matrix equation is analyzed and transformed into the solution of the Ax=b height underdetermined equation. The unknown solution is also transformed into the internal heat source load field. Based on the ill-posed analysis of the problem and the applicability of several related regularization methods, the idea of using the piecewise polynomial spectrum truncated singular value decomposition method (PPTSVD) to solve the regularization method is determined. In order to solve the problem of the inverse problem of heat source, we improve the algorithm. By replacing the differential operator matrix and using the iterative exclusion method, the heat source is separated and then closed. The algorithm can solve the inverse problem of heat source and effectively improve the serious heat source superposition effect in dealing with multiple heat source inversion. Finally, the temperature distribution of all nodes in the model is reconstructed by finite element method according to the internal heat source load field. The validity and accuracy of the algorithm are evaluated by numerical simulation Comsol software and physical experiments, and the performance of the algorithm in homogeneous and heterogeneous multi-heat source heat transfer models is verified. The results show that the algorithm can accurately invert the parameter information of multiple heat sources, and can also accurately reverse the heat source term in the heterogeneous material model and calculate the temperature field in the model effectively. It is proved that this algorithm can be used in material nondestructive testing and infrared medical imaging of human body. Finally, we try to apply the algorithm to the reconstruction of temperature field in the section of human upper arm. In dealing with the inverse problem of heat source in human body, we analyze the complexity of heat transfer system in human body, and use the Pennes's biological heat transfer formula simplified by Liu Jing to invert the comprehensive heat source in human body. After the small improvement of the algorithm, the distributed heat source inversion problem of the corresponding biological thermal field can be solved, and some preliminary results have been obtained. This method is still in its infancy and provides a feasible method for infrared nondestructive detection and infrared imaging of human body.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN219;Q-33
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