【摘要】：以紅外無損測溫技術為基礎的熱源逆問題反演成像研究引發了越來越多的關注。本文主要探討的方向為穩態多熱源及分布式熱源的反演成像技術,并希望嘗試應用在定量化研究人體組織的穩態無損熱源成像上。為研究紅外無損探測穩態熱源反演逆問題,首先建立不同形狀的均質與非均質穩態熱傳導模型,其中內熱源個數、位置、強度、面積均為未知項。基于數值算法中有限元算法對模型進行離散分析,根據對應的形狀設計出不同的簡單有效的有限元網格剖分方案。并分析化簡有限元傳熱矩陣方程,最終轉化為對Ax=b高度欠定方程的求解,求解未知量也變為內熱源載荷場。通過對該欠定問題進行不適定性分析,并在探討了幾種相關的正則化方法的適用性后,確定了利用分段多項式譜截斷奇異值分解法(PPTSVD)的正則化方法求解的思路。對于該方法在研究熱源逆問題中存在的問題,我們對算法進行了改進。通過替換其中的微分算子矩陣及利用迭代排除方法對熱源進行先分后合的過程,使得該算法可以求解熱源逆問題并有效改善了該算法在處理多熱源反演時存在的嚴重的熱源疊加效應。最后根據反演出的內熱源載荷場利用有限元算法計算重構出整個模型內所有節點的溫度分布。運用數值仿真Comsol軟件和具體實物實驗對算法進行有效性和準確性評估,并驗證算法在均質及非均質多熱源熱傳導模型中的表現。結果表明,算法能夠準確反演出多熱源各參量信息,在非均質材料模型中仍能準確的反演出熱源項并有效計算出模型內溫度場,證實該算法可應用于材料無損檢測及人體紅外醫學成像等領域。最終我們嘗試了將算法應用于解決人體上臂組織截面內溫度場重構問題。在處理人體內熱源逆問題時,我們分析了人體內傳熱系統的復雜性,并采用了經劉靜簡化的Pennes生物傳熱公式反演人體內綜合熱源。在對算法進行小幅度改進后,使之可以求解對應生物體熱場的分布式熱源反演問題,并有了初步的成果。該方法目前仍處在起步階段,為紅外無損探測領域及人體醫學紅外成像領域提供了一種可行的方法。
[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.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN219;Q-33

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本文編號：2382499