發(fā)布時(shí)間：2018-12-16 14:22

【摘要】：以紅外無(wú)損測(cè)溫技術(shù)為基礎(chǔ)的熱源逆問(wèn)題反演成像研究引發(fā)了越來(lái)越多的關(guān)注。本文主要探討的方向?yàn)榉�(wěn)態(tài)多熱源及分布式熱源的反演成像技術(shù),并希望嘗試應(yīng)用在定量化研究人體組織的穩(wěn)態(tài)無(wú)損熱源成像上。為研究紅外無(wú)損探測(cè)穩(wěn)態(tài)熱源反演逆問(wèn)題,首先建立不同形狀的均質(zhì)與非均質(zhì)穩(wěn)態(tài)熱傳導(dǎo)模型,其中內(nèi)熱源個(gè)數(shù)、位置、強(qiáng)度、面積均為未知項(xiàng)�；跀�(shù)值算法中有限元算法對(duì)模型進(jìn)行離散分析,根據(jù)對(duì)應(yīng)的形狀設(shè)計(jì)出不同的簡(jiǎn)單有效的有限元網(wǎng)格剖分方案。并分析化簡(jiǎn)有限元傳熱矩陣方程,最終轉(zhuǎn)化為對(duì)Ax=b高度欠定方程的求解,求解未知量也變?yōu)閮?nèi)熱源載荷場(chǎng)。通過(guò)對(duì)該欠定問(wèn)題進(jìn)行不適定性分析,并在探討了幾種相關(guān)的正則化方法的適用性后,確定了利用分段多項(xiàng)式譜截?cái)嗥娈愔捣纸夥?PPTSVD)的正則化方法求解的思路。對(duì)于該方法在研究熱源逆問(wèn)題中存在的問(wèn)題,我們對(duì)算法進(jìn)行了改進(jìn)。通過(guò)替換其中的微分算子矩陣及利用迭代排除方法對(duì)熱源進(jìn)行先分后合的過(guò)程,使得該算法可以求解熱源逆問(wèn)題并有效改善了該算法在處理多熱源反演時(shí)存在的嚴(yán)重的熱源疊加效應(yīng)。最后根據(jù)反演出的內(nèi)熱源載荷場(chǎng)利用有限元算法計(jì)算重構(gòu)出整個(gè)模型內(nèi)所有節(jié)點(diǎn)的溫度分布。運(yùn)用數(shù)值仿真Comsol軟件和具體實(shí)物實(shí)驗(yàn)對(duì)算法進(jìn)行有效性和準(zhǔn)確性評(píng)估,并驗(yàn)證算法在均質(zhì)及非均質(zhì)多熱源熱傳導(dǎo)模型中的表現(xiàn)。結(jié)果表明,算法能夠準(zhǔn)確反演出多熱源各參量信息,在非均質(zhì)材料模型中仍能準(zhǔn)確的反演出熱源項(xiàng)并有效計(jì)算出模型內(nèi)溫度場(chǎng),證實(shí)該算法可應(yīng)用于材料無(wú)損檢測(cè)及人體紅外醫(yī)學(xué)成像等領(lǐng)域。最終我們嘗試了將算法應(yīng)用于解決人體上臂組織截面內(nèi)溫度場(chǎng)重構(gòu)問(wèn)題。在處理人體內(nèi)熱源逆問(wèn)題時(shí),我們分析了人體內(nèi)傳熱系統(tǒng)的復(fù)雜性,并采用了經(jīng)劉靜簡(jiǎn)化的Pennes生物傳熱公式反演人體內(nèi)綜合熱源。在對(duì)算法進(jìn)行小幅度改進(jìn)后,使之可以求解對(duì)應(yīng)生物體熱場(chǎng)的分布式熱源反演問(wèn)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(wú)損探測(cè)領(lǐng)域及人體醫(yī)學(xué)紅外成像領(lǐng)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(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN219;Q-33

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本文編號(hào)：2382499