Fundamental Study On Complex Heat Source Inversion And Non - Destructive Reconstruction Of Temperature Field In Heterogeneous Organisms

The heat source inverse problem of nondestructive detection based on the infrared thermal imaging technology has caused more and more attention. This study mainly discusses the direction of steady-state multiple heat sources and distributed heat source inversion technology. Finally we hope this solution can be applied on the field of quantitative research for the inverse heat source problem in human tissue on steady-state condition.To study the case of internal heat source inversion problem of steady-state, we construct homogeneous and heterogeneous steady heat conduction model of different shapes. The number, location, size and intensity of heat source are unknown. We use the finite element method (FEM) based on numerical algorithm to analyze the two-dimensional model discretely. The internal heat conduction process of model is analyzed. Synthesized temperature field can be decomposed by the temperature field caused by the ambient temperature and given internal heat sources. We simplify the finite element matrix equation according to decomposition process above, eventually, the problem is put into solving the highly underdetermined matrix equation of Ax=b. The unknown x item corresponds to internal thermal heat sources field. We analyze this problem towards its qualitative feature and discuss a few Regularization methods. The piecewise polynomial spectral truncated singular value decomposition (PPTSVD) is applied for the first time for this problem. Its regular operator matrix is changed from the original more order differential operator matrix to regional node weighted matrix. After the replacement this solution improves the effect of heat source field tend to close to the boundary and results of the solution confirms to real heat source field when there are less heat sources or different hear sources are far from the others. But it also exits serious superimposed effect between neighboring heat source. We improve the algorithm to suppress this problem through using the iterative elimination process which complies with the idea of spreading heat source field and then gathering. The iteration tolerance and number of times belong to one single PPTSVD solving process are reduced. Through multiple PPTSVD solving process iteration and reconstructing A, b matrix in every iteration, we get the scatter heat source field distribution surrounding real field. Finally, this scattered distribution solution was gathered again. According to the heat source parameter calculated by algorithm, the temperature field of whole model can be reconstructed using FEM.Comsol numerical simulation software and real physical experiments are performed to verify the validity and accuracy of the algorithm in different heat conduction model. The results demonstrate that the algorithm can access each parameter of multiple heat sources relatively. Even in the heterogeneous model, it can still obtain accurate results and reconstruct the temperature field of the two-dimensional model. At the end, we tried to solve the temperature field reconstruction problem in human upper arm tissue section. In dealing with the human body heat inverse problem, the complexity of heat transfer system in human body is analyzed. We simplify the Pennes biological equation using the model proposed by Liujing. After a slight improvement towards the PPTSVD algorithm, it could solve distributed source inverse problem. The preliminary result is worthy of recognition. This method is still in its infancy, providing an effective method for non-destructive materials detecting and human infrared medical imaging fields.