基于截断奇异值分解的三维火焰温度场重建研究

利用CCD摄像机得到的火焰辐射能图像进行炉膛三维火焰温度场重建，但温度重建矩阵方程是一个不适定方程组，从而重建问题是一个不适定问题.应用截断奇异值分解(truncated singular value decomposition，TSVD)的正则化方法对该不适定方程组进行求解，并且采用了L曲线法对正则化参数进行选取.结合重建算例，采用奇异值分解(singular value decomposition，SVD)与离散Picard条件对这个不适定问题进行了分析.重建结果表明，在不同的模拟测量误差下，TSVD能够成功得到合理的解，重建温度场较好的再现了原始假设温度场的特征.

Study on three-dimensional flame temperature distribution reconstruction based on truncated singular value decomposition

Three-dimensional flame temperature distribution reconstruction in furnace according to the flame radiative energy images captured by CCD cameras was studied. Temperature reconstruction matrix equation is an ill-posed linear system of equations and the reconstruction problem is an ill-posed problem. Truncated singular value decomposition method (TSVD) was introduced to deal with the ill-posed matrix equation and L-curve method was adopted to choose regularization parameter. Singular value decomposition (SVD) and discrete Picard condition were used to analyze the ill-posed characteristics of the reconstruction problem carefully. The results show that reasonable solutions can be obtained by TSVD and the reconstructed temperature distribution can reproduce the feature of the assumed temperature distribution.