Radiative imaging of combustion flame in furnace of power plant plays an increasingly important role in combustion diagnosis. The flame radiation image taken by a charge-coupled device (CCD) camera can reconstruct three-dimensional flame temperature distribution in the furnace. CCD cameras are used for capturing the flame images to obtain the line-of-sight radiation intensities. The temperature reconstruction matrix equation is a seriously pathological equation. Thus the temperature field reconstruction problem is an ill-posed problem. The two algorithms (Tikhonov regularization and truncated singular value decomposition (TSVD)) for solving the temperature field reconstruction are introduced. The size of the numerical simulation system is 10 m × 10 m × 10 m, which is divided into 10 × 10 × 10 volume elements in the three dimensions. Each volume element is a unit cube. Generalized cross-validation (GCV) is used to select the correct regularization parameter. The measured data are simulated by adding different random errors to the exact solution of the direct problem. The reconstructed temperature deviation is calculated by the two algorithms separately. When the measuring errors are 0.05 and 0.10, the reconstruction errors based on Tikhonov are respectively 19.3% and 7.0%, less than those based on TSVD. When the measuring errors are 0, 0.01, 0.03 and 0.07, the differences between the two kinds of errors are all less than 3%. Both the algorithms can reconstruct the correct temperature field. The times required to reconstruct the temperature field by the two algorithms are compared and their effects of the maximum temperature are also compared. When the measuring errors are 0, 0.01, 0.03, 0.05, 0.07 and 0.1, the reconstruction times based on Tikhonov are respectively −0.0917, −0.049, 0.161, 0.002, 0.135 and 0.091 s, shorter than the reconstruction times based on TSVD. There is singular value decomposition (SVD) in TSVD. And this process takes more than 2 s. If the problem is more complicated, SVD takes much more time. The errors of the maximum reconstruction temperature under Tikhonov are smaller. And the position of the maximum reconstruction temperature under Tikhonov is near the position of the exact maximum temperature in space. The maximum reconstruction temperature under TSVD is not so good as that under Tikhonov. Preliminary results indicate that the Tikhonov-based reconstruction is slightly better than the TSVD-based reconstruction, especially in reconstruction error, reconstruction time, and effects of the maximum temperature.%在煤粉锅炉诊断中火焰辐射能图像扮演着越来越重要的角色，通过电荷耦合器件(CCD)获得的辐射能图像可以重建出炉内火焰三维温度场， CCD用于获取视场角内的辐射能图像。温度场重建的矩阵方程是一个严重病态的方程，本文使用两种算法(Tikhonov正则化算法和截断奇异值分解(TSVD)算法)来重建温度场。应用广义交叉检验算法来选取正确的正则化参数。数值模拟的环境为一个10 m×10 m×10 m的三维炉膛，系统被划分为10×10×10的1000个网格，每个网格单元都是边长为1 m的立方体。在正问题求解所得到的CCD接受信号基础上加上不同随机误差以模拟测量时的CCD接受信号。研究两种算法重建后的温度重建误差、两者的重建时间，以及最高温度的重建效果。初步的研究结果显示，一般情况下基于Tikhonov算法重建的温度场比基于TSVD算法重建的温度场误差要小，计算所需时间短，最高温度重建更准确。
展开▼
