三维炉膛温度场重建中病态矩阵方程的求解研究

Study on Solving Ill-posed Matrix Equation in Reconstruction of Three-dimensional Temperature Distribution in Furnace

在利用CCD摄像机所拍摄到的辐射能图像进行三维炉膛温度场重建过程中,会涉及到大型病态矩阵方程的求解问题,一般的求解方法得不到满意的结果。文中采用LSQR算法(least square QR-factorization)对三维温度场重建中的病态矩阵方程进行求解研究。结果表明,对于病态问题,LSQR算法具有较好的数值稳定性和抗测量误差能力强的优点,适于大型电站锅炉燃烧温度场特别是高温区的重建;且计算效率高,重建时间短,显示了其在温度场在线重建方面的潜力。

During three-dimensional temperature distribution reconstruction in furnace using radiative energy images captured by CCD cameras, the problem of solving a large ill-posed matrix equation appears and general methods can not obtain satisfying solutions. LSQR （least square QR-factorization） method was adopted to solve the ill-posed matrix equation in the three-dimensional temperature distribution reconstruction. Results show that LSQR algorithm has good numerical stability and strong anti-errors characteristic, which is suited for combustion temperature distribution reconstruction, especially for high temperature areas reconstruction in large-scale power plant. LSQR algorithm also has high computational efficiency and computational time is short so this algorithm has on-line reconstruction potential.