三维炉膛温度场重建中病态矩阵方程的求解研究
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摘要
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 distribu- tion 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-factoriza- tion) 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.
During three-dimensional temperature distribu- tion 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-factoriza- tion) 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.
引文
[1]韩曙东,周怀春,盛锋,等.基于具有明显测量误差的辐射图象的二维炉膛温度分布重建和快速特征识别研究[J].中国电机工程学报,2000,20(9):67-71.Han Shudong,Zhou Huaichun,Sheng Feng,et al.Study on reconstruction and fast characteristic recognition of temperature distributions in a2-D furnace via radiant energy images with sensitive measurement errors[J].Proceedings of the CSEE,2000,20(9):67-71(in Chinese).
[2]周怀春,韩曙东,盛锋,等.炉膛燃烧温度场三维可视化监测方法模拟研究[J].动力工程,2003,23(1):2154-2159.Zhou Huaichun,Han Shudong,Sheng Feng,et al.Numerical simulation on a visualization monitoring method of three-dimensional temperature distribution in furnace[J].Power Engineering,2003,23(1):2154-2159(in Chinese).
[3]王飞,马增益,卫成业,等.根据火焰图像测量煤粉炉截面温度场的研究[J].中国电机工程学报,2000,20(7):40-43.Wang Fei,Ma Zengyi,Wei Chengye,et al.Study on section temperature measurement of power plant boiler based on flame image[J].Proceedings of the CSEE,2000,20(7):40-43(in Chinese).
[4]王飞,马增益,严建华,等.利用火焰图像重建三维温度场的模型和实验[J].燃烧科学与技术,2004,10(2):140-145.Wang Fei,Ma Zengyi,Yan Jianhua,et al.Model and experiment for three-dimensional temperature measurement based on flame image[J].Journal of Combustion Science and Technology,2004,10(2):140-145(in Chinese).
[5]黄群星,马增益,严建华,等.应用插值滤波反投影快速重建300MW电站锅炉准三维温度场[J].中国电机工程学报,2005,25(6):134-138.Huang Qunxing,Ma Zengyi,Yan Jianhua,et al.300MW boiler quasi-three-dimensional temperature field fast reconstruction based on interpolated filter back projection method[J].Proceedings of the CSEE,2005,25(6):134-138(in Chinese).
[6]李平,许厚泽,朱介寿,等.地震面波频散的层析成像[J].东北地震研究,1998,14(3):39-49.Li Ping,Xu Houze,Zhu Jieshou,et al.Tomography of rayleigh wave dispersion[J].Seismological Research of Northeast China,1998,14(3):39-49(in Chinese).
[7]曹小林,严忠琼,朱介寿,等.井间地震层析成象高精度算法及其在环境工程勘探中的应用[J].地质灾害与环境保护,1997,8(2):53-58.Cao Xiaolin,Yan Zhongqiong,Zhu Jieshou,et al.High resolution algorithm of crosshole seismic tomography and its application in environmental engineering prospecting[J].Journal of Geological Hazards and Environment Preservation,1997,8(2):53-58(in Chinese).
[8]杨文采,杜剑渊.层析成像新算法及其在工程检测上的应用[J].地球物理学报,1994,37(2):239-244.Yang Wencai,Du Jianyuan.A new algorithm of seismic tomography with application to engineering detection[J].Acth Geophysica Sinica,1994,37(2):239-244(in Chinese).
[9]李平,许厚泽,卢造勋,等.LSQRD及解的分辨分析[J].地壳形变与地震,1999,19(3):1-7.Li Ping,Xu Houtze,lu Zaoxun,et al.LSQRD method and resolution analysis for solutions[J].Crustal Deformation and Earthquake,1999,19(3):1-7(in Chinese).
[10]Baglama J,Reichel L.Decomposition methods for large linear discrete ill-posed problems[J].Journal of Computational and Applied Mathematics,2007,198:332-343.
[11]Morigi S,Reichel L,Sgallari F,et al.Iterative methods for ill-posed problems and semiconvergent sequences[J].Journal of Computational and Applied Mathematics,2006,193:157-167.
[12]Paige C C,Saunders M A.An algorithm for sparse linear equations and sparse least squares[J].AMC Transactions.Math,1982,8(2):43-71.
[13]Paige C C,Saunders M A.LSQR:Sparse linear equations and least squares problems[J].AMC Transactions.Math,1982,8(2):195-209.
[14]刘超.超声层析成像的理论与实现[D].杭州:浙江大学,2003.Liu Chao.Theory and realization of ultrasound tomography technique[D].Hangzhou:Zhejiang University,2003(in Chinese).
[15]Farmer J T,Howell J R.Monte Carlo prediction of radiative heat transfer in inhomogeneous,anisotropic,nongray media[J].Journal ofThermo-physics and Heat Transfer,1994,8(1):133-139.
[2]周怀春,韩曙东,盛锋,等.炉膛燃烧温度场三维可视化监测方法模拟研究[J].动力工程,2003,23(1):2154-2159.Zhou Huaichun,Han Shudong,Sheng Feng,et al.Numerical simulation on a visualization monitoring method of three-dimensional temperature distribution in furnace[J].Power Engineering,2003,23(1):2154-2159(in Chinese).
[3]王飞,马增益,卫成业,等.根据火焰图像测量煤粉炉截面温度场的研究[J].中国电机工程学报,2000,20(7):40-43.Wang Fei,Ma Zengyi,Wei Chengye,et al.Study on section temperature measurement of power plant boiler based on flame image[J].Proceedings of the CSEE,2000,20(7):40-43(in Chinese).
[4]王飞,马增益,严建华,等.利用火焰图像重建三维温度场的模型和实验[J].燃烧科学与技术,2004,10(2):140-145.Wang Fei,Ma Zengyi,Yan Jianhua,et al.Model and experiment for three-dimensional temperature measurement based on flame image[J].Journal of Combustion Science and Technology,2004,10(2):140-145(in Chinese).
[5]黄群星,马增益,严建华,等.应用插值滤波反投影快速重建300MW电站锅炉准三维温度场[J].中国电机工程学报,2005,25(6):134-138.Huang Qunxing,Ma Zengyi,Yan Jianhua,et al.300MW boiler quasi-three-dimensional temperature field fast reconstruction based on interpolated filter back projection method[J].Proceedings of the CSEE,2005,25(6):134-138(in Chinese).
[6]李平,许厚泽,朱介寿,等.地震面波频散的层析成像[J].东北地震研究,1998,14(3):39-49.Li Ping,Xu Houze,Zhu Jieshou,et al.Tomography of rayleigh wave dispersion[J].Seismological Research of Northeast China,1998,14(3):39-49(in Chinese).
[7]曹小林,严忠琼,朱介寿,等.井间地震层析成象高精度算法及其在环境工程勘探中的应用[J].地质灾害与环境保护,1997,8(2):53-58.Cao Xiaolin,Yan Zhongqiong,Zhu Jieshou,et al.High resolution algorithm of crosshole seismic tomography and its application in environmental engineering prospecting[J].Journal of Geological Hazards and Environment Preservation,1997,8(2):53-58(in Chinese).
[8]杨文采,杜剑渊.层析成像新算法及其在工程检测上的应用[J].地球物理学报,1994,37(2):239-244.Yang Wencai,Du Jianyuan.A new algorithm of seismic tomography with application to engineering detection[J].Acth Geophysica Sinica,1994,37(2):239-244(in Chinese).
[9]李平,许厚泽,卢造勋,等.LSQRD及解的分辨分析[J].地壳形变与地震,1999,19(3):1-7.Li Ping,Xu Houtze,lu Zaoxun,et al.LSQRD method and resolution analysis for solutions[J].Crustal Deformation and Earthquake,1999,19(3):1-7(in Chinese).
[10]Baglama J,Reichel L.Decomposition methods for large linear discrete ill-posed problems[J].Journal of Computational and Applied Mathematics,2007,198:332-343.
[11]Morigi S,Reichel L,Sgallari F,et al.Iterative methods for ill-posed problems and semiconvergent sequences[J].Journal of Computational and Applied Mathematics,2006,193:157-167.
[12]Paige C C,Saunders M A.An algorithm for sparse linear equations and sparse least squares[J].AMC Transactions.Math,1982,8(2):43-71.
[13]Paige C C,Saunders M A.LSQR:Sparse linear equations and least squares problems[J].AMC Transactions.Math,1982,8(2):195-209.
[14]刘超.超声层析成像的理论与实现[D].杭州:浙江大学,2003.Liu Chao.Theory and realization of ultrasound tomography technique[D].Hangzhou:Zhejiang University,2003(in Chinese).
[15]Farmer J T,Howell J R.Monte Carlo prediction of radiative heat transfer in inhomogeneous,anisotropic,nongray media[J].Journal ofThermo-physics and Heat Transfer,1994,8(1):133-139.
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