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基于阻尼LSQR-LMBC的火焰三维温度场重建

单良 赵腾飞 黄荟云 洪波 孔明

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基于阻尼LSQR-LMBC的火焰三维温度场重建

单良, 赵腾飞, 黄荟云, 洪波, 孔明

Flame 3D temperature field reconstruction based on Damped LSQR-LMBC

Shan Liang, Zhao Teng-Fei, Huang Hui-Yun, Hong Bo, Kong Ming
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  • 光场相机可以解决辐射测温多相机系统光路复杂、同步触发难等问题, 在辐射成像三维温度重建时有其独特优势. LSQR是求解基于大型稀疏矩阵最小二乘问题的经典算法, 该算法用于重建三维温度场时对温度初值依赖较大, 在信噪比较低的情况下重建精度不理想. 本文提出阻尼LSQR-LMBC重建算法, 通过在LSQR方法中添加阻尼正则化项, 提高火焰三维温度场重建的抗噪性能, 并结合LMBC算法, 实现吸收系数和三维温度场同时求解. 在数值模拟部分, 随着信噪比逐渐降低, 阻尼LSQR的重建效果比LSQR更加稳定, 在信噪比达到13.86 dB时, 重建精度大约提高30%. 阻尼LSQR-LMBC的平均重建误差为6.63%. 用丁烷火焰进行了实验, 重建的丁烷火焰三维温度场分布符合辐射火焰燃烧的特征, 和热电偶的测温数据结果进行对比, 相对误差在6.8%左右.
    Light field camera can solve the problems of complex optical path and difficult synchronous trigger of radiation temperature measurement multi camera system, which has some unique advantages in three-dimensional temperature reconstruction of radiation imaging. The LSQR is a classical algorithm for solving the least square problem based on large sparse matrix. When the algorithm is used to reconstruct three-dimensional temperature field, it depends on the initial value of temperature, and the reconstruction accuracy is not ideal when the signal-to-noise ratio is low. In this paper, a damped LSQR-LMBC reconstruction algorithm is proposed. By adding a damped regularization term into the LSQR method, the anti noise performance of flame three-dimensional temperature field reconstruction is improved. By combining the LMBC algorithm, the absorption coefficient and three-dimensional temperature field are solved at the same time. In the numerical simulation part, with the gradual reduction of signal-to-noise ratio, the reconstruction effect of Damped LSQR turns more stable than LSQR. When the signal-to-noise ratio reaches 13.86 dB, the reconstruction accuracy is improved by about 30%. The average reconstruction error of damped LSQR-LMBC is 6.63%. The three-dimensional temperature field distribution of butane flame is consistent with the characteristic of radiation flame combustion. Compared with the temperature measurement data of thermocouple, the relative error is about 6.8%.
      通信作者: 孔明, mkong@cjlu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51874264, 52076200)资助的课题.
      Corresponding author: Kong Ming, mkong@cjlu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51874264, 52076200).
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    Sun X G, Dai J M, Cong D C, Chu Z X 2003 J. Tsinghua Univ., Sci. Technol. 43 916

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    黄苏春 2004 硕士学位论文(上海: 同济大学)

    Huang S C 2004 M. S. Thesis (Shanghai: Tongji University) (in Chinese)

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    黄群星, 刘冬, 王飞, 严建华, 池涌, 岑可法 2007 物理学报 56 6472Google Scholar

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6472Google Scholar

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    Lu Y G, Wang S M, Zhu Z, Lu Y, Xu Y Q 2000 Acta Opt. Sin. 20 570

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    Kazemzadeh F, Jin C, Molladavoodi S, Mei Y, Emelko M B, Gorbet M B, Wong A 2015 Opt. Lett. 40 3862Google Scholar

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    肖相国, 王忠厚, 孙传东, 白加光 2008 光学学报 37 2539

    Xiao X G, Wang Z H, Sun C D, Bai J G 2008 Acta Photonica Sin. 37 2539

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    Su L J, Zhou Z L, Yuan Y, Hu L, Zhang S Y 2015 Optik 126 877Google Scholar

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    Tian L, Waller L 2015 2015 Optica 2 104Google Scholar

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    Fahringer T W, Lynch K P, Thurow B S 2015 Meas. Sci. Technol. 26 115201Google Scholar

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    Horstmeyer R, Euliss G, Athale R 2009 IEEE International Conference on Computational Photography (ICCP) San Francisco, CA USA, April 16–17, 2009 p1

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    Prevedel R, Yoon Y G, Hoffmann M, Pak N, Wetzstein G, Kato S, Schrödel T, Raskar R, Zimmer M, Boyden E S, Vaziri A 2014 Nat. Methods 11 727Google Scholar

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    聂云峰, 相里斌, 周志良 2011 中国科学院大学学报 28 563

    Nie Y F, Xiang L B, Zhou Z L 2011 J. Grad. Univ. Chin. Acad. Sci. 28 563

    [19]

    周志良 2012 博士学位论文 (合肥: 中国科学技术大学)

    Zhou Z L 2012 Ph. D. Dissertation(Hefei: University of Science and Technology of China) (in Chinese)

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    Yuan Y, Liu B, Li S, Tan H P 2016 Int. J. Heat Mass Tran. 102 518Google Scholar

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    Li T J, Li S, Yuan Y, Liu Y D, Xu C L, Shuai Y, Tan H P 2017 Opt. Express 25 8274Google Scholar

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    Sun J, Xu C L, Zhang B, Hossain M M, Wang S M, Qi H, Tan H P 2016 Opt. Express 24 1118Google Scholar

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    Xu C L, Zhao W C, Hu J H, Zhang B, Wang S M 2017 Fuel 196 550Google Scholar

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    Sun J, Hossain M M, Xu C L, Zhang B, Wang S M 2017 Opt. Commun. 390 7Google Scholar

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    Sun J, Hossain M M, Xu C L, Zhang B 2018 Int. J. Heat Mass Transfer 121 1281Google Scholar

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    Zhao W C, Zhang B, Xu C L, Duan L B, Wang S M 2017 IEEE Sens. J. 18 528Google Scholar

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    Adelson E H, Wang J Y 1992 IEEE Trans. Pattern Anal. Mach. Intell. 14 99Google Scholar

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    程万胜, 赵杰, 蔡鹤皋 2008 光学精密工程 16 314

    Cheng W S, Zhao J, Cai H G 2008 Opt. Precis. Eng. 16 314

    [29]

    孙俊 2018 博士学位论文 (南京: 东南大学)

    Sun J 2018 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)

    [30]

    孙俊阳 2018 硕士学位论文 (南京: 东南大学)

    Sun J Y 2018 M. S. Thesis Dissertation (Nanjing: Southeast University) (in Chinese)

    [31]

    杨薇, 刘四新, 冯彦谦 2008 物探与化探 32 199

    Yang W, Liu S X, Feng Y Q 2008 Geophys. Geochem. Explor. 32 199

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    孟祥宁 2012 硕士学位论文 (成都: 成都理工大学)

    Meng X N 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)

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    孟祥宁, 钟峙, 王玉凤 2012 中国西部科技 11 33Google Scholar

    Meng X N, Zhong Z, Wang Y F 2012 Sci. Techno. of West Chin. 11 33Google Scholar

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    Chen B, Pan B 2018 Exp. Mech. 58 831Google Scholar

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    Zhou P, Zhang Y T, Yu Y L, Cai W J, Zhou G Q 2020 Math. Biosci. Eng. 17 654Google Scholar

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    牛春洋 2016 博士学位论文 (哈尔滨: 哈尔滨工业大学)]

    Niu C Y 2016 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)

  • 图 1  光场相机结构示意图

    Fig. 1.  Structure diagram of light field camera.

    图 2  模拟火焰中心切片温度分布

    Fig. 2.  Temperature distribution of simulated flame center slice.

    图 3  模拟火焰光场辐射图像

    Fig. 3.  Simulated flame light field radiation image.

    图 4  QR和阻尼LSQR算法的火焰温度场重建结果

    Fig. 4.  Flame temperature field reconstruction results of LSQR and damped LSQR algorithms.

    图 5  不同噪声水平下, LSQR与阻尼LSQR算法重建误差对比 (a)初值叠加1%噪声; (b) 初值叠加5%噪声; (c) 初值叠加10%噪声; (d) 初值叠加15%噪声; (e) 初值叠加20%噪声

    Fig. 5.  Comparison of reconstruction errors between LSQR and Damped LSQR algorithm under different noise levels: (a) Initial value superimposed 1% noise; (b) initial value superimposed 5% noise; (c) initial value superimposed 10% noise; (d) initial value superimposed 15% noise; (e) initial value superimposed 20% noise.

    图 6  阻尼LSQR-LMBC算法下重建的火焰温度分布图

    Fig. 6.  Flame temperature distribution reconstructed by Damped LSQR-LMBC algorithm.

    图 7  阻尼LSQR-LMBC算法重建的火焰温度的相对误差 (a) –16 mm位置; (b) 火焰–12 mm位置; (c) –8 mm位置; (d) –4 mm位置; (e) 0 mm位置

    Fig. 7.  Relative errors of flame temperature reconstructed by Damped LSQR-LMBC algorithm: (a) –16 mm position; (b) –12 mm position; (c) –8 mm position; (d) –4 mm position; (e) 0 mm position.

    图 8  光场相机辐射强度标定实验装置图

    Fig. 8.  Experimental deviceofradiation intensity calibration of light field camera.

    图 9  不同炉温下的黑体辐射光场图像 (a) 1098.15 K; (b) 1123.15 K; (c) 1148.15 K; (d) 1173.15 K; (e) 1198.15 K; (f) 1123.15 K; (g) 1248.15 K; (h) 1273.15 K

    Fig. 9.  Blackbody radiation light field images at different furnace temperatures: (a) 1098.15 K; (b) 1123.15 K; (c) 1148.15 K; (d) 1173.15 K; (e) 1198.15 K; (f) 1123.15 K; (g) 1248.15 K; (h) 1273.15 K.

    图 10  光场图像灰度值与辐射强度的标定拟合曲线图

    Fig. 10.  Calibration fitting curve of gray value and radiation intensity of light field image.

    图 11  燃烧火焰实验图 (a) 实验装置; (b) 丁烷火焰辐射光场

    Fig. 11.  Experimental diagram of combustion flame: (a) Experimental device; (b) light field of butane flame radiation.

    图 12  丁烷火焰三维温度重建后的不同层温度分布图

    Fig. 12.  Temperature distributions of different layers after three-dimensional temperature reconstruction of butane flame.

    图 13  使用热电偶测量丁烷火焰温度 (a) 热电偶测温实验图; (b) 热电偶定点测温位置图

    Fig. 13.  Measurement of butane flame temperature using thermocouples: (a) Thermocouple temperature measurement experiment diagram; (b) location diagram of thermocouple fixed-point temperature measurement.

    表 1  LSQR与阻尼LSQR温度重建结果相对误差对比表

    Table 1.  Comparison of relative errors of temperature reconstruction results of LSQR and Damped LSQR.

    噪声信噪比/dBLSQR阻尼LSQR
    1%45.950.43%0.41%
    5%29.442.85%2.15%
    10%21.976.66%5.10%
    15%17.3510.26%7.67%
    20%13.8614.58%10.99%
    下载: 导出CSV

    表 2  阻尼LSQR-LMBC重建温度与热电偶修正温度对比表

    Table 2.  Comparison of DampedLSQR-LMBC reconstruction temperature and thermocouple correction temperature.

    测量方法ABCD
    T/ KT/ KT/ KT/ K
    阻尼LSQR-LMBC1121.781396.731351.811077.74
    热电偶1044.351307.51295.36997.61
    下载: 导出CSV
  • [1]

    孙晓刚, 戴景民, 丛大成, 褚载祥 2003 清华大学学报: 自然科学版 43 916

    Sun X G, Dai J M, Cong D C, Chu Z X 2003 J. Tsinghua Univ., Sci. Technol. 43 916

    [2]

    黄苏春 2004 硕士学位论文(上海: 同济大学)

    Huang S C 2004 M. S. Thesis (Shanghai: Tongji University) (in Chinese)

    [3]

    Zhou B, Zhang J Y, Wang S H 2011 IET Image Process 5 382Google Scholar

    [4]

    黄群星, 刘冬, 王飞, 严建华, 池涌, 岑可法 2007 物理学报 56 6472Google Scholar

    Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6472Google Scholar

    [5]

    Gilabert G, Lu G, Yan Y 2007 IEEE Trans. Instrum. Meas. 56 1300Google Scholar

    [6]

    Hossain M M, Lu G, Sun D, Yan Y 2013 Meas. Sci. Technol. 24 074010Google Scholar

    [7]

    陆永刚, 王式民, 朱震, 徐益谦 2000 光学学报 20 570

    Lu Y G, Wang S M, Zhu Z, Lu Y, Xu Y Q 2000 Acta Opt. Sin. 20 570

    [8]

    Zhu H, Wang Q, Yu J Y 2017 Front. Inf. Technol. Electron. Eng. 18 1236Google Scholar

    [9]

    Apelt F, Breuer D, Nikoloski Z, Stitt M, Kragler F 2015 Plant J. 82 693Google Scholar

    [10]

    Fu W X, Yan F, Chen K, Ren Z J 2015 Appl. Opt. 54 6237Google Scholar

    [11]

    Kazemzadeh F, Jin C, Molladavoodi S, Mei Y, Emelko M B, Gorbet M B, Wong A 2015 Opt. Lett. 40 3862Google Scholar

    [12]

    肖相国, 王忠厚, 孙传东, 白加光 2008 光学学报 37 2539

    Xiao X G, Wang Z H, Sun C D, Bai J G 2008 Acta Photonica Sin. 37 2539

    [13]

    Su L J, Zhou Z L, Yuan Y, Hu L, Zhang S Y 2015 Optik 126 877Google Scholar

    [14]

    Tian L, Waller L 2015 2015 Optica 2 104Google Scholar

    [15]

    Fahringer T W, Lynch K P, Thurow B S 2015 Meas. Sci. Technol. 26 115201Google Scholar

    [16]

    Horstmeyer R, Euliss G, Athale R 2009 IEEE International Conference on Computational Photography (ICCP) San Francisco, CA USA, April 16–17, 2009 p1

    [17]

    Prevedel R, Yoon Y G, Hoffmann M, Pak N, Wetzstein G, Kato S, Schrödel T, Raskar R, Zimmer M, Boyden E S, Vaziri A 2014 Nat. Methods 11 727Google Scholar

    [18]

    聂云峰, 相里斌, 周志良 2011 中国科学院大学学报 28 563

    Nie Y F, Xiang L B, Zhou Z L 2011 J. Grad. Univ. Chin. Acad. Sci. 28 563

    [19]

    周志良 2012 博士学位论文 (合肥: 中国科学技术大学)

    Zhou Z L 2012 Ph. D. Dissertation(Hefei: University of Science and Technology of China) (in Chinese)

    [20]

    Yuan Y, Liu B, Li S, Tan H P 2016 Int. J. Heat Mass Tran. 102 518Google Scholar

    [21]

    Li T J, Li S, Yuan Y, Liu Y D, Xu C L, Shuai Y, Tan H P 2017 Opt. Express 25 8274Google Scholar

    [22]

    Sun J, Xu C L, Zhang B, Hossain M M, Wang S M, Qi H, Tan H P 2016 Opt. Express 24 1118Google Scholar

    [23]

    Xu C L, Zhao W C, Hu J H, Zhang B, Wang S M 2017 Fuel 196 550Google Scholar

    [24]

    Sun J, Hossain M M, Xu C L, Zhang B, Wang S M 2017 Opt. Commun. 390 7Google Scholar

    [25]

    Sun J, Hossain M M, Xu C L, Zhang B 2018 Int. J. Heat Mass Transfer 121 1281Google Scholar

    [26]

    Zhao W C, Zhang B, Xu C L, Duan L B, Wang S M 2017 IEEE Sens. J. 18 528Google Scholar

    [27]

    Adelson E H, Wang J Y 1992 IEEE Trans. Pattern Anal. Mach. Intell. 14 99Google Scholar

    [28]

    程万胜, 赵杰, 蔡鹤皋 2008 光学精密工程 16 314

    Cheng W S, Zhao J, Cai H G 2008 Opt. Precis. Eng. 16 314

    [29]

    孙俊 2018 博士学位论文 (南京: 东南大学)

    Sun J 2018 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)

    [30]

    孙俊阳 2018 硕士学位论文 (南京: 东南大学)

    Sun J Y 2018 M. S. Thesis Dissertation (Nanjing: Southeast University) (in Chinese)

    [31]

    杨薇, 刘四新, 冯彦谦 2008 物探与化探 32 199

    Yang W, Liu S X, Feng Y Q 2008 Geophys. Geochem. Explor. 32 199

    [32]

    孟祥宁 2012 硕士学位论文 (成都: 成都理工大学)

    Meng X N 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)

    [33]

    孟祥宁, 钟峙, 王玉凤 2012 中国西部科技 11 33Google Scholar

    Meng X N, Zhong Z, Wang Y F 2012 Sci. Techno. of West Chin. 11 33Google Scholar

    [34]

    Chen B, Pan B 2018 Exp. Mech. 58 831Google Scholar

    [35]

    Zhou P, Zhang Y T, Yu Y L, Cai W J, Zhou G Q 2020 Math. Biosci. Eng. 17 654Google Scholar

    [36]

    牛春洋 2016 博士学位论文 (哈尔滨: 哈尔滨工业大学)]

    Niu C Y 2016 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)

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出版历程
  • 收稿日期:  2021-08-02
  • 修回日期:  2021-09-09
  • 上网日期:  2022-02-12
  • 刊出日期:  2022-02-20

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