Algorithm for Tri-Band Radiation Thermometry Using Dichotomy with Coefficients Stored (DCS)
SHEN Yun-wei1，XIN Cheng-yun1*，DAI Jing-min2
1. School of Electric Power Engineering, China University of Mining and Technology, Xuzhou 221116, China 2. School of Electrical Engineering and Automation, Harbin Institute of Technology，Harbin 150001, China
Abstract：The isothermal surface equation of tri-band radiation thermometry with linear emissivity model has been deduced, based on tri-band radiation measurement equations. The isothermal surface equation is the point multiplication of measurement signal vector and measurement signal coefficient vector. The solution algorithm for tri-band radiation thermometry defined as dichotomy with coefficients stored in this paper has been developed because of the characteristics of measurement signal vector which is only the function of temperature and the advantage of dichotomy in solving non-linear equation. And the solution algorithm has been achieved by C++ program. The curves of isothermal surface equations at specific measurement signal vectors have been investigated and the results show that the curves are monotone at a greater range of temperature and the tail of curves tend to be positive from minus with the increase of V3. The analyses of error and time complexity have been carried out and the results show that the maximum error is (Tmax-Tmin)/2num+1 when the number for the solution algorithm is Num, and there are about 3Num+1 multiplication and 2Num+1 addition in every dichotomy process without division and logarithm, which can crease the solving rate dramatically.
Key words：Color temperature measurement;Primary spectrum pyrometry;Solving;Tri-band
[1] Coates P B. Metrologia，1981，17： 103. [2] Weng K H, Wen C D. Int. J. Heat Mass Tran., 2011, 54: 4834. [3] SUN Xiao-gang, DAI Jing-min, CONG Da-cheng, et al(孙晓刚，戴景民，丛大成, 等). J. Infrared Millim. Waves(红外与毫米波学报)，1998，17： 221. [4] Yang C L, Dai J M, Hu Y. Chin. Phys. Lett., 2003, 20: 1685. [5] Fu T R, Zhao H, Zeng J, et al. Appl. Optics, 2010, 49: 5997. [6] Fu T R, Zhao H, Zeng J, et al. Rev. Sci. Instrum.，2010，81： 124903. [7] DAI Jing-min, SUN Xiao-gang, LU Xiao-dong, et al(戴景民，孙晓刚，卢小冬，等). Theory and Practice of Multi-Spectral Thermometry(多光谱辐射测温理论与应用). Beijing: Higher Education Press(北京： 高等教育出版社)，2002. 4. [8] CAO Peng-tao, ZHANG Qing-chuan, FU Shi-hua, et al(曹鹏涛，张青川，符师桦，等). Acta Phys. Sin.(物理学报)，2010, 59: 458. [9] Dubrov A V, Dubrov V D, Zavalov Y N, et al. Appl. Phys. B-Lasers Opt., 2011, 10: 5537. [10] CHENG Xiao-fang, ZHOU Zhou(程晓舫，周 洲). Sci. China Ser. E(中国科学E辑)，1997，27： 342. [11] Cheng X F, Fu T R, Fan X L. Sci. China Ser., 2005, G48: 142. [12] Fu T R, Cheng X F, Zhong M H, et al. Meas. Sci. Technol.，2006，17： 2751. [13] Incropera F P, DeWitt D P, Bergman T L, et al. Fundamentals of Heat and Mass Transfer(传热和传质基本原理). 6th ed.(六版). Translated by GE Xin-shi, YE Hong(葛新石，叶 宏，译). Beijing: Chemical Industry Press(北京： 化学工业出版社)，2007，445.
