三波段辐射测温的存储二分法求解原理

Algorithm for Tri-Band Radiation Thermometry Using Dichotomy with Coefficients Stored(DCS)

引入线性发射率模型,基于辐射测温方程组推导了三波段辐射测温方法的等温面方程,该方程是测量信号矢量与测量信号系数矢量的点积。根据测量信号系数矢量是温度的单值函数这一特征,结合二分法求解非线性方程的优点,提出了三通道辐射测温方法的存储二分法求解原理,并进行了C++程序实现。基于C++程序研究了特定测量信号矢量条件下的等温面方程曲线,结果表明在较大的温度求解区间内该曲线具有单调特征,随着V3的增加该曲线尾部逐渐上翘由负变正。误差及时间复杂性分析结果表明二分数为Num时最大误差为(T_(max)-T_(min))/2^(num+1),求解过程包括3Num+1次乘法和2Num+1次加法,没有除法和指数对数运算,极大地提高了温度求解速度。

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 therrnometry 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 algo- rithm 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）/2^num＋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.