多光谱辐射测温的正交多项式回归方法

对于多光谱辐射测温问题，传统的数据处理方法多为最小二乘法、多元线性回归拟合和逐步回归拟合。这些处理方法自身都存在一定的缺陷，使得拟合结果与物体表面真温之间存在一定的误差。文章在可变发射率模型的基础上，提出了对多光谱辐射测温数据处理的另一种新方法——正交多项式回归方法。文章阐述了正交多项式回归的数学基础，并根据钨表面在不同温度下的光谱发射率数据，分别采用逐步回归方法和正交多项式回归方法，对钨表面的真温进行了模拟。通过拟合结果的对比发现用正交多项式回归方法来处理数据，其原理简单、运算量小，拟合结果与表面真温之间的相对误差也较小。得出的结论是用正交多项式回归方法对多光谱辐射测温的数据进行处理，拟合结果比传统方法误差小、速度快、精度高。

The Orthogonal Polynomial Regression Method of Multi-Wavelength Radiation Thermometry

For the problem of multi-wavelength radiation thermometry, the traditional data processing methods are the least squares techniques, the multiple linear regression fitting, and the stepwise regression fitting. There are some shortages in these methods, resulting in a certain error between the fitting result and the true temperature of the object surface. A new data processing method of multi-wavelength radiation thermometry the orthogonal polynomial regression method was brought forward in this article on the base of variable emissivity. The mathematic principle of orthogonal polynomial regression method was expounded and according to the surface emissivities of tungsten, the true temperature of tungsten surface was simulated by the stepwise regression method and the orthogonal polynomial regression method. By comparing the fitting results, the authors found that the orthogonal polynomial regression method has the merit of simple principle and small operation, and the relative error between the fitting result and the surface true temperature is smaller. So the authors can draw the conclusion that using the orthogonal polynomial regression method to process the data of the multi-wavelength radiation thermometry, the fitting result has smaller error, it can fit the true temperature of object faster, and the result is more accurate than the traditional data processing methods.