Multi Objective Planck’s Minimization Optimization Method for Multispectral True Temperature Inversion
ZHANG Fu-cai1, 2, SUN Bo-jun1, SUN Xiao-gang1*, LIANG Mei1
1. School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
2. School of Electrical and Control Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China
Abstract：The spectral emissivity is an important parameter of the radiant capacity of the radiator. Through the spectral emissivity, the relationship between the radiator and the blackbody can be setup. Therefore, the theory of the blackbody radiation can be applied to the general radiator. By using the planck formula, each spectral channel of a spectral pyrometer can constitute an equation, which includes the true temperature, the brightness temperature and the spectral emissivity. There are Nmeasurement channels, but N+1 are unknowns (Nunknown emissivities εi and a temperature T). Because the equations are under determined, there are many solutions in theory. In order to solve this equation group, the assumption of mathematical model between the spectral emissivity and wavelength or temperature is required and the number of unknown numbers of the equation group is reduced to N, and then the true temperature can be solved. When the law of the spectral emissivity and wavelength or temperature is correctly obtained, the true temperature can be calculated by multispectral radiation thermometry. Through the analysis of the two commonly the spectral emissivity models, the basic idea of the two methods is to try to find the relationship between the spectral emissivity and the wavelength or the temperature and establish the mathematical model between the spectral emissivity and the wavelength or temperature. Because the spectral emissivity has certain uncertainty, the assumed spectral emissivity model is inconsistent with the variation rule of the actual the spectral emissivity, which will cause larger inversion error. The mathematical model between the spectral emissivity and the wavelength or temperature is needed a lot of experiments and experiences, and the mathematical model is poor in generality. Especially when the measured radiator is changed, the mathematical model is also meaningless. In order to solve the problem of multispectral pyrometer in actual measurement, it is an urgent need to find a multispectral true temperature inversion method which does not have to assume the mathematical model between the spectral emissivity and the wavelength or temperature. Therefore, the idea of optimization is introduced into the multispectral true temperature solution for the first time, and the problem of multispectral true temperature is transformed into a multi objective minimization optimization problem(MMP). The mathematical model between the spectral emissivity and wavelength or temperature is no longer needed, and the complexity and the difficulty of the system is reduced. Based on the planck formula and equality constrained conditions among spectral emissivities, the method constructs six objective functions and the solution of true temperature is realized. The inversion accuracy of new method is greatly improved, and the error of simulation data is less than 1%. With the aid of the actual measurement data in the past, the multi objective planck minimization optimization method is used to realize the inversion of the true temperature.
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