多目标普朗克极小值优化法的多光谱真温反演研究
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摘要
光谱发射率是辐射体辐射能力的重要参数,通过光谱发射率可以建立辐射体与黑体的之间的桥梁,从而黑体辐射的相关理论就可以应用于辐射体。采用普朗克公式,光谱高温计的每一个光谱通道可以构成一个方程,这个方程中包含有真温、亮度温度和光谱发射率。对于N个光谱通道可以构成N个方程,这N个方程中也包含一个真温、N个亮度温度和N个光谱发射率,其中亮度温度是已知量,真温和光谱发射率是未知量。由于方程组是欠定的,理论上存在着大量的解。为了求解这个方程组常需要假设光谱发射率与波长和温度之间的数学模型,使方程组未知数的个数降为N个,实现真温的求解。当光谱发射率与波长或温度之间的规律被正确获得后,多光谱辐射测温法才能反演出正确的真温。通过对上述较为常用两种光谱发射率模型的分析可知,这两种方法的基本思想都是试图找到光谱发射率与波长或温度之间的函数关系,确立光谱发射率与波长或温度之间数学模型。用含有波长或温度的表达式代替光谱发射率,实现方程的求解。由于光谱发射率具有一定的不确定性,假设的光谱发射率模型与实际光谱发射率的变化之间存在一定的差异,有可能导致真温反演产生较大的误差。光谱发射率与波长或温度之间的数学模型是需要通过大量的实验和经验才能获得的,而且这种数学模型通用性较差,尤其是当待测辐射体发生改变时,这种数学模型也就失去了意义。为了解决多光谱高温计在实际测量中存在的问题,找到一种无需假定光谱发射率与波长或温度之间数学模型而且又具有一定通用性的多光谱真温反演方法成为一种迫切的需要。为此,将优化的思想引入到了多光谱求解过程中,将多光谱真温的求解问题转化为多目标普朗克极小值优化(MMP)问题,从而不再需要建立光谱发射率与波长或温度之间的数学模型,降低了系统的复杂性与难度。该方法以普朗克公式和光谱发射率之间的等式约束条件为基础,构造了六个目标函数,实现了真温的求解。新方法在反演精度上得到了较大幅度的提高,仿真数据的误差都小于1%。借助于以往的真实测量数据,利用多目标普朗克极小值优化法实现了真温的反演。
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 ε_i 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.
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 ε_i 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.
引文
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