基于约束优化的多光谱辐射真温反演算法  

Multi Spectral True Temperature Inversion Algorithm Based on Constrained Optimization Method

作　　者：顾伟宏[1] 梁家锋 尹馨 邢键[1] 宋文龙[1] GU Wei-hong;LIANG Jia-feng;YIN Xin;XING Jian;SONG Wen-long(College of Mechanical and Electrical Engineering,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学机电工程学院,黑龙江哈尔滨150040

出　　处：《光谱学与光谱分析》2018年第12期3846-3850,共5页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(61405045;31470714);中央高校基本科研业务费基金项目(2572017DB04)资助

摘　　要：多光谱辐射测温是通过测量待测物某点的多个光谱辐射强度信息,通过普朗克公式反演获得真实温度。但是,通过普朗克公式获得的多光谱辐射测温方程组,是欠定方程组,即N个方程,N+1个未知数(N个未知的光谱发射率ελi和1个待求真温T)。目前,多采用事先假设一组发射率模型(发射率-波长或发射率-温度模型),假设模型与实际情况如果相符,则反演结果能够满足要求,如果假设模型与实际情况不符,则反演结果误差很大。但是,发射率模型受温度、表面状态、波长等诸多因素影响,难以事先确定发射率模型。因此受未知光谱发射率的制约一直是多光谱辐射测温理论面临的主要障碍,能否在无需任何光谱发射率假设模型的情况下,实现真温和光谱发射率的直接反演一直是多光谱辐射测温理论研究的热点和难点。通过对参考温度模型的分析表明,多光谱辐射测温反演过程的实质是寻找一组光谱发射率,使得每个通道方程解得的真温都相同,如不相同则继续寻找合适的光谱发射率,直到每个通道解得的真温都相等。为此,提出将多光谱辐射测温参考温度模型的求解过程转换为约束优化问题,即在光谱发射率0≤ελi≤1的约束条件下,通过梯度投影算法不断寻找光谱发射率,带入多光谱辐射测温参考温度模型方程组后,计算温度反演值的方差,直到每个光谱通道方程获得的温度值应该近似相等,此时各个光谱通道的温度反演值方差最小,这样就把多光谱辐射真温和发射率的反演问题转换为约束优化问题。约束优化算法是解决这一类问题的主要方法,但为了满足Ax≥b的约束条件,将0≤ελi≤1分解为ελi≥0和-ελi≥-1的两个约束条件,从而满足了约束优化问题Ax≥b的约束条件。这样就可以通过约束优化算法在无需任何光谱发射率假设模型的条件下,直接求解真温和光谱发射率。实�Multi-spectral radiation thermometry is a method for obtaining true temperature inversion by Planck formula by measuring a number of spectral radiant intensity information of a point to be measured.However,the multi-spectral radiation thermometry equations obtained by the Planck formula are the underdetermined equations,that is,N equations,and N+1 unknown(N unknown spectral emissivityελi and a waiting true temperature T).At presen t,a set of emissivity models(emissivity-wavelength or emissivity-temperature model)are often assumed.If the assumed model is consistent with the actual sit uation,then the inversion results can meet the requirements,and if the assumed model does not match with the actual situation,the inversion result will have very large errors.The emissivity model is affected by many factors,including temperature,surface state,wavelength and so on.It is difficult to de termine the emissivity model in advance.Therefore,the restriction of unknown spectral emissivity has been the major obstacle to the theory of multi-spectra l radiation thermometry.The direct inversion of true temperature and spectral emissivity without any assumption of spectral emissivity has always been a hot and difficult issue in the theory of multi-spectral radiation t thermometry.Through the analysis of reference temperature model,the essence of multispec tral radiation thermometry inversion is to find a set of spectral emissivity,s o that the true temperature of each channel equation is the same,if different,we’ll continue to find the appropriate spectral emissivity,until the true temperat ure of each channel is equal.Therefore,it is proposed to convert the solving process of the multi-spectral radiation thermometry reference temperature model into a constrained optimization problem.That is,under the constraint of spectral emissivity 0≤ελi≤1,the spectral emissivity is constantly searched through the gradient projection algorithm.After taking the emissivi ty into the multi-spectral radiation thermometry reference tempera

关 键 词：多光谱辐射测温 发射率 约束优化 梯度投影 

分 类 号：TK3[动力工程及工程热物理—热能工程]