基于局部最小的彩虹信号反演算法

Inversion Algorithm of Rainbow Signal Based on Local Minimum

针对标准/全场彩虹信号的反演处理,提出一种基于局部最小的通用性反演算法。该算法基于带修正系数的复角动量理论建立了带不等式约束的非线性最优化目标函数,并采用序列二次规划法对最优化目标函数进行迭代求解。反演前针对标准/全场彩虹信号进行不同的预处理,如去除高频结构、预估反演参数范围等。基于Lorentz-Mie理论对不同折射率和粒径分布(对数正态分布和正态分布)的液滴彩虹信号进行数值模拟,并对有/无粒径的预设分布进行反演,验证了该算法的有效性。结果表明:标准彩虹折射率反演最大绝对误差小于3×10^(-4),最大粒径相对误差为1.3%;各种工况下,全场彩虹反演折射率误差均小于1×10^(-4),平均粒径相对误差小于1.67%。最后对该算法进行了标准和全场彩虹实验数据的验证。

For a parametric inversion of standard or global rainbow signals,this study proposes a local minimabased general inversion algorithm,establishes a nonlinear optimized objective function with inequality constraints based on the complex angular momentum theory theory with correction coefficients and iteratively solves the function using sequential quadratic programming.Before the inversion,a different signal preprocessing,including the removal of the highfrequency structure and the inversion parameter range estimation,was performed for the standard and global rainbow signal.The rainbow signals of the droplets with different refractive indices and droplet size distributions(logarithmic and normal distributions)were numerically simulated based on the Lorenz-Mie theory.The proposed inversions with or without the size distribution were performed to verify the algorithm's effectiveness.The results show that the maximum absolute error of the refractive index of the standard rainbow signal inversion is less than 3×10^(−4),and the maximum relative error of the droplet size is 1.3%.Under various conditions,the error of the refractive index of the global rainbow signal inversion is less than 1×10^(−4),and the relative error of the mean droplet size is less than 1.67%.Finally,the algorithm was verified via the experimental standard and global rainbow data.