非负最小二乘约束的加权贝叶斯反演算法研究  

Research on Weighted Bayesian Inversion Algorithm with Non-negative Least Squares Constraint

作　　者：梁一卓 刘玲 彭力[1,2] 邱健 骆开庆[1,2] 刘冬梅 韩鹏[1,2] LIANG Yi-zhuo;LIU Ling;PENG Li;QIU Jian;LUO Kai-qing;LIU Dong-mei;HAN Peng(School of Physics and Telecommunication Engineering,South China Normal University,Guangzhou 510006,China;Guangdong Provincial Engineering Research Center for Optoelectronic Instrument,Guangzhou 510006,China)

机构地区：[1]华南师范大学物理与电信工程学院,广州510006 [2]广东省光电检测仪器工程技术研究中心,广州510006

出　　处：《光子学报》2020年第10期210-220,共11页Acta Photonica Sinica

基　　金：国家自然科学基金(No.61975058);广东省自然科学基金(No.2019A1515011401);广州市科技计划(Nos.201704020137)。

摘　　要：在多角度动态光散射纳米颗粒粒度分析反演算法中,加权贝叶斯算法具有较好的抗噪性能,然而初值敏感、耗时长等缺点限制了其广泛应用,本文提出非负最小二乘约束下的加权贝叶斯反演算法,利用非负最小二乘法的计算结果作为加权贝叶斯算法先验初值,并限制中值粒径和峰宽的寻优.对不同分布宽度的单峰颗粒系统在不同噪声下进行数据模拟,发现无论是宽分布还是窄分布的单峰颗粒系统,非负最小二乘约束的加权贝叶斯算法都可以显著提升迭代收敛速度和抗噪性能,在大噪声时收敛速度提升8倍以上且保证分布误差在0.0709以内.实验结果证明本文算法能很好地应用于多角度动态光散射的粒度分析.In the multi-angle dynamic light scattering for nanoparticle size analysis,the weighted Bayesian inversion algorithm is proved to have a good anti-noise capability.However,it suffers from initial value sensitivity and long time-consuming.This paper presents a method of non-negative least squares constrained weighted Bayesian inversion algorithm,in which the results of the non-negative least squares method are used as the prior value as well as the optimization range of the median diameter and peak width of the weighted Bayesian algorithm.The simulated and experimental results demonstrate that this method can improve significantly the convergence and the anti-noise performance of the unimodal particle system.When there is a big noise,the convergence speed is increased by more than 8 times and the distribution error is guaranteed to be within 0.0709.

关 键 词：多角度动态光散射 光强自相关函数 非负最小二乘法 加权贝叶斯算法 粒度分布 

分 类 号：O436.2[机械工程—光学工程]