摘要：针对光散射颗粒测量技术中需要求解病态线性方程组的问题,通过研究正则化与矢量相似度预测算法的反演精度和抗噪性能以及这2种算法的缺陷,将这2种算法相结合,提出一种可以有效求解病态问题的自适应正则化算法。结果表明:该算法可以针对不同形态的粒径分布结果做出不同的处理,粒径分布较窄时去掉多余的小峰,粒径分布较宽时进行平滑处理,改善了反演的精度;标准颗粒测试实验证实了算法的有效性。

关键词：反演；粒径分布；矢量相似度；自适应正则化算法

Abstract：Aiming at the problem that the set of linear equations in the inversion of particle size distribution based on light diffraction was ill-posed,a self-adaptive regularization algorithm which could solve this kind of ill-posed problem effectively was proposed. The self-adaptive regularization algorithm was proposed by studying the inversion accuracy and anti-noise performance of the classical regularization algorithm and a vector similarity algorithm,studying the defects of the two algorithms and combining these two algorithms. The results show that this algorithm can make different treatments for different forms of particle size distributions.When the particle size distribution is narrow,the tiny peak is removed.Smooth treatment is made when the particle size distribution is wide. The accuracy of the inversion is improved. The effectiveness of the proposed algorithm is confirmed by a measurement of standard particles.

Keywords: inversion；particle size distribution；vector similarity；self-adaptive regularization algorithm