由 Mie 散射光强反演颗粒粒度分布的一种改进正则化法

基于Mie散射的激光粒度仪广泛地应用在颗粒粒度测量中,其中由光强分布演算出粒度分布的计算方法一直是关注的热点。此反演问题属于第一类Fredholm算子方程,具有不适定性,难以得出准确的稳定解,需要用高效的数值算法。本文提出一种应用于该类仪器颗粒粒度分布反演问题的改进正则化法,采用广义交叉验证法(GCV)来选择正则参数,并引入松弛技术,将迭代值加工成一种松弛值以改善精度,得出了稳定的正则拟解(近似解)。经标准颗粒的验证和计算机模拟证实,此算法是可行和有效的。

Modified regularization method applied to the inversion of particle size distribution from light scattering data

Laser particle size analyzer is one of the instruments for particle size analysis. Recent developments focus on various algorithms for particle size analysis via light energy distribution based on the Mie scattering theory in the laser analyzer. The determination of the particle size distribution (PSD) from the analyzer requires the inversion of the Fredholm integral equation of the first kind. This equation is an ill-posed one, which can be analyzed by effective algorithms. This paper presents a modified regularization method applied to the inversion of the PSD with the independent models. The Generalized Cross-Validation (GCV) method was used for the selection of a regularization parameter. The Successive Over-Relaxation (SOR) iterative method was applied to improve the exactness and stability of the convergent result. The simulation with the models was carried out. The simulated results are in a good agreement with the data measured from nine standard particulate samples as well as their mixtures. It is indicated that this method can be feasible and effective for the simulation of the PSD from the corresponding light scattering data.