非负迭代截断奇异值纳米颗粒粒度分布反演算法

Nonnegative Iterative TSVD Inversion Algorithm for Nanoscale Particle Sizing

截断奇异值分解法能够反演纳米颗粒的粒度分布，但通常难以确定其最优截断参数。在分析截断奇异值算法的基础上，提出非负迭代截断奇异值算法来获取纳米颗粒的粒度分布，并对选取截断参数的L-曲线准则进行了修正。实验结果表明，利用二次截断L-曲线准则选取最优截断参数，使用非负迭代截断奇异值反演算法，能准确地表征单峰分布的颗粒粒径大小及粒径分布，所求平均粒径相对误差小于3％。

Nanoscale Particle size distribution can be inverted by truncated singular value decomposition （TSVD） method. However, it is difficult to select the optimal truncated parameter. Based on the analyzation of TSVD method, we present a nonnegative iterative truncated singular value decomposition （NNI-TSVD） method for obtaining the particle size distribution of nanoscale particle suspensions from dynamic light scattering data. Furthermore, we modify the L-curve criterion for choosing the optimal truncated parameter. Experimental data show that with the NNI-TSVD method, its optimal truncated parameter selected by the second truncated L-curve criterion, can be employed to accurately get the average size and size distribution of unimodal suspensions. The relative error of the inverted average diameter is less than 3 %.