Tikhonov正则化与多重网格技术相结合的动态光散射反演

针对单尺度反演方法中存在的精度偏低问题,结合Tikhonov正则化与瀑布型多重网格技术,提出了一种多尺度Tikhonov正则化(ML-TIK)动态光散射反演方法.该方法利用多重网格技术将原反演问题分解到多尺度的网格空间,按着网格从粗到细的顺序,采用单尺度Tikhonov正则化(TIK)对每个子反演问题进行求解,获取颗粒的粒度分布.分别采用TIK和ML-TIK法对噪声水平为0、0.005、0.01的200～650 nm模拟双峰分布颗粒数据进行了反演.结果表明:ML-TIK法的反演结果与理论分布吻合,平滑性更好;相对于TIK法,ML-TIK法最多可减少粒径峰值误差8.19％,粒径反演误差0.448 2；而TIK法在噪声水平为0.005、0.01时,反演结果双峰特征不明显.因此,ML-TIK方法的反演精度更高、抗干扰能力更强.最后,用60 nm与200nm实测数据的反演结果验证了该结论.

Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique

For the low accuracy of single-level inversion methods to dynamic light scattering,a novel Multi-level Tikhonov regularization inversion(ML-TIK) method combining the Tikhonov regularization method with cascadic multi-grid technique was developed.Firstly,this method divided the original problem into several sub-inversion problems with different grid spaces by a multi-grid technique.Then,from the coarsest scale to the finest scale,each sub-inversion problem was inverted by single-level Tikhonov regularization(TIK) method.Finally,the Particle Size Distribution(PSD) was successively obtained by solving several sub-inversion problems.This method effectively reduces the ill-condition of the original equations.At noise levels 0,0.005 and 0.01,the simulation data of 200~650 nm bimodal distribution particles were respectively inverted by the TIK and ML-TIK.The results indicate that the inversion PSD of ML-TIK is more consistent with that of the theoretical one and it has better smoothness.Comparing to TIK,the ML-TIK can reduce the peak value error by 8.19% and relative error by 0.448 2.However,when the noise level is 0.005 and 0.01,the PSD of TIK has not obvious bimodal features.Therefore,the ML-TIK has improved the inversion accuracy and noise immunity.Inversion results of 60 and 200 nm experimental data verify above conclusions.