结合条件预优的流动气溶胶动态光散射正则化反演

Regularization Inversion with Preconditioner for Flowing Aerosols in Dynamic Light Scattering

为提高流动气溶胶动态光散射粒度反演的准确性,采用结合条件预优的流动气溶胶正则化反演,通过条件预优处理,以先验流速信息和延迟时间构建对角阵形式的条件预优矩阵,对病态方程实现乘法修正,从而降低了流速对反演方程病态性的加剧作用和正则化方法对流速的敏感性。模拟与实测数据的反演结果表明,与Tikhonov正则化反演相比,结合条件预优的Tikhonov正则化反演,可克服正则化在流动颗粒粒度反演中的局限性,显著改善了流动气溶胶动态光散射测量数据的反演性能指标,提高了正则化反演结果的准确性。

Dynamic Light Scattering(DLS)is a technique for submicron and nano Particles Size Distribution(PSD)measurement.With convenience and rapidity and no interference to the measured particle system,it is widely used in science and engineering.Generally,the DLS measurements are carried out with nonflowing samples in suspension,in which particles move only in the form of Brownian motion.In this situation,the fluctuations of scattered light of particles are only caused by the Brownian motion.Different from the DLS measurement of non-flowing particles in suspension,the translational motion of flowing particles leads to extra fluctuations of scattered light,making DLS measurement for flowing aerosols more difficult.The key of flowing aerosol measurement is that the PSD is difficult to accurately recover,because the increase of velocity aggravates the ill-conditioned state of the inversion equation,which is manifested as the increase of the condition number of the kernel matrix.Regularization is a common equation.However,the effectiveness of regularization is restricted by increasing the velocities of flow particles.To solve this problem,in this paper,the inversion equation was preconditioned to reduce the condition number of the kernel matrix before the Tikhonov regularization was used,which significantly improved the accuracy of recovered PSDs for flowing particles.To verify the effectiveness of the proposed method,the recovered PSDs of the 600 nm unimodal aerosols and 200 nm/700 nm bimodal aerosols with different velocities were simulated.The results show that the peak position error(E_(P))and the distribution fitting error(E_(F))of recovered PSDs become significant as the flowing velocity increases,which is represented that the particle size at the peak position is smaller than the true value and the distributions are wider than true distributions.Under the same flowing velocity,the recovered PSDs by preconditioned Tikhonov regularization(Pre-Tik)are closer to the true PSD than Tikhonov regularization(Tik).And the effect of preconditioning is increasingly obvious with the flow velocity increase.When the particle velocity is 2.0 m/s,the E_(P)and E_(F)of the PSD obtained by the Tik is0.0467 and 0.0069 respectively,and by the Pre-Tik is 0.0267 and 0.0057 respectively.The simulated inversions of the 200 nm/700 nm bimodal PSDs show similar results in the particle size at both peaks position and the width of distribution,which results in the value of E_(P)s and E_(F)s rising.However,the performance indices of the inversion results of the two methods were quite different.When the flowing velocity is 2.0 m/s,the E_(P)and E_(F)of the PSD obtained by the Tik method are 0.6600/0.2743 and 0.0121 respectively,while the E_(P)and E_(F)of the PSD obtained by the Pre-Tik method are 0.4600/0.0914 and 0.0091 respectively.The accuracy of the recovered PSDs is improved by using the Pre-Tik method.To further compare the performance of the Tik method and the Pre-Tik method,DLS experiments of flowing aerosols were carried out.The measured ACF data were obtained from a homemade DLS measurement platform for flowing aerosols.For unimodal flowing aerosols at 1.77 m/s,the E_(P)and E_(F)of PSDs reduced from 0.0877 and 0.0124 by using the Tik method to 0.0526 and 0.0086 by the Pre-Tik method.The recovery of the latter method is better than the former.For bimodal aerosol PSDs,the results are similar to unimodal aerosol PSDs.The E_(P)s and E_(F)s of the PSD recovered by the Pre-Tik method are smaller than those obtained by the Tik method,which agrees with the simulations.The inversion results of simulated and experimental data show that the limitations of the regularization method in DLS measurements of flowing particles can be broken through by preconditioning.In this paper,the preconditioner in the form of a diagonal matrix constructed with priori velocity and delay time can weaken the ill-condition state of the inversion equation and makes regularization less sensitive to velocities.Compared with the Tikhonov regularization,the preconditioned Tikhonov regularization can improve the inversion performance significantly for flowing aerosols in DLS measurement.