Regularization Parameters Selection In Regularization Inversion Of Dynamic Light Scattering

Dynamic light scattering technology is an effective method for measuring submicron and nanoparticles.It obtains the particle size and its distribution by retrieving the light intensity autocorrelation function.In the inversion process,it is necessary to solve the first kind of Fredholm integral equations,which is a typical ill-posed problem,and is usually solved by Tikhonov regularization method.When the Tikhonov regularization method is used to solve ill-posed problems,proper regular parameters are needed to balance the solution error and residual error of the objective function and to minimize the sum of errors.The selection of regular parameters has always been the focus and difficulty of Tikhonov regularization methods.In order to select appropriate regular parameters to better balance the solution error and residual error of the objective function and improve the accuracy of particle size inversion,this paper explores the mechanism of regular parameters in the dynamic light scattering regularization inversion.The influence of L-curve criterion on particle size inversion error,and a multi-parameter method based on singular value distribution is proposed for dynamic light scattering regularization inversion,and the inversion performance of each method is analyzed and compared.The main research contents of this article include:1. The mechanism of regularization parameters in dynamic light scattering regularization inversion is studied.The influence of regular parameter selection on the accuracy of regularization method for ill-posed problems is analyzed.In the process of using the regularization method to solve the ill-posed problem,the error is mainly composed of two parts,one is the solution error caused by the error of the input data,and the other is the error generated by the regularization operator to approximate the discontinuous operator at the precise measurement data.,Due to the error of the input data,the solution error is larger when the regular parameter is small,but the error generated by the regularization operator to approximate the discontinuous operator at the precise measurement data is small when the regular parameter is small,so the regularization parameter The choice of must maintain a certain balance between the two errors.On the one hand,the stability of the approximate solution to the error of the input data requires that the regular parameter should not be too small.On the other hand,the approximation of the regularization operator to the discontinuous operator requires that the regular parameter should be as small as possible.The sum of these errors is the smal est.2. Adopt three regular parameter selection methods of L-curve criterion,GCV criterion and Morozov deviation principle to perform regularized particle size inversion on multi-angle dynamic light scattering data of different particle systems.The results show that the peak position of the inversion results of the three regular parameter selection methods using the L-curve criterion,GCV criterion and Morozov deviation principle under the condition of low noise level(noise level of 10^-5)has no significant difference.As the noise level increases,the error of the peak position of the regularization inversion results of the three regular parameter selection methods becomes larger,but the result of the L-curve criterion is more stable and has the best anti-noise performance.3. Study the influence of L-curve criterion on the peak position error and fitting error of different particle systems in the dynamic light scattering regularization inversion.Since the L-curve criterion considers the effects of residual errors and solution errors when selecting regular parameters,in actual dynamic light scattering measurement,more attention is paid to the peak position error and fitting error.Therefore,the L-curve criterion is used to select the regular parameters.On the basis,by delimiting an interval containing the regularization parameter and giving a step size,each regularization parameter obtained from the loop is subjected to multi-angle dynamic light scattering regularization inversion to obtain the peak position error and fitting in the inversion results Error,comparing the L-curve criterion with the inversion of other regular parameters in the interval to obtain the difference between the peak position error and the fitting error shows that the L-curve criterion is more accurate for the peak position of the single-peak narrow distribution particle system,for the single-peak width distribution and double The peak position error of the peak distribution is large.4. Research on optimized multi-parameter dynamic light scattering regularization particle size inversion based on singular value distribution characteristics.Multi-parameter regularization can improve the phenomenon of over-regularization or under-regularization in the dynamic light scattering regularization inversion results.Based on the analysis of singular value distribution characteristics,this paper proposes a multi-parameter selection method based on singular value distribution characteristics.Construct the regular parameter function through the proportional relationship between two adjacent singular values for the initial selection of parameters,and then use fixed-point iteration to optimize the parameters to obtain the regular parameter sequence corresponding to the singular value distribution,thereby suppressing the noise caused by small singular values of magnification.The selection of regular parameters has always been a difficult point in the dynamic light scattering regularization inversion of particle size distribution,and it has also been a research hotspot in recent years.The accuracy of the system's dynamic light scattering regularization inversion,which in turn meets the social needs of increasing measurement accuracy for different particle systems.