Study On The Inversion Of Dynamic Light Scattering Noise Data Based On Improved Regularization

Submicron and nanometer ultrafine particles have unique properties in optics,electricity,magnetism and other aspects,which can effectively improve the performance of products and the quality of materials,and have been widely used in industrial production and People's Daily life.The properties of ultrafine particles depend on the particle size to a great extent,so the particle size detection research has very important theoretical research and practical application value.Dynamic light scattering technology,as an effective method for measuring the particle size of ultra-fine particles at present,can obtain the particle size information by retrieving the dynamic light scattering data.In the process of retrieving the data,Fredholm integral equation of the first class needs to be solved.However,Fredholm equation of the first type is a typical pathological equation,and the noise part in the dynamic light scattering data will be greatly amplified,resulting in the measurement result being far from the real result.Therefore,it is still worth exploring how to obtain accurate particle size information from dynamic light scattering noisy data under the condition that measurement data is inevitably disturbed by noise.In order to accurately retrieve particle size information,the regularized inversion method for dynamic light scattering noisy data is studied in this article.The main innovation points and research work are as follows:Firstly,the influence of regular parameters determined by posterior strategy under unknown error on inversion results is studied.In this article,on the basis of determining that bat algorithm has a good operational efficiency,bat algorithm is combined with Morozov deviation principle to achieve global optimization of regular parameters under error determination and unknown error.In addition to reducing the waste of traditional iterative algorithm computing resources,the results of regularized inversion particle size are compared and analyzed.The results show that after bat algorithm is introduced,the particle size results of inversion under unknown error are similar to the particle size results under error determination,making it possible for Morozov deviation principle to be applied in the actual detection of particle size where error parameters cannot be determined.Secondly,the influence of the singular value three-stage correction algorithm on the inversion results is studied.In order to obtain accurate particle size information from noise data of dynamic light scattering,an improved regularization algorithm is proposed by combining Tikhonov regularization algorithm and TSVD regularization algorithm on the basis of singular value decomposition theory.In this algorithm,the matrix is decomposed into three parts according to the truncation and correction positions of singular values and processed by different filter functions respectively.By comparing and analyzing the particle size results of Tikhonov and TSVD regularization algorithm,it is determined that the inversion results of the new algorithm have higher fitting degree,better accuracy and noise resistance.Finally,the influence of initial matrix model on TSVD regularized inversion is studied.In order to regularize truncated singular value to obtain more particle size information,this paper,on the basis of TSVD algorithm,preserves the large singular value partial matrix unchanged,and modifies the small singular value partial matrix under the conditions of the flattest model matrix,the smoothest model matrix and the minimum model matrix respectively.By comparing and analyzing the results of particle size inversion under three initial model matrices,the influence of different initial model matrices on the results of TSVD algorithm inversion is determined.