Research On The Inversion Algorithm Of PCS In Nano Particle Sizing Measurement Based On Regularization And Particle Swarm Algorithm

Because of its unique electricity, magnetism, force, light, heat and other properties, nanoparticles played an important role in the national economy. The characteristics of nano-particle were related to its size, so the measurement of nanoparticles was important. PCS method was an effective way to measure the particle size and distribution, and the inversion of particle size was one focus of the PCS method, which was also difficulty. In this paper, the inversion algorithm of PCS has been studied, the main research work were as follows:First, we need to solve the Fredholm integral equations of the first kind in order to get the nanoparticle sizing from the light autocorrelation function. The integral equation is the ill-posed problem. In this paper, iterative regularization method was used to inversed mo-dispersed and bi-dispersed particles at different noise levels. The inversion results indicated that the regularization of the inversion errors were 0-10% and the iterative regularization inversion error of 0 to 7% when noise level less than 0.05; when the noise level was 0.05, the regularization was no longer inverted size distribution but the iterative regularization could inverted, the single peak distribution error was less than 8% and the bimodal peak distribution error was less than 12%. In addition, the iterative regularization required the noise was larger, the number of iterations was smaller.Second, the inversion of nanoparticle size can be considered as an optimization problem. In this paper, particle swarm optimization inverted the nanoparticles. Particles inversion results of Single and bimodal peak distribution showed that:when the noise level was less than 0.05, the error is less than 10%; when the noise level were 0.05 and 0.1, the ratio of peak values much higher than the theoretical value. So that the particle size distribution deviated from the true distribution.Third, the objective function of particle swarm optimization affected the speed and accuracy of the inversion. This paper, the flattening functional as the objective function and combined with practical constraints, the particle swarm algorithm was used to invert. The inversion results showed that the particle swarm algorithm could get smooth distribution. The particle saize distribution which over concentrated on the peak was solved.Fourth, based on the L curve criterion, particle swarm optimization was used to invert the single-peak distribution and bimodal distribution of particles. The results showed that the solution were smooth, which solved the size distribution of concentration. This algorithm didn't need a regularization parameter, reducing the amount of calculation.In the PCS technique, the inversion of particle size was the main reason which affected the accuracy of particle measurement.Currently, nano-particle size distribution measurement was still constrainted the broad application of the technology. This will help the development of PCS technology.