Monte Carlo Extinction Model and Inversion Method for Mixed Particle System
For a single-type particle system,the particle sizing model vialight extinction spectroscopy is generally established based on Mie scattering theory and Lambert-Beer law.However,the extinction characteristic of mixed particles composed of various types of particles is becoming rather complicated,whereby particle size and mixing ratio can make a combined contribution to the extinctionspectrum.Thus,a novel extinction model of mixed particles with the Monte Carlo method has been proposed,in which theincident lightbeamis assumed as discrete photons to account for the photon destinations and explore the extinction characteristics of the mixture by tracking all events experienced by photons from emission,reception to escape.The extinction spectra of the single-particle system with polystyrene and glass beadswere computed numerically,respectively.The resultshowsa 2％errorafter being compared with the extinction spectrum predicted by the Lambert-Beer law.The model was then extended to the mixed particle system consisting of polystyrene and glass beads.The extinction spectrum of the mixturecan be observed to increase sequentially with the growing proportion of glass beads(mixing ratio)until it is eventually converted into a single-particle system as the mixing ratio approaches 100％.When the wavelength reduces,the extinction value changes from linear to nonlineargrow th with the increase in mixing ratio,and the greater the difference in particle extinction characteristics,the more obvious the nonlinear trend.It can be interpreted that the extinction value of the mixture is determined by the particle type,mixing ratio,particle size,and light wavelength,and their contributions are coupled with each other.With the computed light extinction spectra,three global optimization algorithmswere employed to implement inversions of mixed particle size and/or mixing ratio,which yields the relative errors of mixing ratio all within 1.5％in the single parameter inversion cases.When performing a two-parameter inversion for particle size,the relative errors for two types of particlesare less than 3％.As to simultaneous inversion for two particle sizes and mixing ratio,the relative errors can obviously increase but do not exceed 10％.Regarding the three inversion algorithms,the PSO algorithm takes several times longer than other algorithms for each inversion,and the IGA has greater results from accuracy to stability.Through the preliminary verification of this work,the Monte Carlo-based model can be applied to predict the light extinction of mixed particle systems,and the simultaneous inversion of the mixing ratio and the two particle sizes in particle systems can be realized.
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