Research on bat algorithms for inversion of particle size distribution in spectral extinction method

Abstract

The development of rapid and effective inversion algorithm is an important subject in the field of particle size distribution (PSD) measurement. An intelligent bat algorithm has been proposed to solve the problem of independent mode inversion in particle size distribution reconstruction based on spectral extinction method. The improved algorithm is more suitable for particle size distribution inversion under extinction method by enriching its behavior mode, improving local search mode and adding greedy strategy. In simulations, uniform spherical particles that obey the unimodal, bimodal and multimodal R-R distribution were used, and the scattering intensity values of the target function was added to the random noise of ±0%, ±3%, ±5%, ±8% respectively. In the inversion calculation of the improved bat algorithm, 400, 800 and 1000 iterations were performed for different distributions, respectively. Compared with modified pattern search method, the improved bat algorithm has strong noise resistance, moderate inversion time, independent of initial solution and high inversion accuracy for complex distribution. Compared with genetic algorithm, the improved bat algorithm has fast convergence speed, high accuracy and short time-consuming. Considering the practical application, the algorithm is suitable for field measurement and has a wide application prospect.

Inversion method of particle size distribution of milk fat based on improved MPGA

“…To avoid errors, the ratio of the first result and the second result was processed and calculated by the computer as the extinction value ( Wang, 2013 ). The excitation experiment was repeated for 20 times on the simulated liquid of milk fat particles with lasers of different wavelengths, and the average of the results was taken as the final light intensity ( Cai et al, 2010 ; Wang, 2013 ; Wang and Sun, 2013 ; Ding et al, 2020 ).…”

“…The sum of infinite series was considered when we calculated the extinction coefficients using Mie scattering theory. The sum upper limit was usually derived by the empirical formula of Wiscombe ( Wang, 2013 ; Wang and Sun, 2013 ): …”

“…There were S types of particle size distribution to be solved, and they were measured using multiple wavelengths. As a result, the linear equation set was obtained ( Wang, 2013 ; Wang and Sun, 2013 ): Where: ; U was the wavelength; and indicated the weight matrix, with all the elements expressed as: ; .…”

“…According to Wang Li’s finding, the method of using regularization to build objective function and establish an improved mode searching model showed a good inversion performance. She also proposed using generalized eikonal approximation to effectively calculate the coefficient of light extinction for measuring the particle size ( Wang, 2013 ; Wang and Sun, 2013 ). Based on angular scattering method, Mroczka et al measured particle size distribution using regularization least squares algorithm with constraints.…”

“…This research suggests an enhanced MPGA based on the total light scattering approach to address these issues. It simplifies the objective function using Tikhonov smooth function ( Wang and Sun, 2013 ) and reduces ill conditions of the inversion equation. Based on the extinction spectra calculated by known specific parameters, an inversion algorithm is built to generate a more precise particle size distribution.…”