Non-negative differential evolution for particle sizing from ultrasonic attenuation spectroscopy

Abstract Ultrasonic attenuation spectroscopy (UAS) is a potentially characterising technique for nano-meter size materials. It is the inversion of the ultrasonic attenuation spectrum to particle size distribution (PSD) by using an optimisation technique. Because the particle size is non-negative number, the inversion has to be optimised in non-negative real number domain. However, many optimisation techniques have traditionally added the non-negative constrain into a cost function as a result the function becoming complex. In this article, the modification of the differential evolution (DE) technique has been proposed to narrow the searching solution domain is in the non-negative real number domain. An absolute function has been add to a mutant vector of the DE technique to guarantee the solution is non-negative real number. This technique is called DE-Nonneg technique. The technique has been demonstrated by characterising size of silica suspension. The optimisation results show that the PSD predictions are comparatively to simulated annealing (SA) technique. Moreover, the performance of DE-Nonneg could be improved via adjusting the parameters (expanding factor, cross over, number of parameters and mutation type) following the guideline addressed here. In addition, it is also possible to predict the PSD without using the structural PSD model. With this advantage, DE-Nonneg could possibly be applied for other non-negative optimisation problems.