Particle size distribution inversion using the Weibull-distribution adaptive-parameters cuckoo search algorithm

Abstract

A Weibull-distribution adaptive-parameters cuckoo search (WACS) algorithm is proposed, which can converge quickly and prevent falling into local optimal values, and thus improve the global search performance of a cuckoo search (CS) algorithm. In simulations, particle size inversions were performed using the proposed algorithm for unimodal and bimodal particle systems obeying Johnson’s SB, Rosin–Rammler, and normal distribution, and the results were compared to the original CS algorithm, Weibull-distribution CS algorithm, and adaptive-parameters CS algorithm. Among them, the WACS algorithm has the best accuracy. The relative root mean squared error (RRMSE) was three to four orders of magnitude lower than the CS algorithm. The noise immunity of the algorithm was verified by comparing the particle size inversion error. Random noise [1%, 10%] was added to the scattered light energy of the target function, in 1% noise increments. The WACS algorithm prevailed, and the advantage became more obvious as the noise increased. A small-angle forward scattering experimental platform was built, and ferric tetroxide particles were selected as the measured particles. Experimental measurements were carried out on a unimodal particle system (50 µm) and bimodal particle system (50 and 100 µm), while the WACS algorithm was used on particle size distribution inversion. Compared to the CS algorithm, the RRMSE of the WACS algorithm was approximately 51% lower on unimodal and 66% lower on bimodal particle population inversions.