Dynamic light scattering inversion based on Tikhonov regularization and parameter-optimized generalized regression neural network

Neural network technology shows certain superiority in the field of dynamic light scattering (DLS) inversion. However, due to the complex problems of training sample and parameter selection, its application has certain limitations. At present, it has not been applied to the inversion of bimodal particle size distribution (PSD). Aiming at training sample generation and smoothing parameter optimization of generalized regression neural network (GRNN), a DLS inversion method combining Tikhonov regularization and parameter-optimized GRNN (Tikhonov-PGRNN) is proposed. In this method, the PSD of Tikhonov regularization inversion is used as prior information to generate the training samples, the one-dimensional search method is used to obtain the optimal smoothing parameter, and the normalized field autocorrelation function data is input into GRNN to estimate the PSD. Simulated data for narrow and broad 522 nm unimodal, 216 nm/667 nm bimodal PSDs were inverted by Tikhonov-PGRNN and Tikhonov under different noise levels. The results show that Tikhonov-PGRNN can realize the inversion of unimodal and bimodal PSDs. Compared with Tikhonov, the peak position error and the distribution error of PSDs inverted by Tikhonov-PGRNN are smaller and the method has higher anti-noise performance. The inversion results of experimental data are consistent with the conclusion of simulation data. The peak position errors of 203 nm, 555 nm unimodal and 33 nm/203 nm, 306 nm/974 nm bimodal particle systems inverted by Tikhonov-PGRNN are 1.48%, 0.39% and 3.55%/0.76%, 7.90%/1.74% respectively, which are better than the inversion results of Tikhonov.