Dynamic light scattering (DLS) is a popular method of particle size measurement, but at ultra-low particle concentrations, the occurrence of number concentration fluctuations limits the use of the technique. Number fluctuations add a non-Gaussian term to the scattered light intensity autocorrelation function (ACF). This leads to an inaccurate particle size distribution (PSD) being recovered if the normal DLS analysis model is used. We propose two methods for inverting the DLS data and recovering the PSDs when number fluctuations are apparent. One is to directly establish the relationship between the non-Gaussian ACF and the PSD by the kernel function reconstruction (KFR) method while including the non-Gaussian term to recover the PSD. The other is to remove the effect of the non-Gaussian term in the ACF by the baseline reset (BR) method. By including the number fluctuation term, the ideal recovered PSD can be obtained from the simulated data, but this will not happen in the experimental measurement data. This is because the measured intensity ACF contains more noise than the simulated ACF at ultra-low concentration. In particular, the baseline noise at the tail of long delay time of ACF overwhelms the number fluctuation term, making it difficult to recover reliable PSD data. Resetting the baseline can effectively remove the digital fluctuation term in ACF, which is also a feasible method to improve PSD recovery under ultra-low concentration. However, increasing noise at ultra-low concentrations can lead to errors in determining an effective baseline. This greatly reduces the accuracy of inversion results. Results from simulated and measured ACF data show that, for both methods, noise on the ACF limits reliable PSD recovery.

To further improve the detection ability of residual current in low-voltage distribution networks, an adaptive residual current detection method based on variational mode decomposition (VMD) and dynamic fuzzy neural network (DFNN) is proposed. First, using the general $K$ -value selection method of VMD proposed in this study, the residual current signal is decomposed into $K$ intrinsic mode functions (IMFs). By introducing the cross-correlation coefficient $R$ and the time-domain energy entropy ratio $E$ as two classification indexes, IMFs are divided into three categories: effective IMFs, noise IMFs and aliasing IMFs. Then, the aliasing IMFs are denoised by recursive least squares (RLS), and the denoised IMFs are superimposed with the effective IMFs to obtain the reconstructed signal. Finally, the dynamic fuzzy neural network (DFNN) is adjusted by the minimum output method to achieve the detection of the reconstructed residual current signal, and the network is used to predict the residual current according to the detection results. The detection results of the simulation and measured data show that the proposed algorithm has high detection accuracy and is superior to the wavelet neural network, empirical mode decomposition-thresholding, and wavelet entropy-auto encoder-back propagation neural network methods in terms of mean square error, goodness of fit and running time. This method provides a reference for further research on new adaptive residual current protection devices.