Non-parametric estimation of particle size distribution from spectral extinction data with PCA approach

Abstract

Non-parametric estimation of particle size distribution (PSD) is carried out with the help of spectral extinction method and Tikhonov regularization method. Meanwhile, a selection principle of optimal measurement wavelengths on the basis of principle component analysis (PCA) approach is proposed to improve the retrieval accuracy. Results show that the optimally selected wavelengths can ensure retrieval accuracy, compared with randomly selected wavelengths. Then, four common PSDs, namely Log-Normal (L-N), Rosin-Rammer (R-R), Normal (N-N) and Gamma distributions, are estimated under different random measurement errors. Numerical tests show that the present methodology can be successfully used to reconstruct the PSDs with high stability in the presence of random errors and low susceptibility to the shape of distributions. Finally, the PSD of aerosol measured over Harbin in China and the PSD of microalgae cell are retrieved, respectively. The study shows that increasing the number of subintervals of the particle size range will improve the retrieval accuracy as well as increase the cost of experiment, so the number of subintervals should be selected reasonably. Moreover, to obtain more reliable results, the measurement sample size should be as large as possible. As a whole, the present methodology provides a reliable and effective technique to estimate the PSDs non-parametrically from the spectral extinction signals.