Inferring soot morphology through multi-angle light scattering using an artificial neural network

Abstract

The morphological parameters of polydisperse aerosolized soot can be found by regressing modeled angularly-resolved elastic light scattering to experimental measurements, but this is an ill-posed problem in the presence of measurement noise or model error. Rayleigh-Debye-Gans Fractal Aggregate (RDG-FA) theory provides a closed-form solution for the light scattering kernel in the measurement model but can be subject to 30% model error (or more) compared to the exact solution, which is amplified by the ill-posedness of the inference problem into significant errors in the recovered morphological parameters. More precise approaches, e.g. the multi-sphere T-matrix method (MSTM), are too expensive for inference problems, which require repeated evaluation of the forward model; this is particularly true when computing posterior probability densities and credibility intervals. In this work, a computationally-efficient artificial feed-forward multi-layered neural network (ANN) is trained using MSTM scattering simulations on randomly-generated soot aggregates sampled from plausible morphological parameters. A fixed value is specified for the refractive index, while the monodisperse primary particle diameters are specified, and sintering, overlap or necking phenomena are ignored for the MSTM simulations. The ANN is then used to approximate the light scattering kernel in the measurement model, which is incorporated into the Bayesian inference procedure. The Bayesian/ANN approach is shown to be more accurate compared to a Bayesian approximation error technique. The Bayesian/ANN is then applied to in-flame measurements of soot and results are compared with transmission electron microscopy results from the literature. Parameters derived from electron micrographs of extracted soot are not contained within 90% credibility intervals; this is likely due to some of the simplifying assumptions in the scattering model, which points the way towards future work.