Estimation of Parameters and States Using a Bayesian Particle Filter for the Sulfate Ion Adsorption Process in a Fixed Bed Column

Abstract

Ensuring that industrial effluents meet quality standards to be released into water bodies is still one of the major environmental concerns. Liquid phase adsoption in fixed bed collumns is one of the most known treatments. Measurements are needed to monitor the process. However, as they are often corrupted by noise from the measuring equipment, performing an accurate analysis becomes an important challenge. The present work demonstrates the effectiveness of particle filter Sampling Importance Resampling as a fast and robust tool for monitoring a problem of sulfate ion removal. Experimental measurements were used to validate the methodology and the particle filter (PF) performance was evaluated by means of error metrics, computational time and compared to the Unscented Kalman Filter. The results show that the PF provides sequentially very accurate estimates for the sulfate adsorption breakthrough curve.

Mathematical Evaluation of Direct and Inverse Problem Applied in Breakthrough Models of Metal Adsorption

“…In several applications, one is more interested in the form presented in Equation (18) of the Bayes equation, where the marginal probability distribution of the measures is considered irrelevant, since what is expected is the optimization of the posterior distribution, which basically depends on the numerator of Formula (17) [30,40,41]:…”