Bayesian-Based Methods for the Estimation of the Unknown Model’s Parameters in the Case of the Localization of the Atmospheric Contamination Source

Abstract

In many areas of application it is important to estimate unknown model parameters in order to model precisely the underlying dynamics of a physical system. In this context the Bayesian approach is a powerful tool to combine observed data along with prior knowledge to gain a current (probabilistic) understanding of unknown model parameters. We have applied the methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) to the problem of the atmospheric contaminant source localization. The algorithm input data are the on-line arriving information about concentration of given substance registered by distributed sensor network. We have examined different version of the MCMC algorithms in effectiveness to estimate the probabilistic distributions of atmospheric release parameters. The results indicate the probability of a source to occur at a particular location with a particular release rate.

A Kalman Filter-Based Approach for Online Source-Term Estimation in Accidental Radioactive Dispersion Events

“…Most of STE approaches are based on the minimisation of an objective function, which gives a measure of the discrepancy between observed data and predictions obtained with the adopted model of dispersion in air. Methods have been proposed which employ simple analytical dispersion models [12,13], or more complex modelling approaches, e.g., the advection-diffusion equation [14,15], CFD [16] and other off-the-shelf tools like the SCIPUFF Lagrangian-puff model [17,18]. Bayesian techniques, which are widely adopted, are based on a statistical approach in which inherent uncertainties affecting measurements or the adopted model of dispersion in air are taken into account together with prior information.…”

Estimating contaminant source in chemical industry park using UAV-based monitoring platform, artificial neural network and atmospheric dispersion simulation

“…The Markov Chain Monte Carlo (MCMC) algorithm is a useful tool for posterior function calculation and source estimation. 3,8,[16][17][18] Some advanced lter or optimization methods such as particle lter, [19][20][21] EnKF, 22 and PSO 23,24 are also widely used in source estimation problems of chemical or nuclear power plants. However, the accuracies of traditional methods including Bayesian inference and optimization largely depend on the error of the model input and the accuracy of the forward dispersion modelling that is used in backward calculation.…”

On-line Dispersion Source Estimation using Adaptive Gaussian Mixture Filter

“…Given a properly constructed Markov chain it can be shown that MCMC reaches the stationary distribution after a typically large number of sampling steps. Application of MCMC to source estimation can be found for instance in Senocak et al [2008], Borysiewicz et al [2012], and Hirst et al [2013].…”