Inverse transport problem of estimating point-like source using a Bayesian parametric method with MCMC

• Published in: Signal processing 2014-03, Vol.96, p.346-361
• Main Authors: Hazart, Aurélien, Giovannelli, Jean-François, Dubost, Stéphanie, Chatellier, Laurence
• Format: Article
• Language: English
• Subjects: Applied sciences; Bayesian analysis; Bayesian parametric estimation; Computer simulation; Detection, estimation, filtering, equalization, prediction; Error analysis; Exact sciences and technology; Gibbs sampling; Groundwater pollution; Information, signal and communications theory; Mathematical models; Metropolis-Hastings; Point-like source; Pollution sources; Regularization; Sensors; Signal and communications theory; Signal, noise; Telecommunications and information theory; Uncertainty
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.08.013

Recovering the origin of an incident after detection of a polluting substance in the environment is crucial to start the remediation procedures. The lack of observations, the measurement errors and the model uncertainties make the problem of source estimation an ill-posed inverse problem that requires regularization to determine a solution. The two most frequent methods of regularization are source parametrization and penalization of undesirable solutions. In this paper, the proposed approach combines both methods in order to obtain a strong regularization that is efficient in case of few and erroneous observations. Point sources with parametric temporal releases and parameter penalizations are incorporated in a Bayesian framework where observations and prior information are combined in a hierarchical probabilistic model and the posterior law is explored with a Markov Chain Monte Carlo sampling algorithm. Estimation of the source parameters is provided by the posterior mean and uncertainties are provided by the posterior variance. To validate the method, several simulated cases with different emission events are considered. Quality of the estimate as well as impact of source model errors are also investigated. Then, a comparison with two existing least squares methods is conducted, in various configurations of sensors and noise level. Finally, the behavior of the method is described on a strongly underdeterminate real case where only one sensor recorded the pollution. •The paper proposes a signal processing method for pollution source identification.•It is an ill-posed inverse problem.•Solution is based on an optimal estimation strategy (MMSE) in a Bayesian framework.•From an algorithmic standpoint, it relies on Markov Chain Monte Carlo sampler.•A large numerical study assesses the method and confirms theoritical optimality.