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

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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.

[1] Bernardo, J. M. & Smith, A. F. M., Bayesian Theory, Wiley, 1994.

[2] Fujimoto, K., Nakabayashi S., Applying GMDH algorithm to extract rules from examples, Systems Analysis Modelling Simulation, 43, 10, 2003. 1311-1319.

[3] Gelman, A., J. Carlin, H. Stern, and D. Rubin, Bayesian Data Analysis, Chapman & Hall/CRC, 2003.

[4] Gifford, F. A. Jr. Atmospheric dispersion calculation using generalized Gaussian Plum model, Nuclear Safety, 1960, 2(2):56-59, 67-68.

[5] Gilks, W., S. Richardson, and D. Spiegelhalter, Markov Chain Monte Carlo inPractice. Chapman & Hall/CRC, 1996, 486.

[6] Ivakhnenko, A.G., Group method of data Handling - A Rival of the Method of Stochastic Approximation, Soviel Automatic Control, 13, 43-71, 1966.

[7] Johannesson, G. et al., Sequential Monte-Carlo based framework for dynamic datadriven event reconstruction for atmospheric release., Proc. of the Joint StatisticalMeeting, Minneapolis, MN, American Statistical Association and Cosponsors, 2005, 73-80.

[8] Johannesson, G., W. Hanley, and J. Nitao, Dynamic Bayesian models via Monte Carlo - An introduction with examples, Lawrence Livermore National Laboratory Tech. Rep., 2004, 53.

[9] Keats, A., E. Yee, and F.-S. Lien, Bayesian inference for source determination with applications to a complex urban environment. Atmos. Environ., 41, 2007, 465-479.

[10] Madala H.R., Ivakhnenko A.G., Inductive Learning Algorithms for Complex SystemsModeling, CRC Press, 1994.

[11] Panofsky, H. A., Dutton, J. A., Atmospheric Turbulence. John Wiley, 1984.

[12] Pasquill, F. The estimate of the dispersion of windborne material, Meteorol Mag.,90, 1063, 1984, 33-49.

[13] Pudykiewicz, J. A., Application of adjoint tracer transport equations for evaluating source parameters. Atmos. Environ., 32, 1998, 3039-3050.

[14] Senocak I., N. W. Hengartner, M. B. Short, W. B. Daniel, Stochastic Event Reconstruction of Atmospheric Contaminant Dispersion Using Bayesian Inference, Atmos. Environ., 42(33) , 2008, 7718-7727.

[15] Thomson, L. C., Hirst, B., Gibson, G., Gillespie, S., Jonathan, P., Skeldon, K. D., Padgett, M. J., An improved algorithm for locating a gas source using inverse methods. Atmospheric Environment, 41, 2007, 1128-1134.

[16] Turner D. Bruce, Workbook of Atmospheric Dispersion Estimates, Lewis Publishers, USA,1994.

[17] Vicenç Puiga,Marcin Witczak, Fatiha Nejjari, Joseba Quevedo, Józef Korbicz, A GMDH neural network-based approach to passive robust fault detection using a constraint satisfaction backward test, Engineering Applications of ArtificialIntelligence, 20, Issue 7, 2007, 886-897.

[18] Watzenig,D., Bayesian inference for inverse problems - statistical inversion. Elektrotechnik and Informationstechnik ,124/7/8, 2007, 240-247.

Foundations of Computing and Decision Sciences

The Journal of Poznan University of Technology

Journal Information

CiteScore 2017: 0.82

SCImago Journal Rank (SJR) 2017: 0.212
Source Normalized Impact per Paper (SNIP) 2017: 0.523

Mathematical Citation Quotient (MCQ) 2017: 0.02

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