Information-driven receptor placement for contaminant source determination

Isolating the source of an unknown contaminant emission is a challenging problem when provided with only a limited and noisy set of mean concentration measurements. A Bayesian approach to this inverse problem yields estimates for the source parameters (location and strength) which depend directly on the quality of the information obtained from an array of detectors. If the data are of poor quality, uncertainties associated with the source parameter estimates may be large, necessitating further exploration (e.g., using mobile detection) in order to better isolate the putative source. We employ Bayesian experimental design with the goal of strategically placing an additional detector in order to maximize the 'expected information' contained in subsequent posterior distributions for the source parameters. The methodology is demonstrated using synthetic data from detectors lying in a horizontally homogeneous, neutrally-stratified atmospheric surface layer. Markov chain Monte Carlo and a posterior sampling technique are used to calculate the expected information over a grid of potential detector locations, and an auxiliary detector measuring both mean concentration and turbulent scalar fluxes is added where the expected information reaches a maximum. The updated posterior distribution (calculated based on the additional measurements) yields significantly improved estimates for the source location and strength.

[1]  Montserrat Fuentes,et al.  Bayesian entropy for spatial sampling design of environmental data , 2007, Environmental and Ecological Statistics.

[2]  A. Robins,et al.  Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer , 1982, Journal of Fluid Mechanics.

[3]  D. Lindley.  On a Measure of the Information Provided by an Experiment , 1956 .

[4]  Fue-Sang Lien,et al.  Bayesian inference for source determination with applications to a complex urban environment , 2007 .

[5]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[6]  GaucherelC.,et al.  Parameterization of a process-based tree-growth model , 2008 .

[7]  R. Baierlein.  Probability Theory: The Logic of Science , 2004 .

[8]  Fue-Sang Lien,et al.  Efficiently characterizing the origin and decay rate of a nonconservative scalar using probability theory , 2007 .

[9]  Claudio Silva,et al.  Optimization of the atmospheric pollution monitoring network at Santiago de Chile , 2003 .

[10]  Katherine von Stackelberg,et al.  Estimation of fugitive lead emission rates from secondary lead facilities using hierarchical Bayesian models. , 2005, Environmental science & technology.

[11]  M. Cheng,et al.  Bayesian treatment of a chemical mass balance receptor model with multiplicative error structure , 2009 .

[12]  David J. C. MacKay,et al.  Information-Based Objective Functions for Active Data Selection , 1992, Neural Computation.

[13]  Ralf S. Klessen,et al.  American Institute of Physics Conference Series , 2010 .

[14]  Maurice Queyranne,et al.  An Exact Algorithm for Maximum Entropy Sampling , 1995, Oper. Res..

[15]  S. Arya.  Air Pollution Meteorology and Dispersion , 1998 .

[16]  Bayesian Adaptive Exploration , 2004, astro-ph/0409386.

[17]  P. Gregory.  Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support , 2005 .

[18]  S. Ravi.  Bayesian Logical Data Analysis for the Physical Sciences: a Comparative Approach with Mathematica® Support , 2007 .

[19]  Fabien Campillo,et al.  Parameterization of a process-based tree-growth model: Comparison of optimization, MCMC and Particle Filtering algorithms , 2008, Environ. Model. Softw..

[20]  J. Zidek,et al.  An entropy-based analysis of data from selected NADP/NTN network sites for 1983–1986 , 1992 .

[21]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[22]  J. Zidek,et al.  Designing and integrating composite networks for monitoring multivariate gaussian pollution fields , 2000 .

[23]  Nicolas W. Hengartner,et al.  Stochastic event reconstruction of atmospheric contaminant dispersion using Bayesian inference , 2008 .

[24]  Duane A. Haugen,et al.  PROJECT PRAIRIE GRASS. A FIELD PROGRAM IN DIFFUSION. VOLUME 3 , 1959 .

[25]  H. Wynn,et al.  Maximum entropy sampling and optimal Bayesian experimental design , 2000 .

[26]  Philip C. Gregory,et al.  Bayesian Logical Data Analysis for the Physical Sciences: Acknowledgements , 2005 .

[27]  J. Bernardo.  Expected Information as Expected Utility , 1979 .

[28]  Fue-Sang Lien,et al.  Bayesian inversion of concentration data: Source reconstruction in the adjoint representation of atmospheric diffusion , 2008 .

[29]  Eugene Yee,et al.  Backward-Time Lagrangian Stochastic Dispersion Models and Their Application to Estimate Gaseous Emissions , 1995 .

[30]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[31]  YangQuan Chen,et al.  Resource-Constrained Sensor Routing for Parameter Estimation of Distributed Systems , 2008 .

[32]  G. Csanady.  Turbulent Diffusion in the Environment , 1973 .

[33]  Eugene Yee,et al.  Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference , 2008 .