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First Thermal and Fluids Engineering Summer Conference

ISSN: 2379-1748
ISBN: 978-1-56700-430-4

AN ANALYSIS OF PRIOR INFORMATION IN BAYESIAN TOMOGRAPHIC RECONSTRUCTION

DOI: 10.1615/TFESC1.cmd.012901
pages 311-321

Samuel J. Grauer
The University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Paul J. Hadwin
Department of Mechanical and Mechatronics Engineering, University of Waterloo 200 University Ave. W, Waterloo, ON, N2L 3G1, Canada

Kyle J. Daun
Department of Mechanical and Mechatronics Engineering, University of Waterloo 200 University Ave. W, Waterloo, ON, N2L 3G1, Canada


KEY WORDS: Chemical species tomography, Bayesian analysis, inverse analysis, prior information, tomographic reconstruction, Tikhonov regularization, turbulence, emissions detection

Abstract

Line-of-sight-attenuation chemical species tomography is a diagnostic in which the spatial distribution of a gaseous species is reconstructed from line-of-sight light-absorption measurements. In this approach, the measurement field is discretized into pixels wherein the species concentration of interest is presumed constant. Because the number of pixels needed to resolve the spatial features of interest almost always exceeds the number of measurement paths, additional assumptions about the distribution must be incorporated into the analysis to identify a unique solution. This paper presents a Bayesian approach to tomographic reconstruction, which formalizes the distinct roles of measurement data and prior information in the construction of an a posteriori distribution estimate. This technique was tested on a large-eddy simulation of a turbulent free-shear methane jet. Three forms of prior information were tested, ordered from most-to-least informative: the spatial covariance data from the simulation; a squared-exponential approximation of the spatial covariance; and a first-order Tikhonov matrix, which operated as a basic spatial-smoothness prior. Preliminary results show reconstruction accuracy improves with increasingly informative priors.

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