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Title: Uncertainty quantification in density estimation from background-oriented Schlieren measurements

Abstract

In this paper, we present an uncertainty quantification methodology for density estimation from background-oriented Schlieren (BOS) measurements, in order to provide local, instantaneous, a posteriori uncertainty bounds on each density measurement in the field of view. Displacement uncertainty quantification algorithms from cross-correlation-based particle image velocimetry are used to estimate the uncertainty in the dot pattern displacements obtained from cross-correlation for BOSs and assess their feasibility. In order to propagate the displacement uncertainty through the density integration procedure, we also develop a novel methodology via the Poisson solver using sparse linear operators. Testing the method using synthetic images of a Gaussian density field showed agreement between the propagated density uncertainties and the true uncertainty. Subsequently, the methodology is experimentally demonstrated for supersonic flow over a wedge, showing that regions with sharp changes in density lead to an increase in density uncertainty throughout the field of view, even in regions without these sharp changes. Lastly, the uncertainty propagation is influenced by the density integration scheme, and for the Poisson solver the density uncertainty on average increases on moving away from the regions where the Dirichlet boundary conditions are specified.

Authors:
ORCiD logo [1];  [1];  [1];  [1]; ORCiD logo [1]
  1. Purdue Univ., West Lafayette, IN (United States)
Publication Date:
Research Org.:
Purdue Univ., West Lafayette, IN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1598804
Grant/Contract Number:  
SC0018156
Resource Type:
Accepted Manuscript
Journal Name:
Measurement Science and Technology
Additional Journal Information:
Journal Volume: 31; Journal Issue: 5; Journal ID: ISSN 0957-0233
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
47 OTHER INSTRUMENTATION; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Rajendran, Lalit K., Zhang, Jiacheng, Bhattacharya, Sayantan, Bane, Sally P. M., and Vlachos, Pavlos P. Uncertainty quantification in density estimation from background-oriented Schlieren measurements. United States: N. p., 2019. Web. https://doi.org/10.1088/1361-6501/ab60c8.
Rajendran, Lalit K., Zhang, Jiacheng, Bhattacharya, Sayantan, Bane, Sally P. M., & Vlachos, Pavlos P. Uncertainty quantification in density estimation from background-oriented Schlieren measurements. United States. https://doi.org/10.1088/1361-6501/ab60c8
Rajendran, Lalit K., Zhang, Jiacheng, Bhattacharya, Sayantan, Bane, Sally P. M., and Vlachos, Pavlos P. Wed . "Uncertainty quantification in density estimation from background-oriented Schlieren measurements". United States. https://doi.org/10.1088/1361-6501/ab60c8. https://www.osti.gov/servlets/purl/1598804.
@article{osti_1598804,
title = {Uncertainty quantification in density estimation from background-oriented Schlieren measurements},
author = {Rajendran, Lalit K. and Zhang, Jiacheng and Bhattacharya, Sayantan and Bane, Sally P. M. and Vlachos, Pavlos P.},
abstractNote = {In this paper, we present an uncertainty quantification methodology for density estimation from background-oriented Schlieren (BOS) measurements, in order to provide local, instantaneous, a posteriori uncertainty bounds on each density measurement in the field of view. Displacement uncertainty quantification algorithms from cross-correlation-based particle image velocimetry are used to estimate the uncertainty in the dot pattern displacements obtained from cross-correlation for BOSs and assess their feasibility. In order to propagate the displacement uncertainty through the density integration procedure, we also develop a novel methodology via the Poisson solver using sparse linear operators. Testing the method using synthetic images of a Gaussian density field showed agreement between the propagated density uncertainties and the true uncertainty. Subsequently, the methodology is experimentally demonstrated for supersonic flow over a wedge, showing that regions with sharp changes in density lead to an increase in density uncertainty throughout the field of view, even in regions without these sharp changes. Lastly, the uncertainty propagation is influenced by the density integration scheme, and for the Poisson solver the density uncertainty on average increases on moving away from the regions where the Dirichlet boundary conditions are specified.},
doi = {10.1088/1361-6501/ab60c8},
journal = {Measurement Science and Technology},
number = 5,
volume = 31,
place = {United States},
year = {2019},
month = {12}
}

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