Uncertainty-based weighted least squares density integration for background-oriented schlieren
Abstract
We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. Here, the method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.
- Publication Date:
- Research Org.:
- Purdue Univ., West Lafayette, IN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1756077
- Grant/Contract Number:
- SC0018156
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Experiments in Fluids
- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 11; Journal ID: ISSN 0723-4864
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING
Citation Formats
Rajendran, Lalit, Zhang, Jiacheng, Bane, Sally, and Vlachos, Pavlos. Uncertainty-based weighted least squares density integration for background-oriented schlieren. United States: N. p., 2020.
Web. doi:10.1007/s00348-020-03071-w.
Rajendran, Lalit, Zhang, Jiacheng, Bane, Sally, & Vlachos, Pavlos. Uncertainty-based weighted least squares density integration for background-oriented schlieren. United States. https://doi.org/10.1007/s00348-020-03071-w
Rajendran, Lalit, Zhang, Jiacheng, Bane, Sally, and Vlachos, Pavlos. Mon .
"Uncertainty-based weighted least squares density integration for background-oriented schlieren". United States. https://doi.org/10.1007/s00348-020-03071-w. https://www.osti.gov/servlets/purl/1756077.
@article{osti_1756077,
title = {Uncertainty-based weighted least squares density integration for background-oriented schlieren},
author = {Rajendran, Lalit and Zhang, Jiacheng and Bane, Sally and Vlachos, Pavlos},
abstractNote = {We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. Here, the method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.},
doi = {10.1007/s00348-020-03071-w},
journal = {Experiments in Fluids},
number = 11,
volume = 61,
place = {United States},
year = {Mon Oct 26 00:00:00 EDT 2020},
month = {Mon Oct 26 00:00:00 EDT 2020}
}
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