Uncertainty-based weighted least squares density integration for background-oriented schlieren

Rajendran, Lalit; Zhang, Jiacheng; Bane, Sally; Vlachos, Pavlos

doi:10.1007/s00348-020-03071-w

Uncertainty-based weighted least squares density integration for background-oriented schlieren

Journal Article · Mon Oct 26 00:00:00 EDT 2020 · Experiments in Fluids

DOI:https://doi.org/10.1007/s00348-020-03071-w· OSTI ID:1756077

Rajendran, Lalit ^[1]; Zhang, Jiacheng ^[2]; Bane, Sally ^[2]; ^[2]

Purdue Univ., West Lafayette, IN (United States); Purdue University
Purdue Univ., West Lafayette, IN (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: SC0018156

OSTI ID:: 1756077

Journal Information:: Experiments in Fluids, Journal Name: Experiments in Fluids Journal Issue: 11 Vol. 61; ISSN 0723-4864

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (26)

Density measurements using the Background Oriented Schlieren technique Venkatakrishnan, L.; Meier, G. E. A. Experiments in Fluids, Vol. 37, Issue 2 https://doi.org/10.1007/s00348-004-0807-1	journal	April 2004
Universal outlier detection for PIV data Westerweel, Jerry; Scarano, Fulvio Experiments in Fluids, Vol. 39, Issue 6 https://doi.org/10.1007/s00348-005-0016-6	journal	August 2005
On velocity gradients in PIV interrogation Westerweel, J. Experiments in Fluids, Vol. 44, Issue 5 https://doi.org/10.1007/s00348-007-0439-3	journal	December 2007
Phase correlation processing for DPIV measurements Eckstein, Adric C.; Charonko, John; Vlachos, Pavlos Experiments in Fluids, Vol. 45, Issue 3 https://doi.org/10.1007/s00348-008-0492-6	journal	March 2008
An evaluation of optical flow algorithms for background oriented schlieren imaging Atcheson, Bradley; Heidrich, Wolfgang; Ihrke, Ivo Experiments in Fluids, Vol. 46, Issue 3 https://doi.org/10.1007/s00348-008-0572-7	journal	October 2008
Reynolds stress estimation up to single-pixel resolution using PIV-measurements Scharnowski, Sven; Hain, Rainer; Kähler, Christian J. Experiments in Fluids, Vol. 52, Issue 4 https://doi.org/10.1007/s00348-011-1184-1	journal	August 2011
Background-oriented schlieren (BOS) techniques Raffel, Markus Experiments in Fluids, Vol. 56, Issue 3 https://doi.org/10.1007/s00348-015-1927-5	journal	March 2015
Dot tracking methodology for background-oriented schlieren (BOS) Rajendran, Lalit K.; Bane, Sally P. M.; Vlachos, Pavlos P. Experiments in Fluids, Vol. 60, Issue 11 https://doi.org/10.1007/s00348-019-2793-3	journal	October 2019
Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments Rajendran, Lalit K.; Bane, Sally P. M.; Vlachos, Pavlos P. Experiments in Fluids, Vol. 61, Issue 6 https://doi.org/10.1007/s00348-020-02978-8	journal	May 2020
IV.—On Least Squares and Linear Combination of Observations Aitken, A. C. Proceedings of the Royal Society of Edinburgh, Vol. 55 https://doi.org/10.1017/S0370164600014346	journal	January 1936
Iterative image deformation methods in PIV Scarano, F. Measurement Science and Technology, Vol. 13, Issue 1 https://doi.org/10.1088/0957-0233/13/1/201	journal	November 2001
Digital particle image velocimetry (DPIV) robust phase correlation Eckstein, Adric; Vlachos, Pavlos P. Measurement Science and Technology, Vol. 20, Issue 5 https://doi.org/10.1088/0957-0233/20/5/055401	journal	April 2009
Assessment of pressure field calculations from particle image velocimetry measurements Charonko, John J.; King, Cameron V.; Smith, Barton L. Measurement Science and Technology, Vol. 21, Issue 10 https://doi.org/10.1088/0957-0233/21/10/105401	journal	August 2010
Particle image pattern mutual information and uncertainty estimation for particle image velocimetry Xue, Zhenyu; Charonko, John J.; Vlachos, Pavlos P. Measurement Science and Technology, Vol. 26, Issue 7 https://doi.org/10.1088/0957-0233/26/7/074001	journal	June 2015
Collaborative framework for PIV uncertainty quantification: comparative assessment of methods Sciacchitano, Andrea; Neal, Douglas R.; Smith, Barton L. Measurement Science and Technology, Vol. 26, Issue 7 https://doi.org/10.1088/0957-0233/26/7/074004	journal	June 2015
A comparative experimental evaluation of uncertainty estimation methods for two-component PIV Boomsma, Aaron; Bhattacharya, Sayantan; Troolin, Dan Measurement Science and Technology, Vol. 27, Issue 9 https://doi.org/10.1088/0957-0233/27/9/094006	journal	August 2016
Particle image velocimetry (PIV) uncertainty quantification using moment of correlation (MC) plane Bhattacharya, Sayantan; Charonko, John J.; Vlachos, Pavlos P. Measurement Science and Technology, Vol. 29, Issue 11 https://doi.org/10.1088/1361-6501/aadfb4	journal	October 2018
PIV/BOS synthetic image generation in variable density environments for error analysis and experiment design Rajendran, Lalit K.; Bane, Sally P. M.; Vlachos, Pavlos P. Measurement Science and Technology, Vol. 30, Issue 8 https://doi.org/10.1088/1361-6501/ab1ca8	journal	July 2019
Uncertainty quantification in particle image velocimetry Sciacchitano, A. Measurement Science and Technology, Vol. 30, Issue 9 https://doi.org/10.1088/1361-6501/ab1db8	journal	July 2019
Uncertainty quantification in density estimation from background oriented schlieren (BOS) measurements Rajendran, Lalit K.; Zhang, Jiacheng; Bhattacharya, Sayantan Measurement Science and Technology https://doi.org/10.1088/1361-6501/ab60c8	journal	December 2019
Two regime cooling in flow induced by a spark discharge Singh, Bhavini; Rajendran, Lalit K.; Vlachos, Pavlos P. Physical Review Fluids, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevFluids.5.014501	journal	January 2020
Penalized weighted least-squares image reconstruction for positron emission tomography Fessler, J. A. IEEE Transactions on Medical Imaging, Vol. 13, Issue 2 https://doi.org/10.1109/42.293921	journal	June 1994
The generalized correlation method for estimation of time delay Knapp, C.; Carter, G. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 24, Issue 4 https://doi.org/10.1109/TASSP.1976.1162830	journal	August 1976
Tracing rays through graded-index media: a new method Sharma, Anurag; Kumar, D. Vizia; Ghatak, A. K. Applied Optics, Vol. 21, Issue 6 https://doi.org/10.1364/AO.21.000984	journal	January 1982
PIV/BOS synthetic image generation in variable density environments for error analysis and experiment design Rajendran, Lalit Purdue University Research Repository https://doi.org/10.4231/p45z-8361	dataset	January 2020
Dot tracking methodology for background-oriented schlieren (BOS) Rajendran, Lalit; Bane, Sally; Vlachos, Pavlos Purdue University Research Repository https://doi.org/10.4231/x101-wk63	dataset	January 2021

Similar Records

Uncertainty quantification in density estimation from background-oriented Schlieren measurements

Journal Article · Tue Dec 10 23:00:00 EST 2019 · Measurement Science and Technology · OSTI ID:1598804

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Journal Article · Fri May 29 00:00:00 EDT 2020 · Experiments in Fluids · OSTI ID:1657789

Dot tracking methodology for background-oriented schlieren (BOS)

Journal Article · Thu Oct 10 00:00:00 EDT 2019 · Experiments in Fluids · OSTI ID:1598795

Related Subjects

42 ENGINEERING

Uncertainty-based weighted least squares density integration for background-oriented schlieren

Citation Formats

References (26)

Similar Records

Related Subjects