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 (PIV) are used to estimate the uncertainty in the dot pattern displacements obtained from cross-correlation for BOS 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. The uncertainty propagation is influenced by the density integration scheme, and for the Poisson solver the density uncertainty increases monotonically on moving away from the regions where the Dirichlet boundary conditions are specified.
Forward and inverse modeling of depth-of-field effects in background-oriented schlieren
Pennsylvania State University（宾夕法尼亚州立大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；Office National d’Études et de Recherches Aérospatiales（法国国家航空航天研究局）
Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
High-resolution pressure imaging via background-oriented schlieren tomography: a spatiotemporal measurement for MHz ultrasound fields and hydrophone calibration
Unified Deflection Estimation and Error Analysis for Background-Oriented Schlieren
Institute of Fluid Mechanics & Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University（北京航空航天大学宁波理工学院流体机械与航空推进实验室）；Tianmushan Laboratory（天目山实验室）
Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS
Pennsylvania State University（宾夕法尼亚州立大学）；CSIR-National Aerospace Laboratories（印度国家航空航天实验室）；Case Western Reserve University（凯斯西储大学）；National Research Council Canada（加拿大国家研究委员会）
