Print Email Facebook Twitter Solenoidal filtering of volumetric velocity measurements using Gaussian process regression Title Solenoidal filtering of volumetric velocity measurements using Gaussian process regression Author Azijli, I. Dwight, R.P. Faculty Aerospace Engineering Department Aerodynamics, Wind Energy & Propulsion Date 2015-10-15 Abstract Volumetric velocity measurements of incompressible flows contain spurious divergence due to measurement noise, despite mass conservation dictating that the velocity field must be divergence-free (solenoidal). We investigate the use of Gaussian process regression to filter spurious divergence, returning analytically solenoidal velocity fields. We denote the filter solenoidal Gaussian process regression (SGPR) and formulate it within the Bayesian framework to allow a natural inclusion of measurement uncertainty. To enable efficient handling of large data sets on regular and near-regular grids, we propose a solution procedure that exploits the Toeplitz structure of the system matrix. We apply SGPR to two synthetic and two experimental test cases and compare it with two other recently proposed solenoidal filters. For the synthetic test cases, we find that SGPR consistently returns more accurate velocity, vorticity and pressure fields. From the experimental test cases, we draw two important conclusions. Firstly, it is found that including an accurate model for the local measurement uncertainty further improves the accuracy of the velocity field reconstructed with SGPR. Secondly, it is found that all solenoidal filters result in an improved reconstruction of the pressure field, as verified with microphone measurements. The results obtained with SGPR are insensitive to correlation length, demonstrating the robustness of the filter to its parameters. To reference this document use: http://resolver.tudelft.nl/uuid:14ac2c0b-b04e-4845-929d-43d10ad86b1f Publisher Springer ISSN 0723-4864 Source https://doi.org/10.1007/s00348-015-2067-7 Source Experiments in Fluids, 56, 2015 Part of collection Institutional Repository Document type journal article Rights © 2015 The Author(s)This article is published with open access at Springerlink.com Files PDF Azijli_2015.pdf 4.66 MB Close viewer /islandora/object/uuid:14ac2c0b-b04e-4845-929d-43d10ad86b1f/datastream/OBJ/view