Pressure Reconstruction from the Measured Pressure Gradient Using Gaussian Process Regression

TL;DR

This paper introduces Gaussian Process Regression as a probabilistic method for reconstructing pressure fields from noisy PIV data, comparing its performance to the Omni-Directional Integration method in turbulence simulations.

Contribution

It demonstrates GPR's comparable accuracy to ODI in turbulence flow reconstruction and analyzes its error propagation and limitations with impulsive signals.

Findings

GPR achieves similar accuracy to ODI in isotropic turbulence.

GPR tends to flatten impulsive signals, limiting detection of flow structures.

Error propagation is analyzed in physical and spectral spaces.

Abstract

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI) method. This study adopts Gaussian Process Regression (GPR), a probabilistic framework with an intrinsic de-noising mechanism to tackle drawbacks of traditional Pressure Poisson solver and compares the performance with ODI. To evaluate the accuracy of the algorithm, GPR and ODI are tested in detail in a canonical setup of forced homogeneous isotropic turbulence from the Johns Hopkins Turbulence Database. According to the result, GPR has the same level of accuracy as ODI with optimized hyper-parameters for the isotropic turbulence flow. However, GPR has the tendency to flatten impulsive signals. Therefore, without further modifications, it is not suitable to detect flow structures with impulsive true signals. The error propagation of the proposed framework is also analyzed and discussed in both physical and spectral spaces.