Semi-empirical calibration of remote microphone probes using Bayesian inference

Abstract

The empirical calibration of remote microphone probes (RMP), used to acquire wall-pressure fluctuations, can introduce spurious resonance into the sensor transfer function due to the difference in the pressure field inside the calibrator geometry over multiple calibration steps. Such spurious resonance subsequently propagates into the unsteady-pressure data at which the calibration is applied, hindering the accuracy of the measurements. Current post-processing methods for tackling these issues are often manual and strongly dependent on the operator's expertise. In this study, we propose an original semi-empirical calibration method to remove spurious resonance in a less operator-reliant manner. The approach is based on fitting an existing analytical fluid-dynamical model for the propagation of pressure waves in the probe to the empirical calibration data using Bayesian inference. The proposed method is successfully applied to three datasets, from a simple probe recessed behind a pinhole to a more complex branching RMP. For all the configurations, spurious resonance is eliminated from the transfer function with a strongly reduced impact of the operator intervention while retaining the resonant features that are characteristic of the RMP. The affected frequency bands are then replaced using the underlying physical model. In this way, the detrimental impact of spurious resonance is removed from the measured wall-pressure spectra. Furthermore, the RMP parameters retrieved by the fit can also be used as inputs to corrective models, specifically to account for averaging effects due to the probe sensing area or for the impact of grazing flow or temperature variations on the transfer function.