Development of a Model-Driven Calibration Method for Remote Microphone Probes Using Bayesian Inference

Unsteady surface pressures shed light on the turbulent structures of boundary-layer flows, which dictate for a large part the aerodynamic and aeroacoustic performance of bodies submersed in a flow. Remote microphone probes (RMP) provide advantages compared to flush-mounted probes because of their reduced sensing area. However, they feature a distinct transfer function (TF) that needs to be taken into account for accurate pressure measurements. The empirical calibration of the probes, e.g., using plane-wave tubes, can introduce spurious resonant frequencies into the TF due to a lack of control of the pressure field inside the calibrator over the multiple calibration steps. Current processing methods of calibration data tend to be manual and strongly related to the operator’s expertise. Depending on the processing, spurious resonance may remain in a given frequency band, or some resonance that is characteristic of the probe may wrongfully be removed. All errors in the TF inadvertently propagate to the measurements performed with the calibrated probe. In this study, a semi-empirical calibration method is proposed with the aim of removing the spurious resonance in a physics-driven manner that is less reliant on the operator. Bayesian inversion is used to fit an analytic model for the TF of the RMP to the empirical calibration data. An inviscid acoustic finite-element method (FEM) simulation serves as a benchmark dataset. As such, the semi-empirical calibration procedure can be tested in an idealized environment. The proposed method is shown to be capable of providing a highly accurate fit to the benchmark data, with much less operator intervention than current processing methods. Its application to experimental calibration data and wall-pressure measurements appears to be a feasible next step, which is bound to show the full promise and potential of the technique.