Single-Step Calibration of Remote Microphone Probes Using Bayesian Inference

The empirical calibration of remote microphone probes, used to acquire unsteady pressure fluctuations in a wide range of fluid-dynamic applications, often introduces spurious resonance into the estimated frequency response, i.e., the transfer function, of the probe over the multiple steps it requires. To prevent this spurious resonance from affecting the unsteady pressure measurements, the transfer functions tend to be manually post-processed. Yet, such a procedure can constitute an additional source of uncertainty that hampers the accuracy of the results. A semi-empirical calibration method based on Bayesian inference was previously developed to tackle this problem: ASSIST (BAyesian proceSsing of SpurIous reSonance in calibraTion data). Through this technique, spurious resonance is removed and replaced with a physically correct alternative in a much less operator-reliant manner. However, its application requires a thorough understanding of the model and the related assumptions. This paper provides the knowledge required to apply ASSIST to the calibration of remote microphone probes. It covers the acquisition of the calibration data, the set-up of the method, the analysis of the results, and the iterative tuning of the input parameters to achieve the optimal fit. These steps are demonstrated on an open-source acoustic finite-element method simulation dataset, allowing the analytic line-cavity model to be compared with a 3D model and the impact of the relevant parameters constituting the method to be discussed. This framework is finally used to propose a novel development of the technique that reduces the calibration process of remote microphone probes to one single step, removing the source of the spurious resonance and enabling their in-situ calibration on non-sealing surfaces.