Semi-Empirical Calibration using Bayesian inference

A novel post-processing method for empirical calibration data of remote microphone probes (RMP), using Bayesian inference (BI) and pre-existing analytical model for the frequency response of the considered probe. https://doi.org/10.1016/j.jsv.2023.118197

Contains code to process empirical calibration data of RMPs, and unsteady pressure measurements with these RMPs. Also includes the code implementation of the Bergh & Tijdeman [1965] model and Whitmore [2006] model for the transfer function of pneumatic systems. As for the BI, a simple Metropolis-Hastings Markov-chain Monte Carlo is provided, as well as helper functions to pre-process the data etc.

1. Project structure

The code is meant to explain the presented method, and highlight its strengths.

a. ./Source

The core functions of the method are written in the Source directory. - BayesianInferenceFunctions: Code used to couple data with models using Bayesian Inference (BI); Metropolis-Hastings (MH), Markov-chain Monte Carlo (MCMC). - BerghTijdemanWhitmoreModels: Implementations of the Bergh & Tijdeman [1965] and Whitmore [2006] models. - CalibrationMeasurement: Code used to ingest calibration and unsteady pressure measurement data from TDMS or CSV files. ! Reading TDMS files requires the npTDMS Python package. - PlottingFunctions: Functions used to plot the results of the calibration/measurement data and MCMC fitting results. - ProcessingFunctions: Functions to process the calibration/measurement data (TDMS or CSV files) into power spectral density, transfer functions etc.

b. Main (SemiEmpiricalCalibrationBayesian)

Example code, using these functions, are provided in the main directory (SemiEmpiricalCalibrationBayesian): - TestDataIngest: Example of how to use Source/CalibrationMeasurement to process calibration (and measurement) data. - BKPinholeMCMC: The semi-empirical calibration method using the Whitmore model, applied to the example calibration data. Outputs the results to ./MCMC_Output. - Process_MCMC: Further processing from the MCMC results from BKPinholeMCMC. Outputs figures to ./MCMC_Figures. - ParaDRAMBKPinhole_MCMC: Similar to BKPinholeMCMC, albeit using the ParaDRAM implementation of ParaMonte. No processing code provided. - ReadFEMdataset: Visualisation for the FEM simulation dataset in ./TestData/FEM_PlaneWaveTube. https://doi.org/10.2514/6.2023-4059.

c. TutorialsInJupyter

These are Jupyter notebooks that aim to explain in a more step-by-step method the problem with idea behind the proposed method, and how to apply the method, and process its results. - Step 1: Similar to TestDataIngest, where one reads the calibration data and observes spurious resonance. - Step 2: A short overview of how the Whitmore model works, e.g., its parameters. - Step 3: Setting up the semi-empirical calibration method for the example dataset. - Step 4: Processing the results of the semi-empirical calibration method. - Extra - Basics of Bayesian Inference (WORK IN PROGRESS): Meant to explain basics of MH MCMC, e.g., the step size of the Gaussian proposal distribution.

2. Sources

• Bergh, H., and Tijdeman, H., “Theoretical and experimental results for the dynamic response of pressure measuring systems,” Tech. Rep. NLR-TR F. 238, National Aerospace Laboratory NLR, Amsterdam, The Netherlands, Jan. 1965. http://resolver.tudelft.nl/uuid:e88af84e-120f-4c27-8123-3225c2acd4ad.
• Whitmore, S. A., “Frequency response model for branched pneumatic sensing systems,” Journal of Aircraft, Vol. 43, No. 6, 2006, pp. 1845–1853. https://doi.org/10.2514/1.20759.

3. Required Python install and packages

• Python >= 3.7
• Numpy >= 1.21
• Scipy >= 1.6.0
• Matplotlib >= 3.4.1
• Seaborn >= 0.12.0
• Pandas (calibration/measurement data files are read into Pandas DataFrames, arrays with named columns) >= 1.2.0
• Optional: npTDMS (reads LabVIEW VI output files, i.e. tdms files) >= 1.4.0

If npTDMS is not installed, the functions and classes of CalibrationMeasurement can still read data from CSV files.

! npTDMS will need to be installed to read TDMS files. Either install the package in the user's preferred manner or simply run ">>> pip install npTDMS" in the Python console.