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Generating a physics-based quantitatively-accurate model of an electrically-heated Rijke tube with Bayesian inference

Accepted version
Peer-reviewed

Type

Article

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Authors

Yoko, M 

Abstract

We perform 7000 experiments at 175 stable operating points on an electrically- heated Rijke tube. We pulse the flow and measure the acoustic response with eight probe microphones distributed along its length. We assimilate the experimental data with Bayesian inference by specifying candidate models and calculating their optimal parameters given prior assumptions and the data. We model the long timescale behaviour with a 1D pipe flow model driven by natural convection into which we assimilate data with an Ensemble Kalman filter. We model the short timescale behaviour with several 1D thermoacoustic network models and assimilate data by minimizing the negative log posterior likelihood of the parameters of each model, given the data. For each candidate model we calculate the uncertainties in its parameters and calculate its marginal likelihood (i.e. the evidence for that model given the data) using Laplace’s method combined with first and second order adjoint methods. We rank each model by its marginal likelihood and select the best model for each component of the system. We show that this process generates a model that is physically-interpretable, as small as possible, and quantitatively accurate across the entire operating regime. We show that, once the model has been selected, it can be trained on little data and can extrapolate successfully beyond the training set. Matlab code is provided so that the reader can experiment with their own models.

Description

Keywords

Thermoacoustics, Data assimilation, Bayesian inference, Adjoint methods, Laplace, Saddle point

Journal Title

Journal of Sound and Vibration

Conference Name

Journal ISSN

0022-460X
1095-8568

Volume Title

Publisher

Elsevier BV
Sponsorship
Cambridge Trusts
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