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

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.

Automated summary

In this study, we conducted 7000 experiments on an electrically-heated Rijke tube and assimilated the data using Bayesian inference. We developed a 1D pipe flow model for long timescale behavior and several 1D thermoacoustic network models for short timescale behavior. The models were ranked based on their marginal likelihood and the best model was selected for each component. The results showed that the selected model was physically-interpretable, simplified, and accurate across the entire operating regime. Furthermore, the model could be trained on limited data and successfully extrapolated beyond the training set.