Physics-Based Statistical Learning in Thermoacoustics

Abstract

Thermoacoustic oscillations arise because of the interaction between acoustic waves inside a duct or a combustion chamber, and heat release rate oscillations at the flame or heater location. When certain conditions are met, these oscillations may grow significantly in time and cause severe problems, particularly in gas turbines used for propulsion, i.e. in systems characterized by high powers. Thermoacoustic oscillations are extremely sensitive to small changes in the system geometry, parameters, and boundary conditions. For this reason, it is challenging to build quantitatively-accurate models that are general.

In this thesis, we propose to generate physics-based qualitatively-accurate reduced-order models, which are general, and then tune their parameters so that they become quantitatively accurate to describe the system under investigation. To do this, we use statistical learning techniques in combination with an experimental dataset consisting of O(10^6) datapoints. The dataset is obtained from more than 210 hours of automated experiments on an electrically-heated vertical Rijke tube. We use the ensemble Kalman filter to infer the parameters of a conjugate heat transfer model driven by natural convection. Then we use the Markov Chain Monte Carlo (MCMC) method to infer the parameters of a linear acoustic model that is driven by the thermoacoustic mechanism and damped by visco-thermal dissipation and by radiation from the ends of the tube. We perform experiments only on the fully-assembled system, rather than on its individual components. We learn model parameters sequentially by using posterior values and uncertainties from early experiments as prior values and uncertainties for later experiments. With access to parameter uncertainties available with the MCMC, we quantitatively compare the marginal likelihood of the data for four tuned heat release rate models, thus finding the best performing model. Because it is physics-based, we find that the best model is quantitatively accurate, with known error bounds, significantly beyond the range of the training set. This process successfully combines physics-based modelling with data-driven methods in order to turn a qualitatively-accurate model into a quantitatively-accurate model, which is a significant challenge in thermoacoustics.