Thermoacoustic damping rate determination from combustion noise using Bayesian statistics

In this paper, we present a method to determine the quantitative stability level of a lean-premixed combustor from dynamic pressure data. Specifically, we make use of the autocorrelation function of the dynamic pressure signal acquired in a combustor where a turbulent flame acts as a thermoacoustic driver. In the proposed approach, the unfiltered pressure signal including several modes is analyzed by an algorithm based on Bayesian statistics. For this purpose, a Gibbs sampler is used to calculate parameters like damping rates and eigenfrequencies in the form of probability density functions (PDF) by a Markov-Chain Monte-Carlo (MCMC) method. The method provides a robust solution algorithm for fitting problems without requiring initial values. A further advantage lies in the nature of the statistical approach since the results can be assessed regarding its quality by means of the PDF and its standard deviation for each of the obtained parameters. First, a simulation of a stochastically forced van-der-Pol oscillator with pre-set input values is carried out to demonstrate accuracy and robustness of the method. In this context it is shown that, despite of a large amount of uncorrelated background noise, the identified damping rates are in a good agreement with the simulated parameters. Secondly, this technique is applied to measured pressure data. By doing so, the combustor is initially operated under stable conditions before the thermal power is gradually increased by adjusting the fuel mass flow rate until a limit-cycle oscillation is established. It is found that the obtained damping rates are qualitatively in line with the amplitude levels observed during operation of the combustor.