Model-Based Output-Only Identication of Coupled Thermoacoustic Modes

Abstract: A model-based output-only method for identifying from time-series data the parameters that determine the dynamics of a stochastically forced thermoacoustic oscillator has previously been implemented in the case of a single standing thermoacoustic mode. This thesis presents an extension of the method in question to two coupled standing modes at the same frequency. An appropriate thermoacoustic model, as used in the previous works, is presented wherein the dynamics and probability distributions of the coupled thermoacoustic oscillator are described by a Langevin equation and its corresponding Fokker-Planck equation. The system identification method consists of fitting the analytical drift and diffusion coefficients to values that are estimated numerically by extrapolating the finite-time Kramers-Moyal coefficients to the short-time limit. This method is shown to be functional for the case of coupled standing modes but areas of improvement remain, in particular concerning computational efficiency. An alternative method of system identification based on iterative finite element solutions of the adjoint Fokker-Planck equation is shown to be unsuitable for coupled standing modes without significant further optimisation in the finite element step. Finally, an exploratory investigation into the system identification of coupled rotating modes at the same frequency is conducted. It is found that the transition probabilities in this case display unusual behavior that is unknown at this stage to be physically correct or due to error.