Real-time data assimilation of nonlinear thermoacoustics.

Thermoacoustic instabilities are commonly modelled using low-order models that provide qualitatively accurate solutions at a low computational cost. We design an ensemble data assimilation algorithm to perform state and parameter estimation, which enables model learning on the fly and makes the model more quantitatively accurate. The algorithm is tested and validated through a multimicrophone twin experiment in a Rijke tube. Bifurcation analysis evidenced the extreme sensitivity of thermoacoustic models to small changes in the parameters, which give rise to complex nonlinear regimes. Hence, a small update in a parameter during the filtering can give rise to large changes in the state that in turn may result in unphysical solutions to the thermoacoustic parameters. We overcome this issue by a combined increase, reject, inflate strategy. The filter is shown to be robust and capable of recovering the true state even for chaotic regions with large uncertainties. Current efforts focus on the application of this technology for state and parameter estimation in the stochastic differential equations governing the slow-varying amplitude and phase of a stochastic model of an axial combustor with real experimental data.