Bias-aware thermoacoustic data assimilation

Ensemble data assimilation algorithms combine experimental data and numerical models to estimate the state and parameters of a system. If the model is unbiased, the estimation concentrates around the true state. Thermoacoustic instabilities are, however, commonly modelled with low-order models, which are biased by definition. We propose the introduction of reservoir computing to represent the model bias. We combine the ensemble square-root Kalman filter with an echo state network to perform, in real time, (1) the estimation of the state of the system, (2) parameter calibration, and (3) model bias estimation. The proposed methodology is tested in a Rijke tube system, with synthetic experimental data from a high order model.