Bias-aware thermoacoustic data assimilation

Abstract

The occurrence and amplitude of nonlinear thermoacoustic instabilities can be quickly estimated with low-order models. Low-order models, however, contain model errors, i.e., the equations do not capture all the physical mechanisms. From a statistical inference point of view, we say that low-order models are biased. We propose a data-assimilation methodology that can simultaneously infer the acoustic state, model parameters and model error from reference data. We propose reservoir computing (echo state networks) to represent the model bias. The echo state network is combined with an ensemble square-root Kalman filter to perform, in real time, (i) the estimation of the acoustic pressure and velocity, (ii) the inference of the flame parameters, and (iii) the learning of the model bias. The proposed methodology is tested on a time-delayed low-order model, with synthetic experimental data from a higher-order model with a flame. This work opens up new possibilities for assimilating data for cheap low-order models to self-correct on-the-fly.