Real-time thermoacoustic data assimilation

TL;DR

This paper introduces a real-time, bias-aware data assimilation method for low-order thermoacoustic models, improving their quantitative accuracy and enabling real-time inference of states, parameters, and model bias using synthetic and high-fidelity data.

Contribution

It develops a Bayesian ensemble data assimilation approach with practical rules for nonlinear regimes and incorporates echo state networks for bias estimation, advancing real-time thermoacoustic modeling.

Findings

Accurately infers acoustic pressure, parameters, and model bias in real-time.

Robust learning despite large observational uncertainties (up to 50%).

Successfully infers both solutions and statistical properties of the system.

Abstract

Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we develop a Bayesian ensemble data assimilation method for a low-order model to self-adapt and self-correct any time that reference data becomes available. Second, we apply the methodology to infer the thermoacoustic states and heat release parameters on the fly without storing data (real-time). We perform twin experiments using synthetic acoustic pressure measurements to analyse the performance of data assimilation in all nonlinear thermoacoustic regimes, from limit cycles to chaos, and interpret the results physically. Third, we propose practical rules for thermoacoustic data assimilation. An increase, reject, inflate strategy is proposed to deal with the rich nonlinear behaviour; and physical time scales for assimilation are proposed in non-chaotic regimes (with the Nyquist-Shannon criterion) and in chaotic regimes (with the Lyapunov time). Fourth, we perform data assimilation using data from a higher-fidelity model. We introduce an echo state network to estimate in real-time the forecast bias, which is the model error of the low-fidelity model. We show that (i) the correct acoustic pressure, parameters, and model bias can be accurately inferred; (ii) the learning is robust as it can tackle large uncertainties in the observations (up to 50% the mean values); (iii) the uncertainty of the prediction and parameters is naturally part of the output; and (iv) both the time-accurate solution and statistics can be successfully inferred. Data assimilation opens up new possibility for real-time prediction of thermoacoustics by synergistically combining physical knowledge and experimental data.