Real-time data assimilation in nonlinear dynamical systems

The overarching goal of this thesis is to develop real-time data assimilation methods, which are applied to create digital twins of thermoacoustic instabilities. Central to digital twins are physics-based low-order models and experimental data. On the one hand, low-order models are computationally cheap, but they may be quantitatively inaccurate and contain model errors. On the other hand, experimental data can be quantitatively accurate, but they may be noisy and sparse. We propose data assimilation methods to make qualitatively low-order models quantitatively (more) accurate by statistically combining information from both physics-based models and data. 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 become available. 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 observations to analyse the performance of data assimilation in all nonlinear thermoacoustic regimes, from limit cycles to chaos, and interpret the results physically. 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). Second, we tackle the problem of model biases. Model biases, also known as model errors or epistemic uncertainties, are difficult to infer because they are “unknown unknowns’', i.e., we may not know their functional form *a priori*. With model biases, traditional real-time data assimilation methods are ill-posed because either the estimators are assumed unbiased, or they rely on an *a priori* parametric model for the bias, or they infer model biases that are not unique for the same model and data. We design a data assimilation framework to perform combined state, parameter, and bias estimation. A mathematical solution to the optimization problem is found with a sequential method, i.e., the *regularized bias-aware ensemble Kalman Filter* (r-EnKF). To estimate the bias in the low-order model, we propose an echo state network, which is a generalized auto-regressive function. We derive the Jacobian of the network and design a robust training strategy with data augmentation to accurately infer the bias in different scenarios. The r-EnKF is tested on nonlinearly coupled oscillators (with and without time-delay) affected by different forms of bias. The r-EnKF infers in real-time parameters and states, and a unique bias. Third, we develop a real-time digital twin of azimuthal thermoacoustics of a hydrogen-based laboratory combustor using data from raw sensors’ measurements (which may be subject to measurement bias). We generalize the bias-regularized ensemble Kalman filter (r-EnKF) to infer both biases in the model and in the measurement, and we design an echo state network to simultaneously infer the two forms of bias. We find that the real-time digital twin (i) autonomously predicts azimuthal dynamics, in contrast to bias-unregularized methods; (ii) uncovers the physical acoustic pressure from the raw data, i.e., it acts as a physics-based filter; and (iii) is a time-varying parameter system, which generalizes existing models that have constant parameters and capture only slow-varying variables. The digital twin generalizes to all operating conditions under investigation, which bridges the gap of existing models. This thesis opens new opportunities for low-order modelling and real-time digital twinning of nonlinear and multi-physics problems.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Nóvoa Martínez, Andrea

Advisor dc:contributor.advisor

• Magri, Luca

• Annular combustor
• Bias
• Data assimilation
• Echo state network
• Ensemble Kalman filter
• Low-order models
• Model error
• Nonlinear dynamics
• Rijke tube
• Thermoacoustics

Licence

• https://www.repository.cam.ac.uk/bitstreams/bf1565dd-42ab-461f-9ca5-d694a0aaf85e/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.113001

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/375253