Combined state and parameter estimation in level-set methods

Yu, Hans; Juniper, Matthew P.; Magri, Luca

doi:10.1016/j.jcp.2019.108950

Cited by 15 publications

(18 citation statements)

References 79 publications

(123 reference statements)

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“…2014; Orchini et al. 2015; Yu, Juniper & Magri 2019) or diffusion flames (Tyagi, Jamadar & Chakravarthy 2007; Magri & Juniper 2014). Solving for the flame dynamics adds many numerical degrees of freedom to the state vector, which makes the calculations computationally more expensive, but it does not change the framework we propose.…”

Section: Thermoacoustic Modelmentioning

confidence: 99%

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Stability, sensitivity and optimisation of chaotic acoustic oscillations

Huhn

Magri

2019

J. Fluid Mech.

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In an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic oscillations, also known as thermoacoustic instabilities, can cause large vibrations up to structural failure. Numerical and experimental studies showed that thermoacoustic oscillations can be chaotic. It is not yet known, however, how to minimise such chaotic oscillations. We propose a strategy to analyse and minimise chaotic acoustic oscillations, for which traditional stability and sensitivity methods break down. We investigate the acoustics of a nonlinear heat source in an acoustic resonator. First, we propose covariant Lyapunov analysis as a tool to calculate the stability of chaotic acoustics making connections with eigenvalue and Floquet analyses. We show that covariant Lyapunov analysis is the most general flow stability tool. Second, covariant Lyapunov vector analysis is applied to a chaotic system. The time-averaged acoustic energy is investigated by varying the heat-source parameters. Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as well as discontinuities in the time-averaged acoustic energy. Third, we embed sensitivities of the time-averaged acoustic energy in an optimisation routine. This procedure achieves a significant reduction in acoustic energy and identifies the bifurcations to chaos.The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. The techniques presented can be used in other unsteady fluid dynamics problems with virtually no modification.

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Section: Thermoacoustic Modelmentioning

confidence: 99%

“…& Sujith 2018). In future work, the heat-release rate,q(t), can be obtained, for example, from the dynamics of premixed flames(Kashinath, Hemchandra & Juniper 2013a,b;Waugh et al 2014;Orchini et al 2015;Yu, Juniper & Magri 2019) or diffusion flames(Tyagi, Jamadar & Chakravarthy 2007;Magri & Juniper 2014).…”

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confidence: 99%

Stability, sensitivity and optimisation of chaotic acoustic oscillations

Huhn

Magri

2019

J. Fluid Mech.

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“…, N . This variation of the Kalman filter, the ensemble Kalman filter, gives for ψ a i and its statistics [11,30]:…”

Section: Data Assimilationmentioning

confidence: 99%

“…the construction of ψ from G, is crucial and not straightforward. Hence, we adopt the level-set data assimilation framework developed by Yu et al [30], which is based on the Hamilton-Jacobi formalism.…”

Section: Data Assimilationmentioning

confidence: 99%

A data-driven kinematic model of a ducted premixed flame

Juniper

Magri

2020

Preprint

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Reduced-order models of flame dynamics can be used to predict and mitigate the emergence of thermoacoustic oscillations in the design of gas turbine and rocket engines. This process is hindered by the fact that these models, although often qualitatively correct, are not usually quantitatively accurate. As automated experiments and numerical simulations produce ever-increasing quantities of data, the question arises as to how this data can be assimilated into physicsinformed reduced-order models in order to render these models quantitatively accurate. In this study, we develop and test a physics-based reduced-order model of a ducted premixed flame in which the model parameters are learned from high speed videos of the flame. The experimental data is assimilated into a level-set solver using an ensemble Kalman filter. This leads to an optimally calibrated reduced-order model with quantified uncertainties, which accurately reproduces elaborate nonlinear features such as cusp formation and pinch-off. The reduced-order model continues to match the experiments after assimilation has been switched off. Further, the parameters of the model, which are extracted automatically, are shown to match the first order behavior expected on physical grounds. This study shows how reduced-order models can be updated rapidly whenever new experimental or numerical data becomes available, without the data itself having to be stored.

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“…By tuning the parameters of the G-equation model to fit a Bunsen flame experiment, a digital twin of the flame is created and its surface area variation in time, which is a proxy for the heat release rate, can be calculated. The ensemble Kalman filter (EnKF) is the current state-of-the-art, which iteratively performs Bayesian inference of the G-equation parameters from G-equation model forecasts generated in LSGEN2D and observations of the flame edge (Yu et al, 2019). The model forecasting is expensive, however, which makes the EnKF too expensive to be used online.…”

Section: Introductionmentioning

confidence: 99%

Online parameter inference for the simulation of a Bunsen flame using heteroscedastic Bayesian neural network ensembles

Croci,

Sengupta,

Juniper

2021

Preprint

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This paper proposes a Bayesian data-driven machine learning method for the online inference of the parameters of a G-equation model of a ducted, premixed flame. Heteroscedastic Bayesian neural network ensembles are trained on a library of 1.7 million flame fronts simulated in LSGEN2D, a G-equation solver, to learn the Bayesian posterior distribution of the model parameters given observations. The ensembles are then used to infer the parameters of Bunsen flame experiments so that the dynamics of these can be simulated in LSGEN2D. This allows the surface area variation of the flame edge, a proxy for the heat release rate, to be calculated. The proposed method provides cheap and online parameter and uncertainty estimates matching results obtained with the ensemble Kalman filter, at less computational cost. This enables fast and reliable simulation of the combustion process. 1

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Combined state and parameter estimation in level-set methods

Cited by 15 publications

References 79 publications

Stability, sensitivity and optimisation of chaotic acoustic oscillations

Stability, sensitivity and optimisation of chaotic acoustic oscillations

A data-driven kinematic model of a ducted premixed flame

Online parameter inference for the simulation of a Bunsen flame using heteroscedastic Bayesian neural network ensembles

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