Uncertainty encountered when modelling self-excited thermoacoustic oscillations with artificial neural networks

Abstract

Artificial neural networks are a popular nonlinear model structure and are known to be able to describe complex nonlinear phenomena. This article investigates the capability of artificial neural networks to serve as a basis for deducing nonlinear low-order models of the dynamics of a laminar flame from a Computational Fluid Dynamics (CFD) simulation. The methodology can be interpreted as an extension of the CFD/system identification approach: a CFD simulation of the flame is perturbed with a broadband, high-amplitude signal and the resulting fluctuations of the global heat release rate and of the reference velocity are recorded. Thereafter, an artificial neural network is identified based on the time series collected. Five data sets that differ in amplitude distribution and length were generated for the present study. Based on each of these data sets, a parameter study was conducted by varying the structure of the artificial neural network. A general fit-value criterion is applied and the 10 artificial neural networks with the highest fit values are selected. Comparing of these 10 artificial neural networks allows to obtain information on the uncertainty encountered. It is found that the methodology allows to capture the forced response of the flame reasonably well. The validation against the forced response, however, depends strongly on the forcing signal used. Therefore, an additional validation criterion is investigated. The artificial neural networks are coupled with a thermoacoustic network model. This allows to model selfexcited thermoacoustic oscillations. If the training time series are sufficiently long, this coupled model allows to predict the trend of the root mean square values of fluctuations of the global heat release rate. However, the prediction of the maximal value of the fluctuation amplitude is poor. Another drawback found is that even if very long-time series are available, the behaviour of artificial neural networks cannot be guaranteed. It is concluded that more sophisticated nonlinear low-order models are necessary.

Synchronization of Thermoacoustic Modes in Sequential Combustors

“…Low-order modelling of thermoacoustic instabilities can be done at different levels, either for predicting them, using for example thermoacoustic network models [21][22][23], or to capture the physics with simplified models that can be used for parameter identification [19,[24][25][26]. In this work, a low-order phenomenological model of the thermoacoustic coupling was developed to investigate the effect of time delay between the two stages.…”

Physics-informed echo state networks

“…Over the past few years, there has been a rapid increase in the development of machine learning techniques, which have been applied with success to various disciplines, from image or speech recognition [1,2] to playing Go [3]. However, the application of such methods to the study and forecasting of physical systems has only been recently explored, including some applications in the field of fluid dynamics [4][5][6][7]. One of the major challenges for using machine learning algorithms for the study of complex physical systems is the prohibitive cost of data generation and acquisition for training [8,9].…”

Modeling of the nonlinear flame response of a Bunsen-type flame via multi-layer perceptron

“…Previous to the present work, Selimefendigil and co-workers [12,13] and Förner and Polifke [14] had already extended the CFD/SI approach to nonlinear regimes using neural networks in the context of nonreacting flows. Another approach was also proposed by Jaensch and Polifke [15] for reacting flows, where they attempted to model the FDF of the Kornilov's flame [16] using neural network models. The results of that study were not satisfactory and possible reasons for this will be discussed in Section 3.3 .…”

“…Following the work in [15] , we formulate a regression problem, which is solved using a multilayer perceptron (MLP). The universal approximation theorem states that, an MLP has the ability to learn any nonlinear function in its subspace [17] .…”