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

Multi-layer perceptrons with different numbers of hidden layers and variable neurons were investigated to model the nonlinear flame response of a Bunsen-type flame. The neural network models demonstrate the ability to learn the flame describing function (FDF) for a laminar premixed flame, while using only one computational fluid dynamics (CFD) simulation. The system is excited with a broadband, low-pass filtered velocity signal that exhibits a uniform distribution of amplitudes within a predetermined range. The obtained time series of flow velocity upstream of the flame and heat release rate fluctuations are used to train the nonlinear model using a multi-layer perceptron. Several models with varying hyperparameters are trained and the dropout strategy is used as a regularizer to avoid overfitting. The best performing model is subsequently used to compute the FDF using mono-frequent excitations. In addition to accurately predicting the FDF, the trained neural network model also captures the presence of higher harmonics in the flame response. As a result, when coupled with an acoustic solver, the obtained neural network model is better suited than a classical FDF model to predict limit cycle oscillations characterized by more than one frequency. The RMS value of the predicted acoustic oscillations, together with the associated dominant frequencies are in excellent agreement with CFD reference data.