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

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 self-excited 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.