Temperature field estimation of an axisymmetric laminar flame via time-of-arrival measurements of acoustic waves, and machine learning

In this study, temperature field estimation was performed via time-of-arrival measurements of acoustic waves and using machine learning. An axisymmetric combustion field created by a McKenna burner was chosen as the measurement region. Electrical discharges served as the acoustic point source, and the acoustic travel times were measured using microphones installed along the periphery of the measurement region. In particular, acoustic waves refract under a temperature gradient, which makes it difficult to obtain an explicit analytic expression for the solution. Hence, a model that predicts the profile from the acoustic travel times was acquired through machine learning. As the number of acoustic paths with different travel times was four, the radial temperature profile was first parameterized by four variables. Then, big data of acoustic travel times corresponding to a set of variable values were produced using a simulator that calculates acoustic trajectories and the corresponding travel times. Finally, the model, in the form of the simplest artificial neural network with a single hidden layer, was trained with the generated big data. The temperature fields were obtained from the measured acoustic travel times using the model and found to match well with those measured using a thermocouple.