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.

在这项研究中，温度场估计是通过声波的到达时间测量和使用机器学习来进行的。选择由 McKenna 燃烧器产生的轴对称燃烧场作为测量区域。放电作为声点源，声传播时间使用安装在测量区域外围的麦克风进行测量。特别是声波在温度梯度下折射，这使得很难获得解的明确解析表达式。因此，通过机器学习获得了根据声波传播时间预测剖面的模型。由于具有不同传播时间的声路径数为四个，因此径向温度分布首先由四个变量参数化。然后，与一组变量值对应的声传播时间大数据是使用计算声学轨迹和相应传播时间的模拟器生成的。最后，该模型以最简单的具有单个隐藏层的人工神经网络的形式，用生成的大数据进行训练。温度场是使用模型从测量的声波传播时间中获得的，发现与使用热电偶测量的温度场非常匹配。