This paper presents work to identify the position of an unsteady heat source in a one-dimensional tube from acoustic pressure measurements with the inverse method. The relationship between the oscillation heat release rate and the pressure can be represented as a Volterra integral equation of the first kind. The discretization method was applied to transform the integral equation into matrix form. To stabilize the solution of the matrix equation, the Tikhonov regularization method was proposed. Experiments were performed to validate the inverse method. A semi-infinite probe system was used to measure the pressure perturbations in the tube, to avoid the high temperature damaging the microphone. Before the pressure measurements were taken, calibration was performed for the semi-infinite probe system to obtain accurate pressure data in the tube. The experiments were performed in three steps. First, the localization of a pure sound source in the tube at ambient temperature was studied. Second, localization of a pure sound source at hot conditions was considered. Third, the pure sound source was replaced with an unsteady heat source, and pressure data were used to determine the position of the unsteady heat source. Results show that calibration and the regularization are both necessary for the determination of the sound source position in the tube. Meanwhile, at the hot and heat release rate conditions, with the consideration of the temperature distribution in the thermoacoustic model, the position of the sound source and the unsteady heat release source can be determined successfully.

本文提出了通过逆方法从声压测量中识别一维管中不稳定热源的位置的工作。振荡放热率与压力之间的关系可以用第一类Volterra积分方程表示。采用离散化方法将积分方程转换为矩阵形式。为了稳定矩阵方程的解，提出了Tikhonov正则化方法。进行实验以验证逆方法。半无限探针系统用于测量管中的压力扰动，以避免高温损坏麦克风。在进行压力测量之前，对半无限探针系统进行校准，以获取管中的准确压力数据。实验分三个步骤进行。首先，研究了环境温度下电子管中纯声源的定位。第二，考虑了在炎热条件下的纯声源定位。第三，将纯声源替换为不稳定的热源，并使用压力数据确定不稳定的热源的位置。结果表明，校准和正则化对于确定管中声源的位置都是必需的。同时，在热和热释放速率条件下，考虑到热声模型中的温度分布，可以成功确定声源和不稳定的热释放源的位置。研究了环境温度下电子管中纯声源的定位。第二，考虑了在炎热条件下的纯声源定位。第三，将纯声源替换为不稳定的热源，并使用压力数据确定不稳定的热源的位置。结果表明，校准和正则化对于确定管中声源的位置都是必需的。同时，在热和放热率条件下，考虑到热声模型中的温度分布，可以成功确定声源和不稳定的放热源的位置。研究了环境温度下电子管中纯声源的定位。第二，考虑了在炎热条件下的纯声源定位。第三，将纯声源替换为不稳定的热源，并使用压力数据确定不稳定的热源的位置。结果表明，校准和正则化对于确定管中声源的位置都是必需的。同时，在热和热释放速率条件下，考虑到热声模型中的温度分布，可以成功确定声源和不稳定的热释放源的位置。将纯声源替换为不稳定的热源，并使用压力数据确定不稳定的热源的位置。结果表明，校准和正则化对于确定管中声源的位置都是必需的。同时，在热和放热率条件下，考虑到热声模型中的温度分布，可以成功确定声源和不稳定的放热源的位置。将纯声源替换为不稳定的热源，并使用压力数据确定不稳定的热源的位置。结果表明，校准和正则化对于确定管中声源的位置都是必需的。同时，在热和放热率条件下，考虑到热声模型中的温度分布，可以成功确定声源和不稳定的放热源的位置。