This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the thermal boundary condition and the thickness of a solid structure are both unknown, while the measurements of the propagation time by ultrasonic sensors are given. We reformulate the inverse problem as a PDE-constrained optimization problem by constructing a proper objective functional. We then develop an alternating iteration scheme which combines the conjugate gradient method and the deepest decent method to solve the optimization problem. Rigorous convergence analysis is provided for the proposed numerical scheme. By using experimental real data from the lab, we conduct extensive numerical experiments to verify several promising features of the newly developed method.

翻译：本文所关注的是一个实际的反向问题,即同时重建表面热通量和从相关超声波测量得出的固体结构厚度。在一个热声波混合模型中,热边界条件和固体结构厚度都未知,而超声波传感器的传播时间测量则被给出。我们通过构建一个适当的客观功能,将反向问题重新表述为受PDE制约的优化问题。然后我们开发一个交替循环系统,将同流梯度法和最深的体面方法结合起来,解决最佳化问题。为拟议的数字方案提供了严格的趋同分析。我们利用实验室的实验性真实数据,进行了广泛的数字实验,以核实新开发的方法中的一些有希望的特点。