论文标题
通过超声测量同时恢复固体结构的表面热通量和厚度
Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurements
论文作者
论文摘要
本文与相关超声测量结果同时重建表面热通量和固体结构的厚度的实际反问题有关。在热声耦合模型中，固体结构的热边界条件和厚度均未知，而超声传感器的传播时间测量值则得到了测量。我们通过构建适当的目标功能来将逆问题重新制定为PDE受限的优化问题。然后，我们开发了一种交替的迭代方案，该方案结合了共轭梯度方法和解决优化问题的最深层实质方法。为拟议的数值方案提供了严格的合并分析。通过使用实验室的实验真实数据，我们进行了广泛的数值实验，以验证新开发方法的几个有希望的特征。
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.
