Research on the multi-parameter identification of thermal-acoustic-solid coupling problem in an inhomogeneous medium

Abstract

This work considers the multi-parameter identification problem in initial-boundary values of variable coefficient coupled partial differential equations. Based on ultrasonic echo time measurements, we identify the surface heat flux and thickness simultaneously, and then achieve the reconstruction of the internal transient temperature field. Through rigorous theoretical analysis, we show the uniqueness recovery result for the multiparameter identification problem. By reformulating the inverse problem as an optimization problem, we propose an efficient alternating iteration algorithm in solving the related optimization problem and provide a rigorous convergence analysis of the algorithm. Finally, the reliability and feasibility of this algorithm are verified by some numerical examples.