Defect identification in heat transfer problems using boundary data

Abstract

The identification of internal defects has been widely focused and employed in the field of nondestructive evaluation (NDE), whereas its application in inverse heat transfer is often restricted by connectedness. Thus, in this paper, a novel identification method of multiple defects based on the parametric level set method (PLSM) and the Method of Moving Asymptotes (MMA) is proposed, where the connectedness limitation is released. In PLSM, the compactly supported radial basis functions (CSRBFs) are utilized to decouple the material related level set function, which endows the PLSM to be capable of forming high curvature portions and capturing local details of the defects. After that, the evolution of guessed level set can be tracked by updating the time-dependent expansion coefficients. Then, a least-square problem is defined to find the optimal coefficients that correspond to the actual defects. To obtain the controllable convergence and stabilize the solving of the ill-posed optimization problem, the MMA is employed to minimize the objective function. Furthermore, no requirement for the mesh reconstruction after the usage of ersatz material model, one also renders the sensitivity prone to compute. The efficiency and accuracy of the proposed method are further validated in several numerical examples by discussing the identification of single and multiple defects.

Keywords:

• Defect identification
• ersatz material model
• method of moving asymptotes
• parametric level set

Acknowledgement

Many thanks to Dr. Dong Liu of the University of Science and Technology of China for his help in using the level set method.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China (No. 11872166) and the International Postdoctoral Exchange Fellowship Program of China (No. 20180096).