2021/10/04 by C. Ahn, Chang-uk Ahn, C. Park +8
Computer Science · Engineering · Mathematics · #65F22 #Advanced Measurement and Metrology Techniques #FOS: Mathematics #G.1.6 #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Structural Health Monitoring Techniques #acm:65F22 #cs.NA #math.NA #msc:65F22
paper · pdf · doi:10.48550/arxiv.2110.01297
25 pages, 13 figures, 4 tables
arxiv created 2021/10/04 · openalex publication_date 2021/10/04 · arxiv updated 2021/10/05 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28
To deal with the ill-posed nature of the inverse heat conduction problem (IHCP), the regularization parameter alpha can be incorporated into a minimization problem, which is known as Tikhonov regularization method, a popular technique to obtain stable sequential solutions. Because alpha is a penalty term, its excessive use may cause large bias errors. Ridge regression was developed as an estimator of the optimal alpha to minimize the magnitude of a gain coefficient matrix appropriately. However, the sensitivity coefficient matrix included in the gain coefficient matrix depends on the time integrator; thus, certain parameters of the time integrators should be carefully considered with alpha to handle instability. Based on this motivation, we propose an effective iterative hybrid parameter selection algorithm to obtain stable inverse solutions.