Defect identification in heat transfer problems using boundary data

References

• S. Bureerat and N. Pholdee, “Inverse problem based differential evolution for efficient structural health monitoring of trusses,” Appl. Soft. Comput., vol. 66, pp. 462–472, 2018. DOI: 10.1016/j.asoc.2018.02.046.
   Web of Science ®Google Scholar
• H. Bang, S. Park, and H. Jeon, “Defect identification in composite materials via thermography and deep learning techniques,” Compos. Struct., vol. 246, pp. 112405, 2020. DOI: 10.1016/j.compstruct.2020.112405.
   Web of Science ®Google Scholar
• C. K. Hsieh and K. C. Su, “A methodology of predicting cavity geometry based on scanned surface temperature data—prescribed surface temperature at cavity side,” J. Heat Transf.-Trans. ASME, vol. 102, no. 2, pp. 324–329, 1980. DOI: 10.1115/1.3244282.
   Web of Science ®Google Scholar
• C. H. Huang and B. H. Chao, “An inverse geometry problem in identifying irregular boundary configurations,” Int. J. Heat Mass Transf., vol. 40, no. 9, pp. 2045–2053, 1997. DOI: 10.1016/S0017-9310(96)00280-3.
   Web of Science ®Google Scholar
• B. Yu, C. Xu, H. L. Zhou, and M. Cui, “A novel non-iterative method for estimating boundary conditions and geometry of furnace inner wall made of FGMs,” Appl. Therm. Eng., vol. 147, pp. 251–271, 2019. DOI: 10.1016/j.applthermaleng.2018.10.075.
   Web of Science ®Google Scholar
• B. Yu, Y. Tong, P. M. Hu, and Q. Gao, “A novel inversion approach for identifying the shape of the cavity by combining Gappy POD with direct inversion scheme,” Int. J. Heat Mass Transf, vol. 150, pp. 119365, 2020. DOI: 10.1016/j.ijheatmasstransfer.2020.119365.
   Web of Science ®Google Scholar
• H. Fazeli and M. Mirzaei, “Shape identification problems on detecting of defects in a solid body using inverse heat conduction approach,” J. Mech. Sci. Technol., vol. 26, no. 11, pp. 3681–3690, 2012. DOI: 10.1007/s12206-012-0842-4.
   Web of Science ®Google Scholar
• M. A. Livani, N. Khaji, and P. Zakian, “Identification of multiple flaws in 2D structures using dynamic extended spectral finite element method with a universally enhanced meta-heuristic optimizer,” Struct. Multidisc. Optim., vol. 57, no. 2, pp. 605–623, 2018. DOI: 10.1007/s00158-017-1767-4.
   Web of Science ®Google Scholar
• C. P. Ma, T. T. Yu, L. V. Lich, and T. Q. Bui, “An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters,” Comput. Struct., vol. 193, pp. 207–225, 2017. DOI: 10.1016/j.compstruc.2017.08.009.
   Web of Science ®Google Scholar
• W. H. Zhao, C. B. Du, and S. Y. Jiang, “An adaptive multiscale approach for identifying multiple flaws based on XFEM and a discrete artificial fish swarm algorithm,” Comput. Meth. Appl. Mech. Eng., vol. 339, pp. 341–357, 2018. DOI: 10.1016/j.cma.2018.04.037.
   Web of Science ®Google Scholar
• H. Sun, H. Waisman, and R. Betti, “A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers,” Int. J. Numer. Meth. Eng., vol. 105, no. 13, pp. 1014–1040, 2016. DOI: 10.1002/nme.5006.
   Web of Science ®Google Scholar
• M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structure design using a homogenization method,” Comput. Meth. Appl. Mech. Eng., vol. 71, no. 2, pp. 197–224, 1988. DOI: 10.1016/0045-7825(88)90086-2.
   Web of Science ®Google Scholar
• M. P. Bendsøe, “Optimal shape design as a material distribution problem,” Struct. Optim., vol. 1, no. 4, pp. 193–202, 1989. DOI: 10.1007/BF01650949.
   Google Scholar
• Y. M. Xie and G. P. Steven, “A simple evolutionary procedure for structure optimization,” Comput. Struct., vol. 49, no. 5, pp. 885–896, 1993. DOI: 10.1016/0045-7949(93)90035-C.
   Web of Science ®Google Scholar
• X. Guo, W. S. Zhang, and W. L. Zhong, “Doing topology optimization explicitly and geometrically—a new moving morphable components based framework,” J. Appl. Mech., vol. 81, no. 8, pp. 081009, 2014.
   Web of Science ®Google Scholar
• W. S. Zhang, J. Yuan, J. Zhang, and X. Guo, “A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model,” Struct. Multidisc. Optim., vol. 53, no. 6, pp. 1243–1260, 2016. DOI: 10.1007/s00158-015-1372-3.
   Web of Science ®Google Scholar
• S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Vol.1). New York: Springer, 2005.
   Google Scholar
• M. Y. Wang, X. M. Wang, and D. M. Guo, “A level set method for structure topology optimization,” Comput. Meth. Appl. Mech. Eng., vol. 192, no. 1-2, pp. 227–246, 2003. DOI: 10.1016/S0045-7825(02)00559-5.
   Web of Science ®Google Scholar
• L. Zhang, L. Yang, and C. L. Fan, “A method on identification of multiple cavities in one finite body based on surface temperature measurements: a numerical and experimental study,” Numer. Heat Transf. A-Appl., vol. 75, no. 1, pp. 40–55, 2019. DOI: 10.1080/10407782.2018.1562743.
   Web of Science ®Google Scholar
• D. Liu and J. Du, “A moving morphable components based shape reconstruction framework for electrical impedance tomography,” IEEE Trans. Med. Imaging, vol. 38, no. 12, pp. 2937–2948, 2019. DOI: 10.1109/TMI.2019.2918566.
   PubMed Web of Science ®Google Scholar
• F. Santosa, “A level-set approach for inverse problems involving obstacles,” ESAIM: COCV, vol. 1, pp. 17–33, 1996. DOI: 10.1051/cocv:1996101.
   Google Scholar
• M. Burger and S. J. Osher, “A survey on level set methods for inverse problems and optimal design,” Eur. J. Appl. Math., vol. 16, no. 2, pp. 263–301, 2005. DOI: 10.1017/S0956792505006182.
   Google Scholar
• S. S. Nanthakumar, T. Lahmer, X. Zhuang, G. Zi, and T. Rabczuk, “Detection of material interfaces using a regularized level set method in piezoelectric structures,” Inverse Probl. Sci. Eng., vol. 24, no. 1, pp. 153–176, 2016. DOI: 10.1080/17415977.2015.1017485.
   Web of Science ®Google Scholar
• W. B. Li, W. T. Lu, J. L. Qian, and Y. G. Li, “A multiple level-set method for 3D inversion of magnetic data,” Geophysics, vol. 82, no. 5, pp. J61–J81, 2017. DOI: 10.1190/geo2016-0530.1.
   Web of Science ®Google Scholar
• S. Y. Wang, K. M. Lim, B. C. Khoo, and M. Y. Wang, “An extended level set method for shape and topology optimization,” J. Comput. Phys., vol. 221, no. 1, pp. 395–421, 2007. DOI: 10.1016/j.jcp.2006.06.029.
   Web of Science ®Google Scholar
• P. Wei, Z. Y. Li, X. P. Li, and M. Y. Wang, “An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions,” Struct. Multidisc. Optim., vol. 58, no. 2, pp. 831–849, 2018. DOI: 10.1007/s00158-018-1904-8.
   Web of Science ®Google Scholar
• A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set method for inverse problems,” SIAM J. Imaging Sci., vol. 4, no. 2, pp. 618–650, 2011. DOI: 10.1137/100800208.
   Web of Science ®Google Scholar
• D. Liu, D. Smyl, and J. F. Du, “A parametric level set based approach to difference imaging in electrical impedance tomography,” IEEE Trans. Med. Imaging, vol. 38, no. 1, pp. 145–155, 2019. DOI: 10.1109/TMI.2018.2857839.
   PubMed Web of Science ®Google Scholar
• M. Eliasof, A. Sharf, and E. Treister, “Multimodal 3D shape reconstruction under calibration uncertainty using parametric level set methods,” SIAM J. Imaging Sci., vol. 13, no. 1, pp. 265–290, 2020. DOI: 10.1137/19M1257895.
   Web of Science ®Google Scholar
• G. L. Lin, X. L. Cheng, and Y. Zhang, “A parametric level set based collage method for an inverse problem in elliptic partial differential equations,” J. Comput. Appl. Math., vol. 340, pp. 101–121, 2018. DOI: 10.1016/j.cam.2018.02.008.
   Web of Science ®Google Scholar
• R. A. Willoughby, “Solutions of ill-posed problems (AN Tikhonov and VY Arsenin)”. SIAM Review, vol. 21, no. 2, pp. 266, 1979.
   Google Scholar
• P. C. Hansen, “The truncated SVD as a method for regularization,” BIT Numer. Math., vol. 27, no. 4, pp. 534–53, 1987. DOI: 10.1007/BF01937276.
   Web of Science ®Google Scholar
• M. Hanke, “A regularizing Levenberg – Marquardt scheme, with applications to inverse groundwater filtration problems,” Inverse. Probl., vol. 13, no. 1, pp. 79–95, 1997. DOI: 10.1088/0266-5611/13/1/007.
   Web of Science ®Google Scholar
• K. Svanberg, MMA and GCMMA, versions September 2007, Optimization and Systems Theory, p. 104, 2007.
   Google Scholar
• K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Meth. Eng., vol. 24, no. 2, pp. 359–373, 1987. DOI: 10.1002/nme.1620240207.
   Web of Science ®Google Scholar
• H. Wendland, “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree,” Adv. Comput. Math., vol. 4, no. 1, pp. 389–396, 1995. DOI: 10.1007/BF02123482.
   Google Scholar
• J. N. Reddy and D. K. Gartling, The finite element method in heat transfer and fluid dynamics. CRC press, 2010.
   Google Scholar