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Estimation of the boundary condition of a 3D heat transfer equation using a modified hybrid conjugate gradient algorithm. (English) Zbl 1525.80003


MSC:

80A19 Diffusive and convective heat and mass transfer, heat flow
Full Text: DOI

References:

[1] Zhang, J.; Chen, D. F.; Zhang, C. Q.; Wang, S. G.; Hwang, W. S.; Han, M. R., Effects of an even secondary cooling mode on the temperature and stress fields of round billet continuous casting steel, J. Mater. Process. Technol., 222, 315-326 (2015)
[2] Vynnychy, M.; Saleem, S., On the explicit resolution of the mushy zone in the modelling of the continuous casting of alloys, Appl. Math. Model., 50, 544-568 (2017) · Zbl 1476.82012
[3] Wang, X.; Wang, Z.; Yu, L.; Du, F.; Man, Y.; Zhang, X., A particle swarm approach for optimization of secondary cooling process in slab continuous casting, Int. J. Heat Mass Transf., 93, 250-256 (2016)
[4] Chen, W. L.; Chou, H. M.; Lee, H. L.; Yang, Y. C., An inverse hyperbolic heat conduction problem in estimating base heat flux of two-dimensional cylindrical pin fins, Int. Commun. Heat Mass Transf., 52, 90-96 (2014)
[5] Cui, M.; Yang, K.; Xu, X.; Wang, S.; Gao, X., A modified Levenberg-Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems, Int. J. Heat Mass Transf., 97, 908-916 (2016)
[6] Cui, M.; Zhao, Y.; Xu, B.; Gao, X. W., A new approach for determining damping factors in Levenberg-Marquardt algorithm for solving an inverse heat conduction problem, Int. J. Heat Mass Transf., 107, 747-754 (2017)
[7] Ladyzhenskaya, O. A., Boundary Value Probelms in Mathematical Physics (1985), Springer Verlag, New York · Zbl 0588.35003
[8] Hasanov, A.; Pektas, B., Identification of an unknown time-dependent heat source term from overspecified Dirichlet boundary data by conjugate gradient method, Comput. Math. Appl., 65, 42-57 (2013) · Zbl 1268.65129
[9] Wang, Y.; Luo, X. C.; Zhang, F.; Wang, S., GPU-based model predictive control for continuous casting spray cooling control system using particle swarm optimization, Control Eng. Pract., 84, 349-364 (2019)
[10] Beck, J. V.; Woodbury, K. A., Inverse heat conduction problem: sensitivity coefficient insights, filter coefficient, and intrinsic verification, Int. J. Heat Mass Transf., 97, 578-588 (2016)
[11] Oliveira, E. P.; Stieven, G. M.; Lins, E. F.; Vaz, R. P., An inverse approach for the interfacial heat transfer parameters in alloys solidification, Appl. Therm. Eng., 155, 365-372 (2019)
[12] Mirsepahi, A.; Mehdizadeh, A.; Chen, L.; O’Neill, B.; Mohammadzaherie, M., Comparison of inverse modelling and optimization-based methods in the heat flux estimation problem of an irradiative dryer/furnace, J. Comput. Sci., 19, 77-85 (2017)
[13] Wang, Z.; Yao, M.; Wang, X.; Zhang, X.; Yang, L.; Lu, H.; Wang, X., Inverse problem-coupled heat transfer model for steel continuous casting, J. Mater. Process. Technol., 214, 44-49 (2014)
[14] Raj, U.; Mulani, K.; Talukdar, P.; Das, A.; Alagirusamyc, R., Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems, Int. J. Heat Mass Transf., 89, 359-378 (2015)
[15] Duda, P., Simplification of 3D transient heat conduction by reducing it to an axisymmetric heat conduction problem and a new inverse method of the problem solution, Int. J. Heat Mass Transf., 143, 118492 (2019)
[16] Duc, N. V.; Minh, L. D.N.; Thanh, N. T., Identifying an unknown source term in a heat equation with time-dependent coefficients, Inverse Probl. Sci. Eng., 1-27 (2020)
[17] Marques, F.; Clain, S.; Machado, G. J.; Martins, B.; Carneiro, O. S.; Nóbrega, J. M., A novel heat transfer coefficient identification methodology for the profile extrusion calibration stage, Appl. Therm. Eng., 103, 102-111 (2016)
[18] Wang, G.; Wan, S.; Chen, H.; Lv, C.; Zhang, D., A double decentralized fuzzy inference method for estimating the time and space-dependent thermal boundary condition, Int. J. Heat Mass Transf., 109, 302-311 (2017)
[19] Sun, S.; Wang, G.; Chen, H.; Zhang, D., An inverse method for the reconstruction of thermal boundary conditions of semitransparent medium, Int. J. Heat Mass Transf., 134, 574-585 (2019)
[20] Fernández-Torrijos, M.; Sobrino, C.; Almendros-Ibáñez, J. A.; Marugán-Cruz, C.; Santana, D., Inverse heat problem of determining unknown surface heat flux in a molten salt loop, Int. J. Heat Mass Transf., 139, 503-516 (2019)
[21] Mohebbi, F.; Sellier, M., Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis, Int. J. Therm. Sci., 99, 258-270 (2016)
[22] Yang, K.; Jiang, G.; Qu, Q., A new modified conjugate gradient method to identify thermal conductivity of transient non-homogeneous problems based on radial integration boundary element method, Int. J. Heat Mass Transf., 133, 669-676 (2019)
[23] He, Q.; Han, B., Accelerating full waveform inversion using HSS solver and limited memory conjugate gradient method, J. Appl. Geophys., 159, 83-92 (2018)
[24] Farahani, S. D.; Kowsary, F.; Jamali, J., Direct estimation of local convective boiling heat transfer coefficient in mini-channel by using conjugated gradient method with adjoint equation, Int. Commun. Heat Mass Transf., 55, 1-7 (2014)
[25] Helmig, T.; Al-Sibai, F.; Kneer, R., Estimating sensor number and spacing for inverse calculation of thermal boundary conditions using the conjugate gradient method, Int. J. Heat Mass Transf., 153, 119638 (2020)
[26] Mohammadiun, M.; Rahimi, A. B.; Khazaee, I., Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method, Int. J. Therm. Sci., 50, 2443-2450 (2011)
[27] Zhou, J.; Zhang, Y.; Chen, J. K.; Feng, Z. C., Inverse estimation of surface heating condition in a three-dimensional object using conjugate gradient method, Int. J. Heat Mass Transf., 53, 2643-2654 (2010) · Zbl 1191.80040
[28] Yu, Y.; Luo, X. C., Estimation of heat transfer coefficients and heat flux on the billet surface by an integrated approach, Int. J. Heat Mass Transf., 90, 645-653 (2015)
[29] Wang, Y.; Luo, X. C.; Yu, Y.; Yin, Q., Evaluation of heat transfer coefficients in continuous casting under large disturbance by weighted least squares Levenberg-Marquardt method, Appl. Therm. Eng., 111, 989-996 (2017)
[30] Kaya, M.; Erdem, A., Simultaneous reconstruction of the source term and the surface heat transfer coefficient, Math. Methods Appl. Sci., 38, 517-526 (2015) · Zbl 1307.35319
[31] Wang, Y.; Luo, X.; Yu, Y.; Cui, H., Optimal control of two-dimensional parabolic partial differential equations with application to steel billets cooling in continuous casting secondary cooling zone, Opt. Control Appl. Methods, 37, 1314-1328 (2016) · Zbl 1353.49039
[32] Wang, Y.; Luo, X.; Song, Y.; Xie, Q., Simultaneous reconstruction of the surface heat flux and the source term in 3d linear parabolic problem by modified conjugate gradient method, Math. Methods Appl. Sci., 40, 2847-2858 (2016) · Zbl 1370.35277
[33] Jian, J.; Han, L.; Jiang, X., A hybrid conjugate gradient method with descent property for unconstrained optimization, Appl. Math. Model., 39, 1281-1290 (2015) · Zbl 1432.90145
[34] Arias, C. A.; Martínez, H. J.; Pérez, R., Global inexact quasi-newton method for nonlinear system of equations with constraints, Appl. Numer. Math., 150, 559-575 (2020) · Zbl 1434.65073
[35] Liu, J. K.; Zhao, Y. X.; Wu, X. L., Some three-term conjugate gradient methods with the new direction structure, Appl. Numer. Math., 150, 433-443 (2020) · Zbl 1437.90163
[36] Yang, K.; Jiang, G. H.; Qu, Q.; Peng, H. F.; Gao, X. W., A new modified conjugate gradient method to identify thermal conductivity of transient non-homogeneous problems based on radial integration boundary element method, Int. J. Heat Mass Transf., 133, 669-676 (2019)
[37] Fletcher, R.; Reeves, C., Function minimization by conjugate gradients, Comput. J., 7, 149-154 (1964) · Zbl 0132.11701
[38] Polyak, B. T., The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys., 9, 94-112 (1969) · Zbl 0229.49023
[39] Dai, Y. H.; Yuan, Y., A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10, 177-182 (1999) · Zbl 0957.65061
[40] Wei, Z. X.; Yao, S. W.; Liu, L. Y., The convergence properties of some new conjugate gradient methods, Appl. Math. Comput., 183, 1341-1350 (2006) · Zbl 1116.65073
[41] Huang, H.; Wei, Z., The proof of the sufficient descent condition of the Wei-Yao-Liu conjugate gradient method under the strong Wolfe-Powell line search, Appl. Math. Comput., 189, 1241-1245 (2007) · Zbl 1131.65049
[42] Yao, S.; Wei, Z.; Hai, H., A note about WYL’s conjugate gradient method and its application, Appl. Math. Comput., 191, 381-388 (2007) · Zbl 1193.90213
[43] Dai, Y. H.; Yuan, Y., An efficient hybrid conjugate gradient method for unconstrained optimization, Ann. Oper. Res., 103, 33-47 (2001) · Zbl 1007.90065
[44] Andrei, N., Hybrid conjugate gradient algorithm for unconstrained optimization, J. Optim. Theory Appl., 141, 249-264 (2009) · Zbl 1168.90017
[45] Liu, J. K.; Department, F. E.; University, Y., A spectral conjugate gradient method for solving large-scale unconstrained optimization, Comput. Math. Appl., 77, 731-739 (2019) · Zbl 1442.90149
[46] Ioannis, E. L.; Pintelas, P., A new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization, J. Comput. Appl. Math., 239, 396-405 (2013) · Zbl 1258.65058
[47] Hu, Y. F.; Storey, C., Global convergence result for conjugate gradient methods, J. Optim. Theory Appl., 71, 399-405 (1991) · Zbl 0794.90063
[48] Marquardt, D. W., An algorithm for least-squares estimation of nonlinear parameters, Jpn. J. Ind. Appl. Math., 11, 431-441 (1963) · Zbl 0112.10505
[49] Brandao, L. C., Contributions to dynamic characteristics of the cutting temperature in the drilling process considering one dimension heat flow, Appl. Therm. Eng., 31, 3806-3813 (2011)
[50] Zhang, S.; Xia, Y.; Zou, C., An adaptive regularization method for low-dose CT reconstruction from CT transmission data in poisson-gaussian noise, Optik, 188, 172-186 (2019)
[51] Li, Q.; Zheng, B.; Zheng, Y., An efficient nonmonotone adaptive cubic regularization method with line search for unconstrained optimization problem, Appl. Math. Lett., 98, 74-80 (2019) · Zbl 1423.90141
[52] Au, V. V.; Phuong, N. D.; Tuan, N. H.; Zhou, Y., Some regularization methods for a class of nonlinear fractional evolution equations, Comput. Math. Appl., 78, 1752-1771 (2019) · Zbl 1442.35530
[53] Yang, J.; Xie, Z.; Ji, Z.; Meng, H., Real-time heat transfer model based on variable non-uniform grid for dynamic control of continuous casting billets, ISIJ Int., 54, 328-335 (2014)
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