An analysis has been made of the problem of identification of mathematical heat-transfer models with lumped parameters that have a nonunique solution. The authors have investigated the possibility of restoring conditionally the uniqueness of a solution to such a problem with supplementary conditions for the selection of solutions in the form of linearly independent time functions of temperature that can be obtained in one experiment with relevant designing, Consideration has been given to the applicability of iteration-regularization methods with a vector regularization parameter to identifying a full set of functions of a thermal-state matrix of mathematical models with lumped parameters. On the basis of computational experiments, the capabilities of a variational principle of selection of solutions for conditionally correct identification problems have been demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. A. Artyukhin, Optimum planning of experiments in the identification of heat-transfer processes, J. Eng. Phys. Thermophys., 56, No. 3, 256–260 (1989).
E. A. Artyukhin, L. I. Guseva, A. P. Tryanin, and A. G. Shibin, Influence of uncertainty in the initial data on the results of planning temperature measurements, J. Eng. Phys. Thermophys., 58, No. 5, 662–666 (1990).
S. A. Budnik and A. V. Nenarokomov, Optimum planning of measurements in determining thermal loading of bodies with moving boundaries, Teplofiz. Vys. Temp., 35, No. 3, 453–457 (1997).
A. G. Pogorelov, Construction of smoothing splines by linear programming methods, J. Eng. Phys. Thermophys., 56, No. 2, 333–337 (1989).
M. R. Romanovskii, Mathematical modeling of experiments with the help of inverse problems, J. Eng. Phys. Thermophys., 57, No. 3, 1112–1117 (1989).
M. R. Romanovskii, Planning an experiment for mathematical model identification, J. Eng. Phys. Thermophys., 58, No. 6, 800–807 (1990).
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
V. V. Mikhailov, Arrangement of the temperature measurement points and conditionality of inverse thermal conductivity problems, J. Eng. Phys. Thermophys., 57, No. 5, 1369–1373 (1989).
I. M. Lagun, Selection of thermosensor inertia in solving the converse thermal conductivity problem, J. Eng. Phys. Thermophys., 56, No. 3, 273–275 (1989).
E. A. Artyukhin, L. I. Guseva, A. P. Tryanin, and A. G. Shibin, Data processing and planning of nonstationary thermophysical experiments, J. Eng. Phys. Thermophys., 56, No. 3, 286–290 (1989).
S. A. Budnik, L. I. Guseva, and A. G. Shibin, Analysis of the method of temperature measurement used to determine the set of characteristics of a thermally protective coating, J. Eng. Phys. Thermophys., 56, No. 3, 301–308 (1989).
A. V. Nenarokomov, A. V. Netelev, and D. M. Titov, Optimum experimental design in investigating surface fracture of heatproof materials, Tepl. Prots. Tekh., 9, No. 4, 163–170 (2017).
A. G. Vikulov and A. V. Nenarokomov, Identifying thermal couplings in mathematical models of outer-space systems, Tepl. Prots. Tekh., 6, No. 6, 274–282 (2014).
A. G. Vikulov and A. V. Nenarokomov, Variational method to identify thermal mathematical models with lumped parameters, Tepl. Prots. Tekh., 8, No. 5, 214–226 (2016).
D. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods [Russian translation], Radio i Svyaz’, Moscow (1987).
A. G. Vikulov, Mathematical modeling of heat transfer in spacecraft, Vestn. VKO “Almaz–Antei,” 21, No. 2, 71–88 (2017).
O. M. Alifanov, Identification of the Heat-Transfer Processes of Air and Space Craft [in Russian], Mashinostroenie, Moscow (1979).
O. M. Alifanov, Inverse Heat-Transfer Problems [in Russian], Mashinostroenie, Moscow (1988).
O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Extreme Methods of Solving Ill-Posed Problems and Their Applications to Inverse Heat-Transfer Problems [in Russian], Fizmatlit, Moscow (1988).
A. G. Vikulov and A. V. Nenarokomov, Identification of mathematical models of the heat exchange in space vehicles, J. Eng. Phys. Thermophys., 92, No. 1, 29–42 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 4, pp. 956–976, July–August, 2020.
Rights and permissions
About this article
Cite this article
Vikulov, A.G., Nenarokomov, A.V. Uniqueness of a Solution to Problems of Identification of Mathematical Heat-Transfer Models with Lumped Parameters. J Eng Phys Thermophy 93, 924–943 (2020). https://doi.org/10.1007/s10891-020-02194-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-020-02194-5