Thermal process management at the exact accounting of geometrical information using S-functions
DOI:
https://doi.org/10.15587/1729-4061.2014.26193Keywords:
management, thermal processes, numerical-analytical method, the structure of solutions, S-functions, functional, identification, model, parallelizationAbstract
A new numerical-analytical method for solving thermal process management problems is proposed. The method is based on solving inverse problems of identification of management functions by the specified optimal thermal conditions in time. In determining the optimality degree of the given thermal modes, all necessary limitations on the distribution of temperature, its gradients and the rate of heating or cooling are taken into account.
Solving inverse problems of identification of management functions is reduced to solving variational problems for the corresponding pair functionals. The temperature of the heating medium or the power of internal thermal energy sources is used as management functions. Analytical or regionally-analytical structures for solving thermal process management problems, exactly satisfying unsteady boundary conditions of heat transfer on the surface of the structural element and accurately at an analytical level taking into account the indefinite management function as the temperature of the heating medium are built. Using S-functions allows accurately solve the corresponding inverse problems of analytical and differential geometry. This allows accurately at the analytical level describe the surfaces of structural elements.
The proposed new approach to solving thermal process management problems divides nonlinear process of solving corresponding inverse heat conduction problems into two linear processes. At the first stage, in the built structures for solving thermal process management problems, the coefficients of the basis functions of solution structures are determined. This allows for the first time to organize a second stage of identifying dozens and hundreds of parameters in real time by parallelizing the process of finding the above two groups of undetermined coefficients. This is the undeniable advantage of this approach to solving thermal process management problems compared to using numerical methods for solving these problems.
References
- Macevityj, Ju. M. (2002). Obratnye zadachi teploprovodnosti: second edition; Vol. 2. prilozhenija. Kiev: Nauk dumka, 391.
- Maljarenko, V. A., Red'ko, A. F., Chajka, Ju. I., Povolochko, V. B. (2001). Tehnicheskaja teplofizika ograzhdajushhih konstrukcij, zdanij i sooruzhenij. Kharkiv: Rubikon, 279.
- Vigak, V. M. (1979). Optimal'noe upravlenie nestacionarnymi temperaturnymi rezhimami. Kiev: Nauk dumka, 359.
- Slesarenko, A. P., Kobrinovich, Ju. O. (2011). Strukturno-raznostnyj podhod matematicheskomu modelirovaniju vysokoskorostnyh teplovyh processov s nestacionarnym teploobmenom na poverhnosti konstruktivnyh jelementov. Problemy mashinostroenija, 14 (3), 66–75.
- Slesarenko, A. P. (2011). S-funkcii v obratnyh zadachah analiticheskoj geometrii i modelirovanija teplovyh processov. Eastern-European Journal of Enterprise Technologies, 3/4 (51), 41–46.
- Slesarenko, A. P. (2012). S-funkcii v obratnyh zadachah differencial'noj geometrii i upravlenii obrazovanija form. Eastern-European Journal of Enterprise Technologies, 1/4 (55), 4–10.
- Samarskij, A. A. (1977). Teorija raznostnyh shem. Moscow Nauka, 656.
- Boltjanskij, V. G. (1973). Optimal'noe upravlenie diskretnymi parametrami. Moscow, Nauka, 446.
- Bogoslovskij, V. N. (1985). Stroitel'naja teplofizika. Moscow Vyssh. shkola, 367.
- Butkovskij, A. G. (1975). Metody upravlenija sistemami s raspredeljonnymi parametrami. Moscow Nauka, 568.
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Copyright (c) 2014 Анатолий Павлович Слесаренко, Юрий Владимирович Журавлёв
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