A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing.
The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM.
The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability.
The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated.
The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials.
Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.
This research has been supported by the Ministry of Education, Youth and Sports of the Czech Republic under the RICE New Technologies and Concepts for Smart Industrial Systems, project No. LO1607 and also by the internal project SGS-2015-035.
Karban, P., Pánek, D. and Doležel, I. (2018), "Model of induction brazing of nonmagnetic metals using model order reduction approach", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 37 No. 4, pp. 1515-1524. https://doi.org/10.1108/COMPEL-08-2017-0356
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