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Fast algorithm for points selection in piecewise-approximation methods of model order reduction

Keywords:

A.A. Dolinina – Post-graduate Student, Department of Computer Engineering and Control Systems, Vladimir State University named after A.&N. Stoletovs
E-mail: anastasiia.dolinina@gmail.com
V.N. Lantsov – Dr. Sc. (Eng.), Professor, Head of Department of Computer Engineering and Control Systems, Vladimir State University named after A.&N. Stoletovs
E-mail: lantsov@vlsu.ru


The article proposes modifications of model order reduction methods based on piecewise linear and piecewise polynomial approximation in combination with the developed algorithm of points selection for crosslinking of local approximations.
Application of the above algorithm can significantly reduce the computational costs during use for piecewise macromodels, due to the fact that:
1. It allows to reduce the number of points for which we need to compute a weight function and significant reduce computational costs;
2. Part of numerically expensive computations performed on the stage of preparation of macromodel and performed once;
3. In addition, during timing analysis usually the point of current state shifts from one integration step to another to much smaller distance, then the distances between the linearization points, so we can use the previous test point as a nearest point.
The results of the work can be directly applied to macromodels of linear and nonlinear devices in Simulink Matlab environment. The results of the work can be applied to commercial CAD systems provided methodological support of these CAD systems is further im-proved in order to ensure the possibility of importing the structures and methods that determine the macromodel.
The algorithm of points selection for crosslinking of local approximations proposed in this paper can have an independent application, including use in control and monitoring systems.

References:
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  8. Lanczov V.N.,Dolinina A.A. Metod ryadov Vol'terra dlya ponizheniya poryadka modelej slozhny'x sistem // Reshenie. Permskij naczional'ny'j issledovatel'skij politexnicheskij universitet. 2016. T. 1. S. 301−302.
  9. Lanczov V.N., Dolinina A.A., Pankratov A.V. Algoritmy' makromodelirovaniya slozhny'x nelinejny'x e'lektronny'x sistem // Dinamika slozhny'x sistem. 2014. № 6. T. 8. S. 23−29. ISSN 2221-2574.
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