scholarly journals A Math Approach with Brief Cases towards Reducing Computational and Time Complexity in the Industrial Systems

2020 ◽  
Author(s):  
Yaroslav Matviychuk ◽  
Tomáš Peráček ◽  
Natalya Shakhovska
Keyword(s):  
Mathematical Models ◽  
Time Complexity ◽  
Order Reduction ◽  
Parametric Identification ◽  
Problem Area ◽  
Model Order ◽  
Industrial Systems ◽  
The Neural Network ◽  
Reduction Methods ◽  
The Given

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

scholarly journals Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models

2018 ◽  
Vol 51 (3) ◽  
pp. 465-483 ◽  
Author(s):  
Peter Benner ◽  
Roland Herzog ◽  
Norman Lang ◽  
Ilka Riedel ◽  
Jens Saak
Keyword(s):  
Model Order Reduction ◽  
Sensor Placement ◽  
Order Reduction ◽  
Optimal Sensor Placement ◽  
Model Order ◽  
Reduction Methods

Recent Advances in Computational Methods for Microsystems

2013 ◽  
Vol 745 ◽  
pp. 13-25 ◽  
Author(s):  
Alberto Corigliano ◽  
Martino Dossi ◽  
Stefano Mariani
Keyword(s):  
Model Order Reduction ◽  
Computing Time ◽  
Order Reduction ◽  
Orthogonal Decomposition ◽  
Coupled Problems ◽  
Strong Reduction ◽  
Model Order ◽  
Solution Strategies ◽  
Reduction Methods ◽  
Proper Orthogonal

An algorithm, which combines the use of Domain Decomposition and Model Order Reduction methods based on Proper Orthogonal Decomposition, is proposed. The algorithm allows for the efficient handling of electro-mechanical coupled problems in MEMS, with a strong reduction of computing time with respect to standard monolithic or staggered solution strategies. Examples of coupled electro-mechanical problems, concerning a vibrating beam subject to variable electrostatic forces, are presented and discussed.

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