Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications

Xin Du; M. Monir Uddin; A. Mostakim Fony; Md. Tanzim Hossain; Md. Nazmul Islam Shuzan

doi:10.3934/naco.2021016

Article Contents

2022, Volume 12, Issue 3: 481-493. Doi: 10.3934/naco.2021016

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Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications

1.
School of Mechatronic Engineering and Automation and, Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai - 200444, China
2.
Department of Mathematics and Physics, North South University, Dhaka - 1229, Bangladesh
3.
Department of Mathematics, Chittagong University, Chittagong - 4331, Bangladesh
4.
Department of Electrical and Computer Engineering, North South University, Dhaka - 1229, Bangladesh

Corresponding author: M. Monir Uddin (E-mail: monir.uddin@northsouth.edu)
Corresponding author: M. Monir Uddin (E-mail: monir.uddin@northsouth.edu)

Received: January 2021

Revised: April 2021

Early access: May 2021

Published: September 2022

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Abstract

This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody dynamics, mechatronics and many other branches of sciences and technologies. By deflecting the algebraic equations the second-order index-3 system can be altered into an equivalent standard second-order system. This can be done by projecting the system onto the null space of the constraint matrix. However, creating the projector is computationally expensive and it yields huge bottleneck during the implementation. This paper shows how to find a reduce order model without projecting the system onto the null space of the constraint matrix explicitly. To show the efficiency of the theoretical works we apply them to several data of second-order index-3 models and experimental resultants are discussed in the paper.

Keywords:

Structured index-3 differential algebraic equations,
sparsity,
Model order reduction,
Iterative Rational Krylov Algorithms.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. Comparison of original and the 30 dimensional reduced models for the DSMS

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Figure 2. Comparison of the original and 30 dimensional reduced models for the TCOM

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Figure 3. Comparison of the original and 30 dimensional reduced models computed by IRKA and balanced truncation for the TCOM

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Figure 4. Time comparisons of both balanced truncation and IRKA for the TCOM

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Table 1. The dimension of the tested models including number of differential and algebraic variables, inputs and outputs

models dimension n₁ and n₂ inputs/outputs

DSMS 2200 2000 and 200 1/3

TCOM 11001 6001 and 5000 1/1

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References

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