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

TL;DR

This paper presents an efficient iterative rational Krylov algorithm for reducing large constrained second-order systems without explicit null space projection, demonstrated on engineering applications involving complex DAEs.

Contribution

The paper introduces a novel approach to model reduction of index-3 DAEs that avoids computationally expensive null space projection, improving efficiency in engineering applications.

Findings

Effective reduction of large sparse second-order index-3 DAEs

Demonstrated computational efficiency over traditional methods

Validated on multiple engineering system models

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 deecting 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.