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

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  • 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.

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


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

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

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

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

    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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