In this paper , we focus on the efficient techniques to estimate the H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA). In general , the classical IRKA can be applied to the second-order system by converting it into an equivalent first-order form and get the reduced model in a first-order form. In this case, the reduced model can not preserve the structure of the second-order system which is however necessary for further manipulation. Here we develop IRKA based algorithms that enable us to generate approximate reduced second-order systems without explicitly converting the systems into a first-order form . On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized \mathcal{H}_2 error norm and attain the rapid rate of convergence. To overcome these problems, this paper discusses competent techniques to determine the optimal \mathcal{H}_2 error norm efficiently for the second-order system. The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale dynamical systems . The computation is done numerically and the achieved results are discussed in both tabular and graphical approaches.
This paper focuses on exploring efficient ways to find H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems via interpolatory projection-based method Iterative Rational Krylov Algorithm (IRKA). To get the reduced models of the second-order systems , the classical IRKA deals with the equivalent first-order converted forms and estimates the first-order reduced models. The drawbacks of that of the technique are failure of structure preservation and abolishing the properties of the original models, which are the key factors for some of the physical applications. To surpass those issues, we introduce IRKA based techniques that enable us to approximate the second-order systems through the reduced models implicitly without forming the first-order forms . On the other hand, there are very challenging tasks to the Model Order Reduction (MOR) of the large-scale second-order systems with the optimal \mathcal{H}_2 error norm and attain the rapid rate of convergence. For the convenient computations, we discuss competent techniques to determine the optimal \mathcal{H}_2 error norms efficiently for the second-order systems. The applicability and efficiency of the proposed techniques are validated by applying them to some large-scale systems extracted form engineering applications. The computations are done numerically using MATLAB simulation and the achieved results are discussed in both tabular and graphical approaches.
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