This paper focuses on exploring efficient ways to find $\mathcal{H}_2$ 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.

翻译：本文聚焦于通过基于内插投影的迭代有理Krylov算法（IRKA）探索高效求解二阶系统 $\mathcal{H}_2$ 最优保结构模型降阶（SPMOR）的途径。为获取二阶系统的降阶模型，经典IRKA需处理等效的一阶转换形式并估计一阶降阶模型。该技术的缺陷在于无法保持结构完整性且会破坏原始模型的关键特性——这些特性正是某些物理应用中的核心要素。为克服上述问题，我们引入基于IRKA的技术，使得在不形成一阶形式的情况下，通过降阶模型隐式逼近二阶系统。另一方面，针对具备最优 $\mathcal{H}_2$ 误差范数且需实现快速收敛的大规模二阶系统模型降阶（MOR）存在极大挑战。为便于计算，我们探讨了高效确定二阶系统最优 $\mathcal{H}_2$ 误差范数的可行技术。通过将所提方法应用于工程领域提取的大规模系统，验证了其适用性与有效性。数值计算采用MATLAB仿真实现，并通过表格与图形两种方式对结果进行了分析讨论。