In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted ${\mathcal{H}}_2$-optimal model order reduction is to construct a local optimum in terms of the ${\mathcal{H}}_2$-norm of the weighted error transfer function. In this paper, a projection-based model order reduction algorithm is proposed that constructs a reduced-order model, which nearly satisfies the first-order optimality conditions for the frequency-weighted ${\mathcal{H}}_2$-optimal model order reduction problem. It is shown that as the order of the reduced model is increased, the deviation in the satisfaction of the optimality conditions reduces further. Numerical methods are also discussed that improve the computational efficiency of the proposed algorithm. Four numerical examples are presented to demonstrate the efficacy of the proposed algorithm.

在基于投影的模型降阶中，原始全阶系统的降阶近似是通过将其投影到包含其主要特征的缩减子空间来获得的。频率加权问题${\mathcal{H}}_2$- 最优模型降阶是根据 ${\mathcal{H}}_2$- 加权误差传递函数的范数。本文提出了一种基于投影的模型降阶算法，该算法构建了一个降阶模型，该模型几乎满足频率加权的一阶最优性条件。${\mathcal{H}}_2$- 最优模型降阶问题。结果表明，随着缩减模型阶数的增加，满足最优性条件的偏差进一步减小。还讨论了提高所提出算法的计算效率的数值方法。给出了四个数值例子来证明所提出算法的有效性。