Higher‐order modal transformation for reduced‐order modeling of linear systems undergoing global parametric variations

Previously, a novel parametric reduced‐order model technique for linear systems was developed based on a frequency‐domain formulation and the so‐called modally equivalent perturbed system. The main advantage of the scheme is that it isolates all the perturbed matrices into a forcing term, allowing for a simple and powerful analysis based on the ordinary differential equation with the forcing input. It was shown that when the parameter variation is limited to a finite dimension, it yields exceptionally accurate reduced‐order models for a wide range of parameter values. In this paper, the original method is improved to cover a larger‐dimensional domain and the global domain of the variation by adding higher‐order terms in the formulation. It is shown that when expressed in powers of incremental matrices, the new formula resembles a well‐known series expansion. The improved parametric reduced‐order model is demonstrated for a computational fluid dynamics model of unsteady air flow around a two‐dimensional airfoil in subsonic flows with Mach variation.