Model reduction based on modal Hankel singular values

Abstract

This paper presents a model reduction method based on modal coordinates and Modal Hankel Singular Values (MHSV). Model reduction has recently become one of the main topics among many numerical engineers, since a reduced model increases its flexibility and adaptability in synchronizing with other models in many numerical multi-physics applications. On the other hand, a full numerical model from various FEM/BEM tools has pin-point modeling accuracy over their modeling domain. The proposed model reduction method reduces the full size model to a smaller size while maintaining the modeling accuracy. The original model reduction theory is established based on state space model that describes a linear dynamic system as a first order differential matrix equation. The magnitude of each state variable is measured by the Hankel Singular Value (HSV), and the reduced model has state variables with large HSVs. In this paper, the model is described using modal coordinates system instead of state space, since most dynamic system is described as a second order system rather than first order. A modal Hankel singular value for each mode is introduced to measure the magnitude of the mode. A numerical example of coupled acoustic and piezoelectric models is included.