Model reduction in the physical domain

Abstract

This paper is concerned with obtaining physical-based low-order approximations of linear physical systems. Low-order models possess some advantages, including the reduction of computational di culty and understanding of the physics of the original system in a simpler manner. Previously, a number of methods have been suggested to develop suitable low-order approximations. However, most of these approaches do not re ect the relation between the mathematical model and the physical subsystems. Speci cally, these techniques do not indicate which of the physical subsystems should be retained or eliminated in the reduced-order model. The proposed model reduction method is based on identifying subsystem types of a physical system using the bond graph method. These subsystems are then removed or retained based on the information from the physical system decomposition procedures and partial fraction expansion residues to obtain a reduced-order model. The physical model reduction procedure is veri ed on physical linear systems.

Physical parameter sensitivity of system eigenvalues and physical model reduction

“…In the next section a sub-procedure for physical model reduction method based on decomposition procedures will be given. This sub-procedure uses the idea of Ye and Youcef-Toumi [14], also see Orbak et al [7].…”

“…Similarly, in [6], a physical-based model reduction procedure is developed and assessed. The method leads to an appropriate reduced-order model while again retaining a physical relevance to the full order model by indicating which subsystems to retain or remove in a systemic way.…”

“…The effect matrices given in this section not only identify the irrelevant components but also give a relative measure of their contribution to the eigenvalue. The use of effect matrices also overcomes the problem of uniform parameters of the method in Orbak et al [6].…”

“…In these methods either the components associated with small power flow are eliminated as they have small contribution to the dynamic behavior of a system [5] or decomposition of physical systems that are useful for the identification of dominant components or subsystems are utilized. Orbak et al [6]. Orbak et al [6] uses the bond graph formulation for a decomposition based physical model reduction method.…”

“…Orbak et al [6] uses the bond graph formulation for a decomposition based physical model reduction method. As discussed in [7], decomposition procedures may fail to identify relevant components when the system has uniform parameters or when the loop gains cannot be distinguished.…”