Physical based analysis and model reduction of engineering systems

Abstract

There is a need for obtaining low order approximations of high order models of physical systems as low order models result in several advantages including the reduction of computational complexity and improved understanding of the original system structure. Different methods have been suggested in literature for obtaining suitable low order approximations, but these approaches do not reflect the relation between the mathematical model and the physical components of a system. In this thesis, some new approaches are provided for model reduction in the physical domain. The approaches that are presented use the idea of decomposition of physical systems, which is useful for the identification of dominant components or subsystems. The procedures are applied to the physical systems that are represented by bond graphs as they lead to better understanding of the system structure. One of the proposed methodologies exploits the idea of decomposition of physical systems. The proposed decomposition and model reduction procedures are directly implemented on the model providing a better perception of the physical model reduction and a better design point of view. As a second methodology, the determination of subsystems and/or components that influence a given eigenvalue of the overall system has been explored. A set of theorems and definitions are proposed that lead to an efficient procedure for this aim. After the calculation of eigenvectors, effect matrices are produced that indicate the relative importance of physical parameters in a selected eigenvalue. Using these matrices, an efficient physical model reduction procedure is constructed. The advantages of the presented approaches over existing methodologies are emphasized through several examples.