A unified derivation and critical review of modal approaches to model reduction

Abstract

Six of the most commonly-used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables. In this representation, the derivation and the cross-comparison of the various methods are greatly facilitated. Each method is then analysed to determine key characteristics, i.e. (i) steady-state agreement, (ii) initial-value agreement, (iii) independence of the reduced model on the choice of retained state variables and inputs, and (iv) eigen vector orientation. Realistic, large-scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically. These studies reveal some important, and often unrecognized, weaknesses of several traditional techniques and confirm the strength of the newly-developed technique of Litz.