Model order reduction of dynamic systems via proper orthogonal decomposition

Abstract

In this chapter, the performance of reduced order modeling of dynamic structural systems based on the proper orthogonal decomposition (POD) technique is investigated. Singular value decomposition and principal component analysis of the so-called snapshot matrix are considered to generate the reduced space, onto which the system equations of motion are projected to speed up the computations. To get intuitions into the achievable computational efficiency and the capability of POD to provide an input-independent reduced model, we consider the 39-story Pirelli tower in Milan-Italy. First, it is assumed that a shear model of the building is excited by the May 18-1940, Mw 7.1, El Centro earthquake, and the ensemble of the data necessary to build the reduced model is acquired. Then, the local and global accuracies of the same reduced model in tracking the dynamics of the building are assessed, if excited by the May 6-1976, Mw 6.4, Friuli earthquake and by the January 17-1995, Mw 6.8, Kobe earthquake, which differ from the El Centro one in terms of excited vibration frequencies. It is shown that POD allows to attain a speedup close to 250, when the reduced order model is required to retain a high fidelity.