Frequency Domain State Space–Based Mode Decomposition Framework

Abstract

For system identification of structures using responses comprised of contributions from multiple modes, one usually decomposes responses into individual modes prior to identifying parameters such as natural frequency, damping, and mode shapes. Conventional mode decomposition techniques such as the frequency domain decomposition (FDD) and the blind source separation (BSS) have been successfully applied to estimate modal matrix (mode shapes) from output-only data. Most of these techniques are formulated in physical coordinates, so the classical damping assumption is implicitly invoked. However, structures with auxiliary damping devices, which have been increasingly incorporated into modern structures over the last several decades, represent a nonclassically damped system. This arrangement may result in modal responses that are not completely decomposed by conventional techniques. In addition, these techniques may suffer from failing to decompose closely spaced modes. To overcome these limitations, a new state space–based mode decomposition (SSBMD) framework is proposed here that involves an optimization procedure to estimate the modal matrix from the eigen problem. Furthermore, the framework can be expanded to identify mode shapes not only in the state-space coordinates but also in physical coordinates, depending on the established performance index. To validate the proposed framework, this study examined a heavily damped three-degree-of-freedom (DOF) nonclassically damped system by way of numerical simulation and the wind-induced full-scale acceleration response of a 40-story steel-framed building with closely spaced modes.