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.

A new output-only system identification (SI) scheme composed of a virtual dynamic shaker (VDS) is proposed. The concept of the VDS is analogous to a secondary system such as a tuned mass damper (TMD), but it is a virtual device that is attached virtually to a primary structure. The SI technique is based on the dynamics of the combined primary structure and the VDS for the estimation of structural modal parameters. The dynamic response of the VDS is amplified around the natural frequency of the primary structure and depends on the level of damping ratio of the VDS. In this manner, the natural frequency of the primary structure can be determined as it represents the frequency at which the variance of the VDS response reaches its maximum. The structural damping ratio can be identified through the derived ratio of the response variances of VDSs attached individually to the primary structure with different damping ratios. The proposed VDS scheme is validated in detail through extensive examples of building structures under wind loads using numerical simulations and full-scale records obtained through full-scale measurements, with emphasis on the damping estimation. In addition, a comparison with other popular output-only SI schemes is made to examine the efficacy of the proposed VDS-based scheme. On the basis of the extensive examples used in this study, the damping estimates by the VDS are overall accurate, comparable with those by other popular schemes, which corroborates the efficacy of the proposed VDS as an easy-to-use approach for the output-only SI.

Damping estimation from laboratory, full‐scale, or computational simulation is critical in response prediction of structures under wind, waves, or earthquake effects. A virtual dynamic shaker (VDS)‐based scheme was recently developed for system identification (SI) of structures for processing (weakly) stationary responses, that is, frequency and damping features that offers, especially the added advantage of its basic simplicity over other schemes. While the VDS has shown performance, equivalent to other popular SI schemes, it is based on the assumption of the global flatness of the load spectrum (i.e., white noise assumption) like used in most other SI schemes, which may not always be appropriate in practical applications. In addition, it is restricted to data from a single‐degree‐of‐freedom (SDOF) response (or unimodal response) to obtain accurate modal characteristics. To address these potential shortcomings, this study revisits the VDS scheme and offers an enhancement by invoking local flatness assumption (EVDS) to possibly improve the damping estimation with the assumption that the load spectrum is flat only around the natural frequencies of the desired modes. A new formulation involving the effect of the ground motion induced vertical vibrations of a building is also introduced for both the VDS and the EVDS. Extensive examples through numerical simulation and full‐scale data, including a comparison with other popular SI schemes, demonstrate the efficacy of the proposed EVDS scheme. To facilitate expeditious and convenient utilization of the proposed EVDS as well as the VDS, this study has implemented a web‐enabled framework, named VDS‐Damping, for on‐demand and on‐the‐fly applications through user‐friendly input and result interfaces. A recently developed mode decomposition scheme, state space‐based mode decomposition (SSBMD), is implemented in the framework to assist in analyzing output from multiple modes and eliminates restriction of SDOF system. Accordingly, the SSBMD can also serve as a stand‐alone mode decomposition tool to separate response in each mode. This framework enables users to estimate damping on‐the‐fly by uploading with ease their data.