Identification of Structural Matrices of Shear Buildings Using Ambient Vibration Tests with Incomplete Measurements
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RESEARCH PAPER
Identification of Structural Matrices of Shear Buildings Using Ambient Vibration Tests with Incomplete Measurements Rasoul Khodayari1 · Omid Bahar2 · Mohsen Ghafory‑Ashtiany2 Received: 20 November 2018 / Accepted: 16 November 2019 © Shiraz University 2020
Abstract System identification methods (SIMs) are powerful tools for structural health monitoring. SIMs are used either for identification of modal parameters or for extraction of structural characteristic matrices. The current study aims to identify the real matrices of a structure using structural dynamics theory and stochastic subspace identification based on realization theory. The study focuses on extraction of the condensed mass and stiffness matrices of shear buildings by means of ambient excitation responses for limited structural degrees of freedom. Realization theory states that there are minimal realizations for appropriate identification of the main real-system matrices. The present study shows that, by using values smaller than the minimal realization, condensed structural matrices can be correctly identified. This is accomplished by accurate estimation of the full real-system order. It is shown that successive repetitions of this approach can lead to complete structural matrices. The practical application of this procedure is examined using an experimental model and an analytical six-story shear model. Analysis revealed that, even in the presence of noise, this method can accurately identify structural matrices in all cases with high precision. Keywords System identification · Minimal realization · Ambient excitation · Incomplete measurement · Shear buildings
1 Introduction System identification (SI) methods reveal the mathematical expression of a real structure without the use of simplifying hypotheses routinely considered in analytical models. SI is used for structural health monitoring and damage detection in order to evaluate the current state of a structure (Alvin et al. 2003). Field tests can be used to evaluate the real condition of a structure for damage detection, but these tests should be repeated many times over the lifetime of a structure and be carried out after severe natural phenomena such as earthquakes or typhoons (Sodestrom and Stoica 2001). SI was first introduced in advanced mechanics and aerospace engineering. Hart and Yao (1977) introduced SI to mechanical engineering, and Liu and Yao (1978) developed it for * Omid Bahar [email protected] 1
Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, Iran
2
structural engineering. In subsequent years, many research efforts were made by civil engineers to convert these analytical methods for practical applications (Juang 1994). SI can be classified into two general categories based on the input excitation forces in vibration tests: input–output methods such as forced or free vibration tests (FVT
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