Time-Frequency Blind Source Separation Using Independent Component Analysis for Output-Only Modal Identification of Highly Damped Structures Yongchao Yang, S.M.ASCE 1 ; and Satish Nagarajaiah 2 Abstract: Output-only algorithms are needed for modal identification when only structural responses are available. The recent years have witnessed the fast development of blind source separation (BSS) as a promising signal processing technique, pursuing to recover the sources using only the measured mixtures. As the most popular tool solving the BSS problem, independent component analysis (ICA) is able to directly extract the time-domain modal responses, which are viewed as virtual sources, from the observed system responses; however, it has been shown that ICA loses accuracy in the presence of higher-level damping. In this study, the modal identification issue, which is incorporated into the BSS formulation, is transformed into a time-frequency framework. The sparse time-frequency representations of the monotone modal responses are proposed as the targeted independent sources hidden in those of the system responses which have been short-time Fourier-transformed (STFT); they can then be efficiently extracted by ICA, whereby the time-domain modal responses are recovered such that the modal parameters are readily obtained. The simulation results of a multidegree-of-freedom system illustrate that the proposed output-only STFT-ICA method is capable of accurately identifying modal information of lightly and highly damped structures, even in the presence of heavy noise and nonsta- tionary excitation. The laboratory experiment on a highly damped three-story frame and the analysis of the real measured seismic responses of the University of Southern California hospital building demonstrate the capability of the method to perform blind modal identification in practical applications. DOI: 10.1061/(ASCE)ST.1943-541X.0000621. © 2013 American Society of Civil Engineers. CE Database subject headings: Damping; Structural stability; Seismic effects; Experimentation. Author keywords: Output-only modal identification; Blind source separation; Independent component analysis; Time-frequency analysis; Seismic responses. Introduction Modal identification, which is one of the most popular linear system identification techniques, is of essential importance in various appli- cations of structural dynamics, e.g., the modal-based damage detection methods (Doebling et al. 1996), structural model updating (Friswell and Mottershead 1995), smart-tuned mass damper control (Spencer and Nagarajaiah 2003; Nagarajaiah 2009), and time-frequency system identification (Nagarajaiah and Basu 2009; Basu et al. 2008), to name a few. Whereas many modal identification methods are derived from the relationship of both inputs and outputs, output-only modal identification techniques show superiority when only system responses are available in many real-world applications. This is especially true for the large-scale infrastructures, where measuring the excitation is extremely difficult, if not impossible, in certain cases. In the past two decades, quite a few modal identifica- tion methods, most of which are parameter-dependent, have been proposed for this purpose, among which, the frequency domain de- composition (FDD) method (Brincker et al. 2001), the eigensystem realization algorithm (ERA) (Juang and Pappa 1985), the stochastic subspace iteration (SSI) (VanOverschee and De Moor 1996), the Ibrahim time domain (ITD) method (Ibrahim and Mikulcik 1973), and natural excitation technique (NExT) (James et al. 1995) are widely used. The presence of noise, nonstationary excitation, and computational demand, however, significantly influence the effi- ciency of these methods; hence, more robust techniques are needed to perform effective modal identification. The group of writers re- cently developed a number of time-domain and time-frequency identification methods (Nagarajaiah 2009; Nagarajaiah and Basu 2009; Basu et al. 2008; Nagarajaiah and Dharap 2003; Nagarajaiah and Li 2004). Recent years have witnessed the fast development of blind source separation (BSS) as a promising signal processing tech- nique extensively studied in many fields, such as acoustics (Bell and Sejnowski 1995), communication (Madhow 1998), and neural science (Hyvärinen et al. 2010). BSS essentially recovers source signals using only the observed mixtures; it is thus suitable for an unsupervised learning algorithm. Independent component analysis (ICA) (Hyvärinen and Oja 2000) and second-order blind identifi- cation (SOBI) (Belouchrani et al. 1997) are two popular tools to solve the BSS problem, and have been recently introduced in structural dynamics (Antoni 2005). ICA assumes the sources are statistically independent; it ignores the temporal structure of signals, as long as the recovered com- ponents are as independent as possible to estimate the sources. Kerschen et al. (2007) proposed the concept of virtual source and directly extracted the modal responses from the system responses in 1 Doctoral Student, Dept. of Civil and Environmental Engineering, Rice Univ., Houston, TX 77005. E-mail: Yongchao.Yang@rice.edu 2 Professor, Dept. of Civil and Environmental Engineering and Dept. of Mechanical Engineering and Material Science, Rice Univ., Houston, TX 77005 (corresponding author). E-mail: Satish.Nagarajaiah@rice.edu Note. This manuscript was submitted on September 2, 2011; approved on March 30, 2012; published online on April 11, 2012. Discussion period open until March 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engi- neering, Vol. 139, No. 10, October 1, 2013. ©ASCE, ISSN 0733-9445/ 2013/10-1780–1793/$25.00. 1780 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / OCTOBER 2013 J. Struct. Eng. 2013.139:1780-1793. Downloaded from ascelibrary.org by WILLIAM MARSH RICE UNIVERSITY on 05/23/14. Copyright ASCE. For personal use only; all rights reserved.