1D system identification of buildings during earthquakes by seismic interferometry with waveform inversion of impulse responses—method and application to Millikan library Mohammadtaghi Rahmani, Maria I. Todorovska n University of Southern California, Department of Civil Eng., Los Angeles, CA 90089-2531, United States article info Article history: Received 7 November 2011 Received in revised form 4 August 2012 Accepted 24 September 2012 Available online 1 November 2012 abstract Two new algorithms have been introduced as a further development of a robust interferometric method for structural health monitoring (SHM) of buildings during earthquakes using data from seismic sensors. The SHM method is intended to be used in an automatic seismic alert system, to issue a warning of significant damage during or immediately after the earthquake, and facilitate decision making on evacuation, to avoid loss of life and injury from possible collapse of the weekend structure during aftershock shaking. The method identifies a wave velocity profile of the building by fitting an equivalent layered shear beam model in impulse response functions (virtual source at roof) of the recorded earthquake response. The structural health is monitored by detecting changes in the identified velocities in moving time windows, the initial window being used as reference. Because the fit involves essentially matching phase difference between motion at different floors, the identified velocity profile is not affected by rigid body rocking, and soil-structure interaction in general, as demonstrated in this paper. Consequently, detected changes in wave velocity during an earthquake are not affected by changes in the soil-foundation system, which is a major advantage over SHM by detecting changes in the observed modal frequencies. Further, the method is robust when applied to real buildings and large amplitude earthquake response, as demonstrated in previous work. The new fitting algorithms introduced are the nonlinear least squares (LSQ) fit and the time shift matching (TSM) algorithms. The former involves waveform inversion of the impulse responses, and the latter - iterative matching of the pulse time shifts, both markedly reducing the identification error as compared to the previously used direct ray algorithm, especially for more detailed models, i.e., with fewer floors per layer. Results are presented of identification of the NS, EW and torsional responses of the densely instrumented Millikan Library (9-story reinforced concrete building in Pasadena, California) during a small earthquake. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction This paper presents a significant new development of a method for system identification (SI) of buildings from earth- quake records by wave travel time analysis, for use in structural health monitoring (SHM), being developed by the authors. The method involves fitting a layered shear beam model of the building in recorded earthquake response by matching pulse time shifts in impulse response functions (IRF) with virtual source at roof [1–3]. Since their first use for analysis of seismic response of buildings [4], impulse response functions have shown to be a very useful tool for analysis and system identification of buildings. This paper introduces two new fitting algorithms, both iterative, which reduce markedly the error as compared to the previously used ‘‘direct’’ algorithm [1–3,5–7]. As shown in [1], the accuracy of the ‘‘direct’’ algorithm is poor for fitting more detailed models (with fewer floors per layer), and inadequate for SHM. The first one is a waveform inversion algorithm, which we call ‘‘nonlinear least squares (LSQ) fit algorithm’’, and which employs the Levenberg–Marquardt method [8]. The second one is an iterative ray algorithm, which we call ‘‘time shift matching (TSM) algo- rithm’’, and which fits only the time shifts of the direct pulses, recursively from top to bottom. The resolution and accuracy of the method are discussed in detail. Good accuracy of identifica- tion of more detailed models is essential for detecting local damage, which has been a challenge [9–11]. This paper also presents an application of the new algorithms to the NS, EW and torsional responses of Millikan library (9-story reinforced concrete building in Pasadena, California) during Yorba Linda Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/soildyn Soil Dynamics and Earthquake Engineering 0267-7261/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.soildyn.2012.09.014 n Corresponding author. E-mail addresses: mrahmani@usc.edu (M. Rahmani), mtodorov@usc.edu (M.I. Todorovska). Soil Dynamics and Earthquake Engineering 47 (2013) 157–174