Abstract
A simple approach is introduced to identify and calibrate analytical models of multi-story buildings from their vibration records. The method is based on the Transfer Matrix formulation of the response, and requires that vibration time histories are known at every floor of the building. Since this is typically not the case, first a methodology is developed to estimate vibration time histories at non-instrumented floors of the building from those recorded at the instrumented floors, based on the assumption that the mode shapes of a multi-story building can be approximated as a linear combination of the mode shapes of a shear beam and a bending beam. Once the vibration time histories are known at every floor, it is shown by using the Transfer Matrix formulation that the top-to-bottom spectral ratio of the records at a particular story is dependent only on the properties of this story and the stories above. In other words, any change in the characteristics of the stories below does not affect the spectral ratio for this story. Therefore, starting from the top story, we can identify frequency of each story (i.e., story stiffness/story mass), or directly story stiffness if the story mass is known. In addition to system identification, the approach also provides a simple tool to calibrate analytical models of multi-story buildings from their vibration records.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bernal D, Ussia A (2015) Sequential deconvolution input reconstruction. Mech Syst Signal Process 50–51:41–55
Chang PC, Flatau A, Liu SC (2003) Review paper: health monitoring of civil structure. Struct Health Monit 2(3):257–267
Chopra AK (2007) Dynamics of structures: theory and applications to earthquake engineering. Prentice-Hall, Upper Saddle River, USA
Doebling SW, Farrar CR, Prime MB, Shevitz DW (1996) Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, Report LA-13070-MS. Los Alamos National Laboratory, Los Alamos, NM
Eftekhar AS, Chatzi E, Papadimitriou C (2015) A dual Kalman filter approach for state estimation via output-only acceleration measurements. Mech Syst Signal Process 60–61:866–886
Erazo K, Hernandez EM (2014) A model-based observer for state and stress estimation in structural and mechanical systems: experimental validation. Mech Syst Signal Process 43:141–152
Erdik M (2001) Report on 1999 Kocaeli and Duzce (Turkey) earthquakes. In: Proceedings of the 3rd international workshop on structural control, structural control for civil and infrastructure engineering. Casciati F., Magonette G., World Scientific
Fan W, Qiao P (2011) Vibration-based damage identification methods: a review and comparative study. Struct Health Monit 10(1):83–111
Goel RK (2008) Mode-based procedure to interpolate strong motion records of instrumented buildings. ISET J Earthq Technol Tech Note 45(3–4):97–113
Hadjileontiadis LJ, Douka E (2007) Crack detection in plates using fractal dimension. Eng Struct 29:1612–1625
Han SM, Benaroya B, Wei T (1999) Dynamics of transversely vibrating beams using four engineering theories. J Sound Vib 225(5):935–988
Holzer H (1921) Die berechung der drehscwingungen. Springer, Berlin, Germany
Kaya Y, Safak E (2014) Real-time analysis and interpretation of continuous data from structural health monitoring (SHM) systems health monitoring (SHM) systems. Bull Earthq Eng 13(3):917–934
Kim JT, Stubbs N (2003) Crack detection in beam-type structures using frequency data. J Sound Vib 259:145–160
Kohler MD, Davis PM, Safak E (2005) Earthquake and ambient vibration monitoring of the steel-frame UCLA Factor building. Earthq Spectra 21(3):715–736
Limongelli MP (2003) Optimal location of sensors for reconstruction of seismic response through spline function interpolation. Earthq Eng Struct Dynam 32(7):1055–1074
Lourens E, Papadimitriou C, Gillijns S, Reynders E, De Roeck G, Lombaert G (2012) Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors. Mech Syst Signal Process 29:310–327
Naeim F (1997) Performance of extensively instrumented buildings during the January 17, 1994 northridge earthquake: an interactive information system, JAMA report 97-7530.68. John A. Martin & Associates, Los Angeles, USA
Naeim F, Lee H, Bhatia H, Hagie S, Skliros K (2004) CSMIP instrumented building response analysis and 3-D visualization system (CSMIP-3DV). In: Proceedings of the SMIP04 seminar on utilization of strong-motion data. Sacramento, USA, pp 83–102
Naets F, Croes J, Desmet W (2015a) An online coupled state/input/parameter estimation approach for structural dynamics. Comput Methods Appl Mech Eng 283:1167–1188
Naets F, Cuadrado J, Desmet W (2015b) Stable force identification in structural dynamics using Kalman filtering and dummy-measurements. Mech Syst Signal Process 50–51:235–248
Pandey AK, Biswas M, Samman MM (1991) Damage detection from changes in curvature mode shapes. J Sound Vib 145:321–332
Ratcliffe CP (1997) Damage detection using a modified laplacian operator on mode shape data. J Sound Vib 204:505–517
Safak E (1995) Detection and identification of soil-structure interaction in buildings from vibration recordings. J Struct Eng 121:899–906
Skolnik D, Lei Y, Yu E, Wallace JW (2006) Identification, model updating, and response prediction of an instrumented 15-story steel-frame building. Earthq Spectra 22(3):781–802
Stubbs N, Kim JT, Farrar CR (1995) Field verification of a nondestructive damage localization and severity estimation algorithm. In: Proceedings of 13th international modal analysis conference, vol 1, pp 210–218
Thomas WT (2003) Theory of vibration with applications, 4th edn. Nelson Thornes Ltd., Cheltenham, UK, p 387
UCLA Factor Seismic Array (2013) http://factor.gps.caltech.edu [10 January 2015]
William HKL, Hiroo K, Paul J, Carl K (2003) International handbook of earthquake and engineering seismology, part 2. Academic Press, London, UK
Acknowledgments
The data used in this research is gathered from the UCLA Factor building seismic array. The authors are thankful to the USGS ANSS program and the NSF Center for Embedded Networked Sensing at UCLA for providing the data online.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaya, Y., Kocakaplan, S. & Şafak, E. System identification and model calibration of multi-story buildings through estimation of vibration time histories at non-instrumented floors. Bull Earthquake Eng 13, 3301–3323 (2015). https://doi.org/10.1007/s10518-015-9774-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-015-9774-6