Abstract
This paper presents a novel method for recovering base shear forces of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics and real modes, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. A sum (or weighted sum) of the resulting vector of inertial forces gives the base shear. The proposed algorithm is suitable for linear and nonlinear hysteretic structural systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abe, M., Fujino, Y., Yoshida, J.: Dynamic behaviour and seismic performance of base-isolated bridges in observed seismic records. In: Proceedings of 12th World Conference on Earthquake Engineering (2000)
Ahmadi, G., Fan, F., Noori, M.: A thermodynamically consistent model for hysteretic materials. Iran. J. Sci. Technol. 21(3), 257–278 (1997)
Alhan, C., Gavin, H.: A parametric study of linear and non-linear passively damped seismic isolation systems for buildings. Eng. Struct. 26(4), 485–497 (2004)
Cadzow, J.A.: Signal enhancement-a composite property mapping algorithm. IEEE Trans. Acoust. Speech Signal Process. 36(1), 49–62 (1988)
Celebi, M.: Successful performance of a base-isolated hospital building during the 17 January 1994 Northridge earthquake. Struct. Des. Tall Build. 5, 95–109 (1996)
Chaudhary, M., Abe, M., Fujino, Y.: Identification of soil–structure interaction effect in base-isolated bridges from earthquake records. Soil Dyn. Earthq. Eng. 21(8), 713–725 (2001)
Chaudhary, M.T.A., Abe, M., Fujino, Y., Yoshida, J.: System identification of two base-isolated bridges using seismic records. J. Struct. Eng. 126(10), 1187–1195 (2000)
Ding, Y., Law, S., Wu, B., Xu, G., Lin, Q., Jiang, H., Miao, Q.: Average acceleration discrete algorithm for force identification in state space. Eng. Struct. 56, 1880–1892 (2013)
Erlicher, S., Point, N.: Thermodynamic admissibility of Bouc-Wen type hysteresis models. Comptes Rendus Méc. 332(1), 51–57 (2004)
Furukawa, T., Ito, M., Izawa, K., Noori, M.N.: System identification of base-isolated building using seismic response data. J. Eng. Mech. 131(3), 268–275 (2005)
Gavin, H.P., Scruggs, J.T.: Constrained optimization using lagrange multipliers. CEE 201L. Duke University (2012)
Golyandina, N., Nekrutkin, V., Zhigljavsky, A.A.: Analysis of Time Series Structure: SSA and Related Techniques. CRC, New York (2001)
Huang, M.-C., Wang, Y.-P., Lin, T.-K., Chen, Y.-H.: Development of physical-parameter identification procedure for in-situ buildings with sliding-type isolation system. J. Sound Vib. 332(13), 3315–3328 (2013)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 454, pp. 903–995. The Royal Society (1998)
Hyvärinen, A.: Complexity pursuit: separating interesting components from time series. Neural Comput. 13(4), 883–898 (2001)
Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis bouc-wen model, a survey. Arch. Comput. Meth. Eng. 16(2), 161–188 (2009)
Juang, J.-N., Pappa, R.S.: An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. Control. Dyn. 8(5), 620–627 (1985)
Juang, J.-N., Phan, M., Horta, L.G., Longman, R.W.: Identification of observer/kalman filter Markov parameters-theory and experiments. J. Guid. Control. Dyn. 16(2), 320–329 (1993)
Kampas, G., Makris, N.: Time and frequency domain identification of seismically isolated structures: advantages and limitations. Earthq. Struct. 3(3–4), 249–270 (2012)
Kijewski, T., Kareem, A.: Wavelet transforms for system identification in civil engineering. Comput.-Aided Civ. Infrastruct. Eng. 18(5), 339–355 (2003)
Ljung, L.: Prediction error estimation methods. Circuits Syst. Signal Process. 21(1), 11–21 (2002)
Loh, C.-H., Weng, J.-H., Chen, C.-H., Lu, K.-C.: System identification of mid-story isolation building using both ambient and earthquake response data. Struct. Control. Health Monit. 20(2), 139–155 (2013)
Mahmoudvand, R., Zokaei, M.: On the singular values of the Hankel matrix with application in singular spectrum analysis. Chilean J. Stat. 3(1), 43–56 (2012)
Markovsky, I.: Structured low-rank approximation and its applications. Automatica 44(4), 891–909 (2008)
Markovsky, I.: Low Rank Approximation: Algorithms, Implementation, Applications. Springer Science & Business Media, New York (2011)
Nagarajaiah, S., Xiaohong, S.: Response of base-isolated USC hospital building in Northridge earthquake. J. Struct. Eng. 126(10), 1177–1186 (2000)
Oliveto, N.D., Scalia, G., Oliveto, G.: Time domain identification of hybrid base isolation systems using free vibration tests. Earthq. Eng. Struct. Dyn. 39(9), 1015–1038 (2010)
Peeters, B., De Roeck, G.: Reference-based stochastic subspace identification for output-only modal analysis. Mech. Syst. Signal Process. 13(6), 855–878 (1999)
Siringoringo, D.M., Fujino, Y.: Seismic response analyses of an asymmetric base-isolated building during the 2011 great east Japan (Tohoku) earthquake. Struct. Control. Health Monit. 22(1), 71–90 (2015)
Staszewski, W.: Identification of damping in MDOF systems using time-scale decomposition. J. Sound Vib. 203(2), 283–305 (1997)
Stewart, J.P., Conte, J.P., Aiken, I.D.: Observed behavior of seismically isolated buildings. J. Struct. Eng. 125(9), 955–964 (1999)
Takewaki, I., Nakamura, M.: Stiffness-damping simultaneous identification under limited observation. J. Eng. Mech. 131(10), 1027–1035 (2005)
Takewaki, I., Nakamura, M.: Temporal variation in modal properties of a base-isolated building during an earthquake. J. Zhejiang Univ. Sci. A 11(1), 1–8 (2010)
Trefethen, L.N., Bau III, D.: Numerical Linear Algebra, vol. 50. SIAM (1997)
Xu, C., Chase, J.G., Rodgers, G.W.: Physical parameter identification of nonlinear base-isolated buildings using seismic response data. Comput. Struct. 145, 47–57 (2014)
Yang, J.N., Lei, Y., Pan, S., et al.: System identification of linear structures based on Hilbert-Huang spectral analysis. part 1: normal modes. Earthq. Eng. Struct. Dyn. 32(9), 1443–1468 (2003)
Yang, Y., Nagarajaiah, S.: Output-only modal identification with limited sensors using sparse component analysis. J. Sound Vib. 332(19), 4741–4765 (2013)
Yoshimoto, R.: Damage detection of base-isolated buildings using multi-inputs multi-outputs subspace identification. Ph.D Thesis, Department of System Design Engineering, Keio University (1776)
Acknowledgements
This material is based in part upon work supported by the National Science Foundation under Grant Number CMMI-1258466. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Yin, B., Gavin, H. (2016). Inelastic Base Shear Reconstruction from Sparse Acceleration Measurements of Buildings. In: Pakzad, S., Juan, C. (eds) Dynamics of Civil Structures, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29751-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-29751-4_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29750-7
Online ISBN: 978-3-319-29751-4
eBook Packages: EngineeringEngineering (R0)