Output-Error Methods in Structural Modal Identification

Document Type : Research Article

Authors

1 Department of Civil Engineering, Sarab Branch, Islamic Azad University, Sarab, Iran.

2 Department of Civil Engineering, Malekan Branch, Islamic Azad University, Malekan, Iran.

Abstract

Stochastic subspace identification (SSI) is a process that linearizes the identification problem by utilizing singular value decomposition (SVD) and QR factorization. This technique enables the extraction of system matrices through linear least squares. However, the estimated systems in these methods are affected by the user-defined dimensions of the data space (Hankel matrix). Also, SSI does not explicitly minimize a cost function for estimating system matrices, making statistical analysis difficult. To enhance the accuracy of modal specifications obtained from SSI, especially the damping ratios, this research suggests using output-error methods (OEM). During OEM, the process involves iteratively adjusting the model parameters to match the outputs of the simulated model with those of the observed system. The following steps are taken to enhance the OEM for extracting structural properties: Firstly, the initial term is derived using the SSI to reduce the number of optimization iterations. Secondly, by using the Gauss-Newton approach, the nonlinearity of the objective function is reduced by treating the second-order derivatives as a linear system. Finally, Gradient project minimization is utilized in SSI to ensure the injectivity of estimated systems. The OEM was validated by analyzing the response of a 3-DOF excited by white noise with an SNR of 1 db.  Then, the model was then applied to seismic observations of Pacoima Dam during the 2001 San Fernando and 2008 Chino Hills earthquakes. The two main modes of the structure were extracted, and they had the least error compared to the developed finite element models.

Keywords

Main Subjects

References

[1] O.C. Celik, H.P. Gülkan, Processing forced vibration test records of structural systems using the analytic signal, Journal of Vibration and Control, 27(19-20) (2021) 2253-2267.
[2] J.P. Gomes, J.V. Lemos, Characterization of the dynamic behavior of a concrete arch dam by means of forced vibration tests and numerical models, Earthquake Engineering & Structural Dynamics, 49(7) (2020) 679-694.
[3] J. Brownjohn, M. Bocian, D. Hester, Forced vibration testing of footbridges using calibrated human shaker and wireless sensors, Procedia Engineering, 199 (2017) 417-422.
[4] M. Viberg, Subspace-based methods for the identification of linear time-invariant systems, Automatica, 31(12) (1995) 1835-1851.
[5] P. Van Overschee, B.L. De Moor, Subspace identification for linear systems: theory, implementation, applications, Kluwer academic publishers Dordrecht, 1996.
[6] V. Verdult, Non linear system identification: a state-space approach, University of Twente, Enschede, The Netherlands, 2002.
[7] K. Peternell, W. Scherrer, M. Deistler, Statistical analysis of novel subspace identification methods, Signal Processing, 52(2) (1996) 161-177.
[8] D. Bauer, M. Deistler, W. Scherrer, User choices in subspace algorithms, in:  Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No. 98CH36171), IEEE, 1998, pp. 731-736.
[9] M. Jansson, B. Wahlberg, On consistency of subspace methods for system identification, Automatica, 34(12) (1998) 1507-1519.
[10] P. Van Overschee, B. De Moor, Subspace identification for linear systems: Theory—Implementation—Applications, Springer Science & Business Media, 2012.
[11] P. Van Overschee, B. De Moor, N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems, Automatica, 30(1) (1994) 75-93.
[12] T. Katayama, Subspace methods for system identification, Springer, 2006.
[13] G. Picci, T. Katayama, Stochastic realization with exogenous inputs and ‘subspace-methods’ identification, Signal Processing, 52(2) (1996) 145-160.
[14] R.A. Fisher, On the mathematical foundations of theoretical statistics, Philosophical transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character, 222(594-604) (1922) 309-368.
[15] J.R. Raol, G. Girija, J. Singh, Modelling and parameter estimation of dynamic systems, Iet, 2004.
[16] P. Kabaila, On output-error methods for system identification, IEEE Transactions on Automatic Control, 28(1) (1983) 12-23.
[17] Y. Tomita, A.A. Damen, P.M.V.D. HOF, Equation error versus output error methods, Ergonomics, 35(5-6) (1992) 551-564.
[18] M. Kosaka, H. Uda, E. Bamba, H. Shibata, State-space model identification using input and output data with steady state values zeroing multiple integrals of output error,  (2006).
[19] J.J. Moré, The Levenberg-Marquardt algorithm: implementation and theory, in:  Numerical analysis, Springer, 1978, pp. 105-116.
[20] B. Peeters, System Identification and Damage Detection in Civil Engeneering, Katholieke Universiteit Leuven, Heverlee (Belgium), 2000.
[21] M. Verhaegen, V. Verdult, Filtering and system identification: a least squares approach, Cambridge university press, 2007.
[22] B. David, Parameter estimation in nonlinear dynamical systems with correlated noise, UCL-Université Catholique de Louvain, 2001.
[23] L.C.S. Góes, E.M. Hemerly, B.C.d.O. Maciel, W.R. Neto, C. Mendonca, J. Hoff, Aircraft parameter estimation using output-error methods, Inverse problems in science and engineering, 14(6) (2006) 651-664.
[24] D.A. Dutra, Collocation-based output-error method for aircraft system identification, in:  AIAA Aviation 2019 Forum, 2019, pp. 3087.
[25] M. Brunot, A. Janot, F. Carrillo, J. Cheong, J.-P. Noël, Output error methods for robot identification, Journal of Dynamic Systems, Measurement, and Control, 142(3) (2020) 031002.
[26] S. Dong, T. Liu, W. Wang, J. Bao, Y. Cao, Identification of discrete-time output error model for industrial processes with time delay subject to load disturbance, Journal of Process Control, 50 (2017) 40-55.
[27] C.-T. Chen, Linear system theory and design, Oxford University Press, Inc., United States of America, New York, 1995.
[28] M. Verhaegen, Identification of the deterministic part of MIMO state space models given in innovations form from input-output data, Automatica, 30(1) (1994) 61-74.
[29] J.-H. Weng, C.-H. Loh, J.P. Lynch, K.-C. Lu, P.-Y. Lin, Y. Wang, Output-only modal identification of a cable-stayed bridge using wireless monitoring systems, Engineering Structures, 30(7) (2008) 1820-1830.
[30] M. Verhaegen, Subspace model identification part 3. Analysis of the ordinary output-error state-space model identification algorithm, International Journal of control, 58(3) (1993) 555-586.
[31] M. Verhaegen, P. Dewilde, Subspace model identification part 2. Analysis of the elementary output-error state-space model identification algorithm, International journal of control, 56(5) (1992) 1211-1241.
[32] M. Verhaegen, P. Dewilde, Subspace model identification part 1. The output-error state-space model identification class of algorithms, International journal of control, 56(5) (1992) 1187-1210.
[33] T. McKelvey, A. Helmersson, System identification using an over-parametrized model class-improving the optimization algorithm, in:  Proceedings of the 36th IEEE Conference on Decision and Control, IEEE, 1997, pp. 2984-2989.
[34] L.H. Lee, K. Poolla, Identification of linear parameter-varying systems using nonlinear programming,  (1999).
[35] M. Pastor, M. Binda, T. Harčarik, Modal assurance criterion, Procedia Engineering, 48 (2012) 543-548.
[36] P. Andersen, Identification of civil engineering structures using vector ARMA models, Aalborg University, Aalborg, Denmark, 1997.
[37] M. Vigsø, T. Kabel, M. Tarpø, R. Brincker, C. Georgakis, Operational modal analysis and fluid-structure interaction, in:  Procedings of the International Conference on Noise and Vibration Engineering, ISMA, 2018.
[38] S. Alves, J. Hall, Generation of spatially nonuniform ground motion for nonlinear analysis of a concrete arch dam, Earthquake engineering & structural dynamics, 35(11) (2006) 1339-1357.
[39] S.W. Alves, Nonlinear analysis of Pacoima Dam with spatially nonuniform ground motion, California Institute of Technology, 2005.
[40] S. Alves, J. Hall, System identification of a concrete arch dam and calibration of its finite element model, Earthquake engineering & structural dynamics, 35(11) (2006) 1321-1337.
[41] M. Isari, R. Tarinejad, A. TaghaviGhalesari, A. Sohrabi-Bidar, A new approach to generating non-uniform support excitation at topographic sites, Soils and Foundations, 59(6) (2019) 1933-1945.
[42] R. Tarinejad, Effects of blast loading on the response of concrete arch dam (Case study: Karun 4), Modares Civil Engineering journal, 18(1) (2018) 43-54.
[43] L. Cheng, C. Ma, X. Yuan, J. Yang, L. Hu, D. Zheng, A Literature Review and Result Interpretation of the System Identification of Arch Dams Using Seismic Monitoring Data, Water, 14(20) (2022) 3207.
[44] R. Tarinejad, R. Fatehi, Modal identification of an arch dam during various earthquakes, in:  Proceedings of the 1st International Conference On Dams And Hydropower, 2012.
AUT Journal of Civil Engineering
Volume 7, Issue 1
March 2023
Pages 49-66

Files

Share

How to cite

Statistics