Finding Reliable Identification Results for Nonlinear SDOF Systems, based on Sensitivity Analyses

Document Type : Research Article


1 Associate Professor, Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

2 Ph.D. Candidate, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran


Post-earthquake assessment of buildings is one of the fundamental questions that needs to be answered immediately after a strong seismic event. Taking a building out of service after an earthquake can have a financial impact even greater than the earthquake itself. Up to now, damaged buildings are categorized in three groups, with red, yellow, or green labels, by engineering judgment based on visual screening. To have a more accurate method, the response of the buildings in aftershocks can be focused on new vibration-based system identification methods. But determining the system parameters is still a challenging subject; involving parameters with low identifiability, or correlated parameters can potentially influence the results in model updating problems. In this paper, a sensitivity matrix-based method is introduced to prioritize parameter estimability. The matrix-based process is capable of quickly determining the correlation between different parameters. Moreover, this method provides an explicit criterion for determining the optimal number of identifiable parameters. To indicate the efficiency of the method, a nonlinear Single-Degree of Freedom (SDOF) system has been simulated. Multiple model updating procedures have been carried out on the selected system, using the Unscented Kalman Filter (UKF). The result shows that system identification based on the sensitivity analysis outcome improves the quality of the identification precision. Additionally, this method decreases identification time by 35 percent that this amount can be crucial for updating large-scaled models.


Main Subjects

  1. Galloway, B., Hare, J., & Brunsdon, D. (2014) Lessons from the Post-Earthquake Evaluation of Damaged Buildings in Christchurch. Earthquake Spectra, 30(1), 451-474. doi:10.1193/022813EQS057M.
  2. ATC (1989) ATC-20, Procedures for Postearthquake Safety. Redwood City, California: Applied Technology Council (ATC).
  3. ATC (1995) ATC 20-2, Addendum to the ATC-20 postearthquake building safety evaluation procedures. Redwood City, CA: Technical report, Applied Technology Council (ATC).
  4. ATC (1996-a) ATC 20- 3, Case Studies in Rapid Postearthquake Safety Evaluation of Buildings. Redwood City, California: Technical report, Applied Technology Council (ATC).
  5. ATC (1996b) ATC-40, Seismic evaluation and retrofit of concrete buildings. Redwood City, CA: Applied Technology Council (ATC).
  6. Goulet, J.-A., Michel, C. & Kiureghian, A.D. (2015) Data-driven post-earthquake rapid structural safety assessment. Earthquake Engineering & Structural Dynamics, 44(4), 549–562.
  7. Astroza, R., Ebrahimian, H., & Conte, J.P. (2014) Material Parameter Identification in Distributed Plasticity FE Models of Frame-Type Structures Using Nonlinear Stochastic Filtering. Journal of Engineering Mechanics, 141(5), doi:10.1061/(ASCE)EM.1943-7889.0000851.
  8. Astroza, R., Ebrahimian, H., Li, Y., & Conte, J.P. (2017) Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures. Mechanical Systems and Signal Processing, 93, 661–687.
  9. Moaveni, B., Conte, J.P. & Restrepo, J.I. (2010) Damage identification study of a seven-story full-scale building slice tested on the ucsd-nees shake table. Structural Safety, 32(5), 347–356.
  10. Reuland, Y., Lestuzzi, P., & Smith, I.F. (2019) An engineering approach to model-class selection for measurementsupported post-earthquake assessment. Engineering Structures, 197, doi:10.1016/j.engstruct.2019.109408.
  11. Erazo, K. & Hernandez, E. M. (2016) Bayesian model–data fusion for mechanistic postearthquake damage assessment of building structures. Journal of Engineering Mechanics, 142(9).
  12. Kalman, R.E. (1960) A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1), 35–45.
  13. Hoshiya, M. & Saito, E. (1984) Structural identification by extended kalman filter. Journal of Engineering Mechanics, 110(12), 1757–1770.
  14. Julier, S.J., Uhlmann, J. & Durrant-Whyte, H.F. (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 45(3), 477–482.
  15. Khalil, H. (2002) Nonlinear Systems (3rd), Upper Saddle River: Prentice Hall.
  16. Capellari, G., Chatzi, E. & Mariani, S. (2017) Parameter Identifiability through Information Theory. 2nd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering. Rhodes Island, doi:10.7712/120217.5376.17179.
  17. Kirsch, U. (1994) Efficient sensitivity analysis for structural optimization. Computer Methods in Applied Mechanics and Engineering, 117(1-2), 143-156.
  18. Saltelli, A., Tarantola, S. & Campolongo, F. (2000) Sensitivity Analysis as an Ingredient of Modeling. Statistical Science, 15(4), 377-395.
  19. Razavi, S., Jakeman, A., Saltelli, A. & Prieur, C. (2021) The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support. Environmental Modelling & Software, 137.
  20. Michael, S. & Haukaas, T. (2008) Software Framework for Parameter Updating and Finite-Element Response Sensitivity Analysis. Journal of Computing In Civil Engineering, 22(5), 281-291.
  21. Ramanacha, M.K, Astroza, R., Madarshahian, R., & Conte, J.P. (2022) Bayesian updating and identifiability assessment of nonlinear finite element models. Mechanical Systems and Signal Processing, 108517, 167.
  22. Gu, Q., Liu, Y., Li, Y., & Lin, C. (2018) Finite element response sensitivity analysis of three-dimensional soil-foundation-structure interaction (SFSI) systems. Earthquake Engineering and Engineering Vibration, 17(3), 555-566, doi:
  23. Yao, K.Z., Shaw, B.M., Kou, B., McAuley, K.B., & Bacon, D.W. (2003) Modeling ethylene butene copolymerization with multi-site catalysts: parameter estimability and experimental design. React. Eng., 11(3), 563–588, doi:10.1081/PRE-120024426.
  24. Wan, E., & van der Merwe, R. (2000) The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (pp. 153-158). Lake Louise, Alberta, Canada: IEEE. doi:10.1109/ASSPCC.2000.882463.
  25. Baker, S., Poskar, C.H., & Junker, B.H. (2011) Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models. EURASIP Journal on Bioinformatics and Systems Biology, 1(7), doi:10.1186/1687-4153-2011-7.
  26. Sengupta, Piyali, Li, Bing (2013) Modified Bouc–Wen model for hysteresis behavior of RC beam–column joints with limited transverse reinforcement. Engineering Structures, 46, 392-406. doi:
  27. Brink, K.M. (2017) Partial-Update Schmidt–Kalman Filter. Journal of Guidance, Control, and Dynamics, 40(9), 2214-2228.