Skip to main content
Log in

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

  • Published:
Earthquake Engineering and Engineering Vibration Aims and scope Submit manuscript

Abstract

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least-square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc-Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baber TT (1981), “Random Vibration of Hysteretic Degrading System,” Journal of Engineering Mechanics, ASCE, 107:1069–1087.

    Google Scholar 

  • Baber TT and Noori MN (1986), “Modeling General Hysteresis Behavior and Random Vibration Application,” J. Vib. Acoust. Stress Reliab. Des., ASCE, 108: 411–420.

    Google Scholar 

  • Buckle IG, Constantinou MC, et al. (2006), “Seismic Isolation of Highway Bridges,” Special Report MCEER-06-SP07.

  • Chen BJ, Tsai CS and Chung LL et al. (2006), “Seismic Behavior of Structures Isolation with a Hybrid System of Rubber Bearings,” Structural Engineering and Mechanics, 22(6): 761–783.

    Google Scholar 

  • Clark PW, Aiken ID and Kelly JM (1997), “Experimental Studies of the Ultimate Behavior of Seismically-isolated Structures,” Technical Report EERC-97-18, Earthquake Engineering Research Center, University of California Berkeley, California, U.S.A.

    Google Scholar 

  • Hoshiya M and Saito E (1984), “Structural Identification by Extended Kalman Filter,” Journal of Engineering Mechanics, ASCE, 110(12): 1757–1771.

    Article  Google Scholar 

  • Huang HW, Yang JN, and Zhou L (2009), “Adaptive Quadratic Sum-squares Error with Unknown Inputs for Damage Identification of Structures,” Journal structural Control and Health Monitoring, Published online in Wiley InterScience, DOI: 10.1002/stc.318.

  • Huang JW and Zhao B (2000), “The Nonlinear Dynamic Response of Multistory Base Isolated Building with Laminated Rubber Bearings,” Journal of Xi’an University of Science & Technology, 20(4): 317–321. (in Chinese)

    Google Scholar 

  • Jangid RS and Datta TK (1995), “Seismic Behavior of Base Isolated Building: A State-of-the-art Review,” Structures and buildings, 110: 186–203.

    Article  Google Scholar 

  • Kasalanati A and Constantinou MC (1999), “Experimental Study of Bridge Elastomeric and Other Isolation and Energy Dissipation System with Emphasis on Uplift Prevention and High Velocity Near-source Seismic Excitation,” Technical Report MCEER-99-0004, University at Buffalo, State University of New York, U.S.A.

    Google Scholar 

  • Kelly JM (1986), “A Seismic Base Isolation: Review and Bibliography,” Soil Dynamics and Earthquake Engineering, 5: 202–216.

    Article  Google Scholar 

  • Kelly JM (1997), Earthquake-Resistant Design with Rubber, 2nd ed, London.

  • Komodromos P (2000), Seismic Isolation for Earthquake-Resistant Structures, Ashurst: WIT Press.

    Google Scholar 

  • Lin JW, Betti R, Smyth WA and Longman RW (2001), “On-line Identification of Nonlinear Hysteretic Structural System Using a Variable Trace Approach,” Earthquake Engineering and Structural Dynamics, 30: 1279–1303.

    Article  Google Scholar 

  • Loh CH, Lin CY and Huang CC (2000), “Time Domain Identification of Frames under Earthquake Loadings,” Journal of Engineering Mechanics, ASCE, 126(7): 693–703.

    Article  Google Scholar 

  • Ma F, Zhang H, Bockstedte A, Foloente GC and Paevere P (2004), Parameter Analysis of the Differential Model of Hysteresis, ASCE, Journal of Applied Mechanics, 71: 342–349.

    Article  Google Scholar 

  • Maruyama O, Yun CB, Hoshiya M and Shinozuka M (1989), “Program EXKAL2 for Identification of Structural Dynamical Systems,” Technical Report NCEER-89-0014, National Center for Earthquake Engineering Research, Buffalo.

    Google Scholar 

  • Naeim F and Kelly JM (1999), Design of Seismic Isolated Structures-From Theory to Practice, John Wiley & Sons, Inc.

  • Sato T, Honda R and Sakanoue T (2001), “Application of Adaptive Kalman Filter to Identify a Five Story Frame Structure Using NCREE Experimental Data,” Proc. Structural Safety and Reliability, ICOSSA2001, Swets & Zeitinger: Lisse, CD-ROM, 7 pages.

  • Sato T and Takei K (1998), “Development of a Kalman Filter with Fading Memory.” Proc. Structural Safety and Reliability, ICOSSA, Balkma, Rotterdam, 387–349.

    Google Scholar 

  • Skinner RI, Robinson WH and McVerry GH (1993), An Introduction to Seismic Isolation, John Wiley & Sons, Inc.

  • Wang XM and Zhou L (2008), “Modeling of a Rubber Bearing and Its Parameters Estimation Based on Its Dynamic Response,” Journal of Vibration and Shock, 27(1): 146–150. (in Chinese)

    Google Scholar 

  • Wen YK (1976), “Method for Random Vibration of Hysteretic Systems,” J. Eng. Mech. Div., 102(2): 249–263.

    Google Scholar 

  • Wen YK (1980), “Equivalent Linearization for Hysteretic Systems under Random Excitations,” Journal of Applied Mechanics, ASME, 47(1): 150–154.

    Article  Google Scholar 

  • Wong CW, Ni YQ and Lau SL (1994), “Steady-State Oscillation of Hysteretic Differential Model II: Performance analysis,” Journal of Engineering Mechanics, ASME, 120: 2299–2325.

    Article  Google Scholar 

  • Wu SY and Zhou L (2007), “A Finite-horizon Adaptive Kalman Filter for Structural Damage Identification,” Journal of Vibration Engineering, 20(4): 401–406. (in Chinese)

    Google Scholar 

  • Yang JN and Huang HW (2007), “Sequential Non-linear Least-square Estimation for Damage Identification of Structures with Unknown Inputs and Unknown Outputs,” International Journal of Non-linear Mechanics, 42(5): 789–801.

    Article  Google Scholar 

  • Yang JN, Huang HW and Lin S (2006a), “Sequential Non-linear Least-square Estimation for Damage Identification of Structures, International Journal of Non-linear Mechanics, 41(1): 124–140.

    Article  Google Scholar 

  • Yang JN, Huang HW and Pan S (2009), “Adaptive QuadraticSum Squares Error for Structural Damage Identification,” Journal of Engineering Mechanics, ASCE, 135(2), 67–77.

    Article  Google Scholar 

  • Yang JN and Lin S (2004), “On-Line Identification of Nonlinear Hysteretic Structures Using an Adaptive Tracking Technique,” International Journal of Nonlinear Mechanics, 39: 1481–1491.

    Article  Google Scholar 

  • Yang JN and Lin S (2005), “Identification of Parametric Variations of Structures Based on Least Square Estimation and Adaptive Tracking Technique,” Journal of Engineering Mechanics, ASME, 131(3): 290–298.

    Article  Google Scholar 

  • Yang JN, Lin SL, Huang HW and Zhou L (2006b), “An Adaptive Extended Kalman Filter for Structural Damage Identification,” Journal of Structural Control and Health Monitoring, 13(4): 849–867.

    Article  Google Scholar 

  • Yang JN, Pan SW and Huang HW (2006c), “An Adaptive Extended Kalman Filter for Structural Damage Identification II: Unknown Inputs,” Journal of Structural Control and Health Monitoring, 14(3): 497–521.

    Article  Google Scholar 

  • Yun CB, Lee HJ and Lee CG (1997), “Sequential Prediction Error Method for Structural Identification,” Journal of Engineering Mechanics, ASCE, 123(2), 115–123.

    Article  Google Scholar 

  • Zhou L, Wu SY and Yang JN (2008), “Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification,” Journal of Infrastructure Systems, ASME, 14(1): 42–51.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li Zhou.

Additional information

Supported by: National Natural Science Foundation of China Under Grant No. 10572058; the Science Foundation of Aeronautics of China Under Grant No.2008ZA52012

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yin, Q., Zhou, L. & Wang, X. Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation. Earthq. Eng. Eng. Vib. 9, 375–383 (2010). https://doi.org/10.1007/s11803-010-0022-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11803-010-0022-4

Keywords

Navigation