Skip to main content
SpringerLink
Log in

Use of active control algorithm for optimal design of base-isolated buildings against earthquakes

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This study presents a new design method that concurrently determines the stiffness and damping coefficient in a base isolation system. This design method is developed based on the similarity between the active and passive control system. Then, the stiffness and damping coefficient are derived from the linear quadratic regulator control algorithm to a single degree of freedom superstructure and formed as a function of single weighting. The best design of a base isolation system is determined by optimizing this weighting from the minimum H∞-norm responses of base displacement and roof acceleration. A parametric study is performed to understand the influence of superstructures to the resulting optimized base isolation system. Moreover, this study also provides a numerical example to validate the optimal design of base isolation systems. The potential to design nonlinear lead-rubber bearings with added viscous dampers based on the proposed method is also investigated. As a result, the proposed method yields a high-performance base isolation system for a known superstructure.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Buckle I, Nagarajaiah S, Ferrell K (2002) Stability of elastomeric isolation bearings: experimental study. J Struct Eng 128(1):3–11

    Article  Google Scholar 

  • Chang CM, Spencer BF, Shi P (2014) Multiaxial active isolation for seismic protection of buildings. Struct Control Health Monit 21(4):484–502

    Article  Google Scholar 

  • Conn AR, Schienburg K, Vicente LN (2009). Introduction to derivative-free optimization. MPS/SIAM Book Series on Optimization. SIAM, Philadelphia, PA.

  • Constantinou MC, Tadjbakhsh IG (1985). Optimum characteristics of isolated structures. ASCE Journal of Structural Engineering 111(12): 2733–2750.

  • Du Y, Li H, Spencer BF (2002) Effect of non-proportional damping on seismic isolation. Struct Control Health Monit 9(3):205–236

    Article  Google Scholar 

  • Dyke SJ, Spencer BF Jr, Quast P, Sain MK, Kaspari DC, Soong TT (1994) Experimental verification of acceleration feedback control strategies for an active tendon system. NCEER rep. 94-0024, state Univ. of New York at Buffalo, New York

  • International Conference of Building Officials (1997) Uniform building code. Earthquake Regulation for Seismic-Isolated Structures, 2, Appendix, Chap. 16, Whittier, CA

  • Jangid RS, Kelly JM (2001) Base isolation for near-fault motions. Earthq Eng Struct Dyn 30(5):691–707

    Article  Google Scholar 

  • Kang S, Yoshida K (1992) Vibration isolation control with feedforward link using H∞ control theory. Trans Jpn Soc Mech Eng Series C 58(556):3627–3633

    Article  Google Scholar 

  • Kelly JM (1986) Aseismic base isolation: review and bibliography. Soil Dyn Earthq Eng 5(4):202–216

    Article  Google Scholar 

  • Kelly JM (1999) The role of damping in seismic isolation. Earthq Eng Struct Dyn 28(1):3–20

    Article  Google Scholar 

  • Kelly JM, Leitmann G, Soldatos AG (1987) Robust control of base-isolated structures under earthquake excitation. J Optim Theory Appl 53(2):159–180

    Article  MathSciNet  MATH  Google Scholar 

  • Kulkarni JA, Jangid RS (2002) Rigid body response of base-isolated structures. Struct Control Health Monit 9(3):171–188

    Article  Google Scholar 

  • Lilhanand K, Tseng W (1988). Development and application of realistic earthquake time histories compatible with multiple-damping design spectra. Proc., 9th World Conf. on Earthquake Engineering. Indian Institute of Technology, Kanpur, pp 819–824

  • Lin BC, Tadjbakhsh IG, Papageorgiou AS, Ahmadi G (1989) Response of base-isolated buildings to random excitations described by the Clough-Penzien spectral model. Earthq Eng Struct Dyn 18(1):49–62

    Article  Google Scholar 

  • Liu W, Tong M, Lee GC (2005) Optimization methodology for damper configuration based on building performance indices. J Struct Eng 131(11):1746–1756

    Article  Google Scholar 

  • Marano GC, Trentadue F, Greco R (2007) Stochastic optimum design criterion for linear damper devices for seismic protection of buildings. Struct Multidiscip Optim 33(6):441–455

    Article  Google Scholar 

  • Marano GC, Quaranta G, Greco R (2009) Multi-objective optimization by genetic algorithm of structural systems subject to random vibrations. Struct Multidiscip Optim 39(4):385–399

    Article  Google Scholar 

  • Nagarajaiah S, Ferrell K (1999) Stability of elastomeric seismic isolation bearings. J Struct Eng 125(9):946–954

    Article  Google Scholar 

  • Politopoulos I (2008) A review of adverse effects of damping in seismic isolation. Earthq Eng Struct Dyn 37(3):447–465

    Article  Google Scholar 

  • Providakis CP (2009) Effect of supplemental damping on LRB and FPS seismic isolators under near-fault ground motions. Soil Dyn Earthq Eng 29(1):80–90

    Article  Google Scholar 

  • Ramallo JC, Johnson EA, Spencer BF Jr (2002) “Smart” base isolation systems. J Eng Mech 128(10):1088–1099

    Article  Google Scholar 

  • Riley MA, Reinhorn AM, Nagarajaiah S (1998) Implementation issues and testing of a hybrid sliding isolation system. Eng Struct 20(3):144–154

    Article  Google Scholar 

  • Ryan KL, Chopra AK (2004) Estimation of seismic demands on isolators based on nonlinear analysis. J Struct Eng 130(3):392–402

    Article  Google Scholar 

  • Ryan KL, Polanco J (2008) Problems with Rayleigh damping in base-isolated buildings. J Struct Eng 134(11):1780–1784

    Article  Google Scholar 

  • Spencer BF Jr, Suhardjo J, Sain MK (1994) Frequency domain optimal control strategies for aseismic protection. J Eng Mech 120(1):135–158

    Article  Google Scholar 

  • Su L, Ahmadi G, Tadjbakhsh IG (1989) Comparative study of base isolation systems. J Eng Mech 115(9):1976–1992

    Article  Google Scholar 

  • Warn GP, Ryan KL (2012) A review of seismic isolation for buildings: historical development and research needs. Buildings 2:300–325

    Article  Google Scholar 

  • Wongprasert N, Symans MD (2005) Experimental evaluation of adaptive elastomeric base-isolated structures using variable-orifice fluid dampers. J Struct Eng 131(6):867–877

    Article  Google Scholar 

  • Yang JN, Wu JC, Reinhorn AM, Riley M (1996) Control of sliding-isolated buildings using sliding-mode control. J Struct Eng 122(2):179–186

    Article  Google Scholar 

  • Yoshioka H, Ramallo JC, Spencer BF Jr (2002) “Smart” base isolation strategies employing magnetorheological dampers. J Eng Mech 128(5):540–551

    Article  Google Scholar 

  • Zou XK (2008) Integrated design optimization of base-isolated concrete buildings under spectrum loading. Struct Multidiscip Optim 36(5):493

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the Ministry of Science and Technology in Taiwan under Grant No. MOST 106-2221-E-002-048-MY2.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, National Taiwan University, Taipei, 10617, Taiwan

    Chia-Ming Chang & Syuan Shia

  2. National Center for Research on Earthquake Engineering, Taipei, 10688, Taiwan

    Cho-Yen Yang

Authors
  1. Chia-Ming Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Syuan Shia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cho-Yen Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chia-Ming Chang.

Appendix

Appendix

1.1 Design of Lead-Rubber Bearings

Each type of base isolation system are assumed to comprise of four LRBs. These LRBs are modeled by a bilinear hysteretic loop as illustrated in Appendix Fig. 11. In the LRB modelling, a maximum displacement D2 should be determined in advance. The preyield to postyield stiffness ratio α is fixed to 13, while the equivalent damping ratio ζb is up to 5%. The equivalent stiffness in this modelling is identical to the designed stiffness k1. If the designed damping coefficient c1 exceeds \( {\overline{c}}_1 \) that the LRBs can provide, the remaining damping coefficient (i.e., \( {c}_1-{\overline{c}}_1 \)) is realized by viscous dampers. Therefore, the preyield stiffness Ku and postyield stiffness Kd are determined by

$$ {\displaystyle \begin{array}{l}{K}_d=\frac{k_1{D}_2}{n_{\mathrm{iso}}\left({D}_2-\left(1-\alpha \right){D}_1\right)},{K}_u=\alpha {K}_d\\ {}{\zeta}_b=\frac{{\overline{c}}_1}{2\sqrt{k_1\left({m}_1+{m}_2\right)}}=\frac{4Q\left({D}_2-{D}_1\right){n}_{\mathrm{iso}}}{2\pi {k}_1{D}_2}\le 5\%,{\overline{c}}_1\le {c}_1\end{array}} $$
(18)

where niso is the number of LRBs used in a base isolation system. Note that (18) would result in two sets of parameters, and this study selects the set with a smaller D1. This LRB model with D2 = 0.15 m is then employed to perform nonlinear dynamic analysis. The LRBs used in these four types of isolation systems are listed in Appendix Table 2.

Fig. 11
figure 11

Illustration of bilinear hysteretic model for modelling of lead-rubber bearing

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, CM., Shia, S. & Yang, CY. Use of active control algorithm for optimal design of base-isolated buildings against earthquakes. Struct Multidisc Optim 58, 613–626 (2018). https://doi.org/10.1007/s00158-018-1913-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-018-1913-7

Keywords

Search

Navigation