Encyclopedia of Earthquake Engineering

2015 Edition
| Editors: Michael Beer, Ioannis A. Kougioumtzoglou, Edoardo Patelli, Siu-Kui Au

Structural Optimization Under Random Dynamic Seismic Excitation

  • Christian BucherEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-35344-4_324


Optimal design; Random vibration; Response surface; Seismic isolation; Structural reliability


In civil engineering, the design of structures has always been governed by fulfilling the needs of both safety and economy. Ideally, the designer would want to minimize cost while simultaneously maximizing safety. To a large extent, these objectives are in conflict; therefore, suitable compromises need to be found. A well-established tool for finding this set of best compromises is Pareto optimization. Figure 1 illustrates the trade-off between two conflicting objectives, both of which should be minimized. Reducing one objective automatically implies increasing the other one. Good compromises are to be found on the Pareto front.
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  1. Bamer F, Bucher C (2012) Application of the proper orthogonal decomposition for linear and nonlinear structures under transient excitations. Acta Mech 223:2549–2563zbMATHCrossRefGoogle Scholar
  2. Box GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New YorkzbMATHGoogle Scholar
  3. Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. J R Stat Soc Ser B 13:1–45MathSciNetzbMATHGoogle Scholar
  4. Breitung KW (1984) Asymptotic approximations for multinormal integrals. J Eng Mech 110(3):357–366MathSciNetzbMATHCrossRefGoogle Scholar
  5. Brenner CE, Bucher C (1995) A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading. Probabilist Eng Mech 10:265–273CrossRefGoogle Scholar
  6. Bucher C (2009a) Computational analysis of randomness in structural mechanics. In: Frangopol DM (ed) Structures and infrastructures book series, vol 3. Taylor & Francis, LondonGoogle Scholar
  7. Bucher C (2009b) Asymptotic sampling for high-dimensional reliability analysis. Probabilist Eng Mech 24:504–510CrossRefGoogle Scholar
  8. Bucher C (2009c) Probability-based optimization of friction damping devices. Struct Saf 31:500–507CrossRefGoogle Scholar
  9. Bucher C, Macke M (2005) Response surface methodology. In: Nikolaidis E, Ghiocel DM, Singhal S (eds) Structural reliability handbook. CRC Press, Boca Raton, p 19, 1–19, 23Google Scholar
  10. Clough RW, Penzien J (1993) Dynamics of structures, 2nd edn. McGraw-Hill, New YorkzbMATHGoogle Scholar
  11. Constantinou MC, Tadjbakhsh IG (1983) Probabilistic optimum base isolation of structures. J Struct Eng 109(3):676–689CrossRefGoogle Scholar
  12. Faravelli L (1989) Response-surface approach for reliability analysis. J Eng Mech 115:2763–2781CrossRefGoogle Scholar
  13. Fujimura K, Kiureghian AD (2007) Tail-equivalent linearization method for nonlinear random vibration. Probabilist Eng Mech 22:63–76CrossRefGoogle Scholar
  14. Furuta H, Kameda T (2006) Application of multi-objective genetic algorithm to bridge maintenance. In: Ceragioli F, Dontchev A, Futura H, Marti K, Pandolfi L (eds) System modeling and optimization. IFIP International Federation for Information Processing, Boston, pp 139–148CrossRefGoogle Scholar
  15. Gasser M, Schuëller GI (1997) Reliability-based optimization of structural systems. Math Method Oper Res 46:287–307MathSciNetzbMATHCrossRefGoogle Scholar
  16. Gollwitzer R, Rackwitz R (1988) An efficient numerical solution to the multinormal integral. Probabilist Eng Mech 3(2):98–101CrossRefGoogle Scholar
  17. Hill WJ, Hunter WG (1966) A review of response surface methodology: a literature survey. Technometrics 8:571–590MathSciNetCrossRefGoogle Scholar
  18. Iemura H, Taghikhany T, Jain S (2007) Optimum design of resilient sliding isolation system for seismic protection of equipments. Bull Earthquake Eng 5(1):85–103CrossRefGoogle Scholar
  19. Jangid RS (1996) Optimum damping in a non-linear base isolation system. J Sound Vibration 189(4):477–487CrossRefGoogle Scholar
  20. Jangid RS (2005) Optimum friction pendulum system for near-fault motions. Eng Struct 27(3):349–359CrossRefGoogle Scholar
  21. Kim S-H, Na S-W (1997) Response surface method using vector projected sampling points. Struct Saf 19:3–19CrossRefGoogle Scholar
  22. Liu M, Frangopol DM (2005) Bridge annual maintenance prioritization under uncertainty by multiobjective combinatorial optimization. Comp-Aided Civil Inf Eng 20(5):343–353CrossRefGoogle Scholar
  23. Mead R, Pike DJ (1975) A review of response surface methodology from a biometric view-point. Biometrics 31:803–851zbMATHCrossRefGoogle Scholar
  24. Myers RH (1999) Response surface methodology – current status and future directions. J Qual Technol 31:30–44Google Scholar
  25. Myers RH, Khuri AI, Carter JWH (1989) Response surface methodology: 1966–1988. Technometrics 31:137–157MathSciNetzbMATHGoogle Scholar
  26. Naess A, Gaidai O (2008) Monte Carlo methods for estimating the extreme response of dynamical systems. J Eng Mech 134(8):628–636CrossRefGoogle Scholar
  27. Naess A, Gaidai O, Batsevych O (2010) Prediction of extreme response statistics of narrow-band random vibrations. J Eng Mech 136(3):290–298CrossRefGoogle Scholar
  28. Ngatchou PN, Zarei A, Fox WLJ, El-Sharkawi MA (2008) Pareto multiobjective optimization. In: Lee KY, El-Sharkawi MA (eds) Modern heuristic optimization techniques. Wiley-Interscience, Piscataway, pp 189–207Google Scholar
  29. Ouypornprasert W, Bucher C, Schuëller GI (1989) On the application of conditional integration in structural reliability analysis. In: Ang AHS, Shinozuka M, Schuëller GI (eds) Proceeding 5th international conference on structural safety and reliability. San Francisco, pp 1683–1689Google Scholar
  30. Qin J, Nishijima K, Faber MH (2012) Extrapolation method for system reliability assessment: a new scheme. Adv Struct Eng 15(11):1893–1909CrossRefGoogle Scholar
  31. Rackwitz R (1982) Response surfaces in structural reliability. Berichte zur Zuverlässigkeitstheorie der Bauwerke. Heft 67, MünchenGoogle Scholar
  32. Roberts JB, Spanos P (2003) Random vibration and statistical linearization. Dover Publications, MineolazbMATHGoogle Scholar
  33. Roussis PC, Constantinou MC (2006) Uplift-restraining friction pendulum seismic isolation system. Earthquake Eng Struct Dyn 35(5):577–593CrossRefGoogle Scholar
  34. Zheng Y, Das PK (2000) Improved response surface method and its application to stiffened plate reliability analysis. Eng Struct 22:544–551CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Building Construction and TechnologyVienna University of TechnologyWienAustria