Encyclopedia of Earthquake Engineering

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

Structural Seismic Reliability Analysis

  • Shankar SankararamanEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-35344-4_280


First-order reliability method; Monte Carlo sampling; Probability of failure; Reliability analysis; Uncertainty


Perhaps, no other discipline within engineering has to deal with as much uncertainty as the field of earthquake engineering (Der Kiureghian 1996). To begin with, the occurrence of earthquakes in time and space is completely random in nature, and this leads to a large amount of uncertainty while predicting the intensities of ground motions resulting from earthquakes. Further, it is challenging to precisely assess the load-carrying capacity of the structural system of interest, due to the inherent variability across different structural members that constitute the overall structural system. It is necessary to analyze all of these different sources of uncertainty and assess the safety of the structure by accounting for such sources of uncertainty. Structural safety assessment is important both during the design of the structural system and for analyzing...

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


  1. Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2):174–188CrossRefGoogle Scholar
  2. Au S, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277CrossRefGoogle Scholar
  3. Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468CrossRefGoogle Scholar
  4. Bickel PJ, Doksum KA (1977) Mathematical statistics: basic ideas and selected topics. Holden Day, San FranciscozbMATHGoogle Scholar
  5. Breitung K (1984) Asymptotic approximations for multinormal integrals. J Eng Mech 110(3):357–366MathSciNetzbMATHCrossRefGoogle Scholar
  6. Chen X, Lind NC (1983) Fast probability integration by three-parameter normal tail approximation. Struct Saf 1(4):269–276CrossRefGoogle Scholar
  7. Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman and Hall, LondonzbMATHCrossRefGoogle Scholar
  8. Cruse TA, Mahadevan S, Huang Q, Mehta S (1994) Mechanical system reliability and risk assessment. AIAA J 32(11):2249–2259zbMATHCrossRefGoogle Scholar
  9. Daigle M, Sankararaman S (2013) Advanced methods for determining prediction uncertainty in model-based prognostics with application to planetary rovers. In: Annual conference of the Prognostics and Health Management Society, New Orleans, pp 262–274Google Scholar
  10. Der Kiureghian A (1996) Structural reliability methods for seismic safety assessment: a review. Eng Struct 18(6):412–424CrossRefGoogle Scholar
  11. Der Kiureghian A, Ditlevsen OD (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105–112CrossRefGoogle Scholar
  12. Der Kiureghian A, Lin HZ, Hwang SJ (1987) Second-order reliability approximations. J Eng Mech 113(8):1208–1225CrossRefGoogle Scholar
  13. Der Kiureghian A, Zhang Y, Li CC (1994) Inverse reliability problem. J Eng Mech 120(5):1154–1159CrossRefGoogle Scholar
  14. Ditlevsen OD, Madsen HO (1996) Structural reliability methods. Wiley, ChichesterGoogle Scholar
  15. Fiessler B, Rackwitz R, Neumann HJ (1979) Quadratic limit states in structural reliability. J Eng Mech Div 105(4):661–676Google Scholar
  16. Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New YorkGoogle Scholar
  17. Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100(1):111–121Google Scholar
  18. Hohenbichler M, Rackwitz R (1983) First-order concepts in system reliability. Struct Saf 1(3):177–188CrossRefGoogle Scholar
  19. Iman RL (2008) Latin hypercube sampling. Wiley Online LibraryGoogle Scholar
  20. Kalos MH, Whitlock PA (2008) Monte carlo methods. Wiley, WeinheimGoogle Scholar
  21. Karamchandani A, Bjerager P, and Cornell, AC (1989) Adaptive Importance Sampling, Proceedings, International Conference on Structural Safety and Reliability (ICOSSAR), San Francisco, pp 855–862Google Scholar
  22. Liu P, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probab Eng Mech 1(2):105–112CrossRefGoogle Scholar
  23. Mahadevan S, Raghothamachar P (2000) Adaptive simulation for system reliability analysis of large structures. Comput Struct 77(6):725–734CrossRefGoogle Scholar
  24. Mahadevan S, Zhang R, Smith N (2001) Bayesian networks for system reliability reassessment. Struct Saf 23(3):231–251CrossRefGoogle Scholar
  25. Melchers RE (1989) Importance sampling in structural systems. Struct Saf 6(1):3–10CrossRefGoogle Scholar
  26. Najm HN (2009) Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annu Rev Fluid Mech 41:35–52MathSciNetzbMATHCrossRefGoogle Scholar
  27. Rasmussen CE (2004) Gaussian processes in machine learning. In: Advanced lectures on achine learning. Springer, pp 63–71Google Scholar
  28. Stein ML (1999) Interpolation of spatial data: some theory for kriging. Springer, New YorkzbMATHCrossRefGoogle Scholar
  29. Tvedt L (1990) Distribution of quadratic forms in normal space-application to structural reliability. J Eng Mech 116(6):1183–1197CrossRefGoogle Scholar
  30. Wu, YT (1992) An adaptive importance sampling method for structural system reliability analysis. In: Cruse TA (ed) Reliability technology 1992, ASME winter annual meeting, vol AD-28), Anaheim, pp 217–231Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Intelligent Systems DivisionSGT Inc., NASA Ames Research CenterMoffett FieldUSA