, Volume 34, Issue 6, pp 967–986 | Cite as

Stochastic sensitivity analysis using HDMR and score function

  • Rajib Chowdhury
  • B. N. RaoEmail author
  • A. Meher Prasad


Probabilistic sensitivities provide an important insight in reliability analysis and often crucial towards understanding the physical behaviour underlying failure and modifying the design to mitigate and manage risk. This article presents a new computational approach for calculating stochastic sensitivities of mechanical systems with respect to distribution parameters of random variables. The method involves high dimensional model representation and score functions associated with probability distribution of a random input. The proposed approach facilitates first-and second-order approximation of stochastic sensitivity measures and statistical simulation. The formulation is general such that any simulation method can be used for the computation such as Monte Carlo, importance sampling, Latin hypercube, etc. Both the probabilistic response and its sensitivities can be estimated from a single probabilistic analysis, without requiring gradients of performance function. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of sensitivities of statistical moments or reliability of structural system.


Stochastic sensitivity structural reliability high dimensional model representation score function statistical moment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alis OF, Rabitz H 2001 Efficient implementation of high dimensional model representations. J. Mathematical Chem. 29(2): 127–142zbMATHCrossRefMathSciNetGoogle Scholar
  2. Au S K 2005 Reliability-based design sensitivity by efficient simulation. Computers and Structures 83(14): 1048–1061CrossRefGoogle Scholar
  3. Chowdhury R, Rao B N, Prasad A M 2009 High Dimensional Model Representation for Structural Reliability Analysis. Communications in Numerical Methods in Engineering 25: 301–337zbMATHCrossRefMathSciNetGoogle Scholar
  4. Gavin H P, Yau S C 2008 High-order limit state functions in the response surface method for structural reliability analysis. Structural Safety 30(2): 162–179CrossRefGoogle Scholar
  5. Glasserman P 1991 Gradient estimation via perturbation analysis (Boston, MA: Kluwer Academic Publishers)zbMATHGoogle Scholar
  6. Haug E J, Choi K K, Komkov V 1986 Design sensitivity analysis of structural systems (New York: Academic Press)zbMATHGoogle Scholar
  7. Ho Y C, Cao X R 1991 Discrete event dynamic systems and perturbation analysis (Boston, MA: Kluwer Academic Publishers)Google Scholar
  8. Hohenbichler M, Gollwitzer S, Kruse W, Rackwitz R 1987 New light on first- and second-order reliability methods. Structural Safety 4: 267–284CrossRefGoogle Scholar
  9. Lancaster P, Salkauskas K 1986 Curve and surface fitting: An introduction (London: Academic Press)zbMATHGoogle Scholar
  10. L’Ecuyer P, Perron G 1994 On the convergence rates of IPA and FDC derivative estimators. Operations Research 42(4): 643–656zbMATHCrossRefMathSciNetGoogle Scholar
  11. Li G, Rosenthal C, Rabitz H 2001a High dimensional model representations. J. Phys. Chem. A 105(33): 7765–7777CrossRefGoogle Scholar
  12. Li G, Wang S W, Rosenthal C, Rabitz H 2001b High dimensional model representations generated from low dimensional data samples-I. mp-Cut-HDMR. J. Mathematical Chem. 30(1): 1–30CrossRefMathSciNetGoogle Scholar
  13. Liu P L, Der Kiureghian A 1991 Finite element reliability of geometrically nonlinear uncertain structures. J. Eng. Mech. ASCE 117(8): 1806–1825CrossRefGoogle Scholar
  14. Melchers R E, Ahammed M 2004 A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability. Computers and Structures 82(1): 55–61CrossRefGoogle Scholar
  15. Rabitz H, Alis O F 1999 General foundations of high dimensional model representations. J. Mathematical Chem. 25(2–3): 197–233zbMATHCrossRefMathSciNetGoogle Scholar
  16. Rabitz H, Alis O F, Shorter J, Shim K 1999 Efficient input-output model representations. Computer Phys. Commun. 117(1–2): 11–20zbMATHCrossRefGoogle Scholar
  17. Rubinstein R Y, Shapiro A 1993 Discrete event systems — sensitivity analysis and stochastic optimization by the score function method (New York: John Wiley & Sons)zbMATHGoogle Scholar
  18. Sobol I M 2003 Theorems and examples on high dimensional model representations. Reliability Engineering and System Safety 79(2): 187–193CrossRefMathSciNetGoogle Scholar
  19. Wang S W, Levy II H, Li G, Rabitz H 1999 Fully equivalent operational models for atmospheric chemical kinetics within global chemistry-transport models. J. Geophys. Res. 104(D23): 30417–30426CrossRefGoogle Scholar
  20. Wen Y K 1976 Method for random vibration of hysteretic systems. J. Eng. Mech. Division, ASCE 102(EM2): 249–263Google Scholar

Copyright information

© Indian Academy of Sciences 2009

Authors and Affiliations

  1. 1.School of EngineeringSwansea UniversitySwanseaUK
  2. 2.Structural Engineering Division, Department of Civil EngineeringIndian Institute of Technology MadrasChennaiIndia

Personalised recommendations