Reliability-based design optimization of uncertain stochastic systems: Gradient-based scheme

Journal of Engineering Mechanics

Volumn 138, Issue 1, 2011, Pages 60-70

  Jensen, H A ^a   Kusanovic, D S ^a   Valdebenito, M A ^a   Schueller G I ^b  

^a DEPARTAMENTO DE FÍSICA   (Chile)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

High dimensions; Reliability analysis; Reliability based optimization; Uncertain stochastic systems

Indexed keywords

BUILDING MODEL; DEMAND FUNCTION; DESIGN PROCESS; DESIGN SCHEME; EARTHQUAKE EXCITATION; FAILURE DOMAINS; FAILURE PROBABILITY; FEASIBLE DESIGN; GRADIENT BASED; GROUND MOTIONS; HIGH DIMENSIONS; HIGH-DIMENSIONAL; INTERIOR POINT ALGORITHM; LINE SEARCHES; MONTE CARLO SIMULATION; NUMERICAL RESULTS; OPTIMIZATION PROCESS; RELIABILITY BASED OPTIMIZATION; RELIABILITY PROBLEMS; RELIABILITY-BASED DESIGN OPTIMIZATION; SHEAR-BUILDING MODEL; STOCHASTIC EXCITATIONS; STRUCTURAL SYSTEMS; UNCERTAIN STOCHASTIC SYSTEMS;

FUNCTIONS; MACHINE DESIGN; MONTE CARLO METHODS; RELIABILITY ANALYSIS;

OPTIMIZATION;

ALGORITHM; COMPUTER SIMULATION; FAILURE ANALYSIS; GROUND MOTION; MONTE CARLO ANALYSIS; OPTIMIZATION; RELIABILITY ANALYSIS; STOCHASTICITY; UNCERTAINTY ANALYSIS;

EID: 84857201614     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)EM.1943-7889.0000304     Document Type: Article

References (31)

1. Alexandrov N. Dennis J.,. Lewis R. Torczon V. trust-region framework for managing the use of approximation models in optimization. Struct. Multidiscip. Optim. 1998, 15(1):16-23. SMOTB4, 1615-1488, 10.1007/BF01197433.
2. Au S. Beck J. Estimation of small failure probabilities in high dimensions by subset simulation. Prob. Eng. Mech. 2001, 16(4):263-277. PEMEEX, 0266-8920, 10.1016/S0266-8920(01)00019-4.
3. Bathe K. Finite element procedures 1996, Prentice Hall, Upper Saddle River, NJ.
4. Beck J. Au S. Schuëller G. Reliability of dynamic systems using stochastic simulation. Structural Dynamics EURODYN 2005-Proc., 6th Int. Conf. on Structural Dynamics 2005, 1:23-30. C. Soize Vol. and eds., Millpress, Rotterdam, Netherlands.
5. Beck J. Chan E. Irfanoglu A. Papadimitriou C. Multi-criteria optimal structural design under uncertainty. Earthquake Eng. Struct. Dyn. 1999, 28(7):741-761. IJEEBG, 1096-9845, 10.1002/(SICI)1096-9845(199907)28:7<741::AID-EQE840>3.0.CO;2-6.
6. Bonnans J.F. Gilbert J. Lemaréchal C. Sagastizábal C. Numerical optimization 2003, and Springer-Verlag, Berlin.
7. Ching J. Hsieh Y. Local estimation of failure probability function and its confidence interval with maximum entropy principle. Prob. Eng. Mech. 2007, 22(1):39-49. PEMEEX, 0266-8920, 10.1016/j.probengmech.2006.05.002.
8. Clough R. Penzien J. Dynamics of structures 1975, and McGraw-Hill, New York.
9. Gasser M. Schuëller G. Reliability-based optimization of structural systems. Math. Meth. Oper. Res. 1997, 46(3):287-307. ZMMRFZ, 1432-2994, 10.1007/BF01194858.
10. Haftka R. Gürdal Z. Elements of structural optimization 1992, and 3rd Ed., Kluwer, Dordrecht, Netherlands.
11. Herskovits J. Santos G. On the computer implementation of feasible direction interior point algorithms for nonlinear optimization. Struct. Optim. 1997, 14(2-3):165-172. SOPTEQ, 0934-4373, 10.1007/BF01812519.
12. Jensen H. Catalan M. On the effects of non-linear elements in the reliability-based optimal design of stochastic dynamical systems. Int. J. Non-linear Mech. 2007, 42(5):802-816. IJNMAG, 0020-7462, 10.1016/j.ijnonlinmec.2007.03.003.
13. Jensen H. Valdebenito M. Schuëller G. An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation. Comput. Methods Appl. Mech. Eng. 2008, 198(1):72-87. CMMECC, 0045-7825, 10.1016/j.cma.2008.01.003.
14. Jensen H. Valdebenito M. Schuëller G. Kusanovic D. Reliability-based optimization of stochastic systems using line search. Comput. Methods Appl. Mech. Eng. 2009, 198(49-52):3915-3924. CMMECC, 0045-7825, 10.1016/j.cma.2009.08.016.
15. Kanda J. Ellingwood B. Formulation of load factors based on optimum reliability. Struct. Saf. 1991, 9(3):197-210. STSADI, 0167-4730, 10.1016/0167-4730(91)90043-9.
16. Katafygiotis L. Cheung S. Application of spherical subset simulation method and auxiliary domain method on benchmark reliability study. Struct. Saf. 2007, 29(3):194-207. STSADI, 0167-4730, 10.1016/j.strusafe.2006.07.003.
17. Katafygiotis L. Wang J. Reliability analysis of wind-excited structures using domain decomposition method and line sampling. Struct. Eng. Mech. 2009, 32(1):37-51. SEGMEQ, 1225-4568.
18. Koutsourelakis P. Pradlwarter H. Schuëller G. Reliability of structures in high dimensions, part I: Algorithms and applications. Prob. Eng. Mech. 2004, 19(4):409-417. PEMEEX, 0266-8920, 10.1016/j.probengmech.2004.05.001.
19. Kushner H. Yin G. Stochastic approximation and recursive algorithms and applications 2003, and Springer, New York.
20. Lind N. Approximate analysis and economics of structures. J. Struct. Div., Am. Soc. Civ. Eng. 1976, 102(6):1177-1196. JSDEAG, 0044-8001.
21. Murthy P. Subramanian G. Minimum weight analysis based on structural reliability. AIAA J. 1968, 6(10):2037-2039. AIAJAH, 0001-1452, 10.2514/3.4931.
22. Nocedal J. Wright S. Numerical optimization 1999, and Springer-Verlag, New York.
23. Papadrakakis M. Lagaros N. Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput. Methods Appl. Mech. Eng. 2002, 191(32):3491-3507. CMMECC, 0045-7825, 10.1016/S0045-7825(02)00287-6.
24. Pellissetti M.F. Schuëller G.I. Pradlwarter H.J. Calvi A. Fransen S. Klein M. Reliability analysis of spacecraft structures under static and dynamic loading. Comput. Struct. 2006, 84(21):1313-1325. CMSTCJ, 0957-3720, 10.1016/j.compstruc.2006.03.009.
25. Pradlwarter H.J. Schuëller G.I. Equivalent linearization-A suitable tool for analyzing MDOF-systems. Probab. Eng. Mech. 1993, 8(2):115-126. PEMEEX, 0266-8920, 10.1016/0266-8920(93)90005-G.
26. Schuëller G. Pradlwarter H. Koutsourelakis P. critical appraisal of reliability estimation procedures for high dimensions. Probab. Eng. Mech. 2004, 19(4):463-474. PEMEEX, 0266-8920, 10.1016/j.probengmech.2004.05.004.
27. Taflanidis A. Beck J. Stochastic subset optimization for optimal reliability problems. Probab. Eng. Mech. 2008, 23(2-3):324-338. 0266-8920, 10.1016/j.probengmech.2007.12.011.
28. Valdebenito M. Schuëller G. Efficient strategies for reliability-based optimization involving non linear, dynamical structures. 2009 Technical Report IfM-Int. Work. Rep. No. 3-61, Institute of Engineering Mechanics, Univ. of Innsbruck, Austria.
29. Valdebenito M.A. Schuëller G.I. Reliability-based optimization considering design variables of discrete size. Eng. Struct. 2010, 32(9):2919-2930. ENSTDF, 0141-0296, 10.1016/j.engstruct.2010.05.011.
30. van Keulen F. Vervenne K. Gradient-enhanced response surface building. Struct. Muldiscip. Optim 2004, 27(5):337-351. 10.1007/s00158-004-0392-1.
31. Zienkiewicz O. Taylor R. The finite element method 2000, I, II, and III. and Vols , 5th Ed., Butterworth-Heinemann, Woburn, MA.