A survey on approaches for reliability-based optimization

Structural and Multidisciplinary Optimization

Volumn 42, Issue 5, 2010, Pages 645-663

  Valdebenito, Marcos A ^a   Schuëller, Gerhart I ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Advanced simulation methods; Approximate reliability methods; Reliability assessment; Reliability based optimization

Indexed keywords

ADVANCED SIMULATION; APPROXIMATE RELIABILITY METHODS; DESIGN SOLUTIONS; OPTIMIZATION PROBLEMS; RELIABILITY ASSESSMENT; RELIABILITY-BASED OPTIMIZATION; SIMULTANEOUS SOLUTION; THEORETICAL FOUNDATIONS;

RELIABILITY ANALYSIS; STRUCTURAL DESIGN; SURVEYS;

OPTIMIZATION;

EID: 79951720640     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-010-0518-6     Document Type: Review

References (150)

1. Agarwal H, Renaud J (2004) Reliability based design optimization using response surfaces in application to multidisciplinary systems. Eng Optim 36(3):291-311
2. Agarwal H, Renaud J (2006) New decoupled framework for reliabilitybas (Pubitemid 44212396)
3. Agarwal H, Mozumder C, Renaud J, Watson L (2007) An inversemeasure- based unilevel architecture for reliability-based design optimization. Struct Multidisc Optim 33(3):217-227 (Pubitemid 46198779)
4. Aoues Y, Chateauneuf A (2008) Reliability-based optimization of structural systems by adaptive target safety-application to RC frames. Struct Saf 30(3):144-161 (Pubitemid 350167109)
5. Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidisc Optim 41(2):277-294
6. Arora J (1989) Introduction to optimum design. McGraw-Hill, New York
7. Arora J (ed) (2007) Optimization of structural and mechanical systems. World Scientific, Singapore
8. Au S (2005) Reliability-based design sensitivity by efficient simulation. Comput Struct 83(14):1048-1061 (Pubitemid 40423306)
9. Au S (2006) Critical excitation of SDOF elasto-plastic systems. J Sound Vib 296(4-5):714-733 (Pubitemid 44067035)
10. Au S, Beck J (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4): 263-277 (Pubitemid 33018562)
11. Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86(19-20):1904-1917
12. Basudhar A, Missoum S (2009) A sampling-based approach for probabilistic design with random fields. Comput Methods Appl Mech Eng 198(47-48):3647-3655
13. Basudhar A, Missoum S, Sanchez A (2008) Limit state function identification using support vector machines for discontinuous responses and disjoint failure domains. Probab Eng Mech 23(1):1-11
14. Beer M, Liebscher M (2008) Designing robust structures-a nonlinear simulation based approach. Comput Struct 86(10):1102-1122 (Pubitemid 351471769)
15. Beyer HG, Schwefel HP (2002) Evolution strategies-a comprehensive introduction. Nat Comput 1(1):3-52
16. Bichon B, Eldred M, Swiler L, Mahadevan S, McFarland J (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459-2468
17. Bichon B, Mahadevan S, Eldred M (2009) Reliability-based design optimization using efficient global reliability analysis. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Palm Springs, California, AIAA 2009-2261
18. Bjerager P, Krenk S (1989) Parametric sensitivity in first order reliability theory. J Eng Mech 115(7):1577-1582 (Pubitemid 21685932)
19. Bonnans JF, Gilbert J, Lemaréchal C, Sagastizábal C (2003) Numerical optimization. Springer, Heidelberg
20. Breitung K (1994) Asymptotic approximations for probability integrals. In: Lecture notes in mathematics, vol 1592. Springer, Berlin
21. Broding W, Diederich F, Parker P (1964) Structural optimization and design based on a reliability design criterion. J Spacecr Rockets 1(1):56-61
22. Bucher C, Bourgund U (1990) A fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57-66 (Pubitemid 20647315)
23. Chan KY, Skerlos S, Papalambros P (2006) Monotonicity and active set strategies in probabilistic design optimization. J Mech Des 128(4):893-900 (Pubitemid 44123178)
24. Chan KY, Skerlos S, Papalambros P (2007) An adaptive sequential linear programming algorithm for optimal design problems with probabilistic constraints. J Mech Des 129(2):140-149 (Pubitemid 46736245)
25. Chandu S, Grandhi R (1995) General purpose procedure for reliability based structural optimization under parametric uncertainties. Adv Eng Softw 23(1):7-14
26. Charnes A, Cooper WW (1959) Chance-constrained programming. Manage Sci 6(1):73-79
27. Chen X, Hasselman T, Neill D (1997) Reliability-based structural design optimization for practical applications. In: Proceedings of the 38th AIAA structures, structural dynamics, and materials conference, Florida
28. Cheng G, Xu L, Jiang L (2006) A sequential approximate programming strategy for reliability-based structural optimization. Comput Struct 84(21):1353-1367
29. Ching J, Hsieh Y (2007a) Approximate reliability-based optimization using a three-step approach based on subset simulation. J Eng Mech 133(4):481-493 (Pubitemid 46454879)
30. Ching J, Hsieh Y (2007b) Local estimation of failure probability function and its confidence interval with maximum entropy principle. Probab Eng Mech 22(1):39-49 (Pubitemid 44635991)
31. Cox D, Reid N (2000) The theory of the design of experiments. Chapman & Hall/CRC, Boca Raton
32. Davidson J, Felton L, Mart G (1977) Optimum design of structures with random parameters. Comput Struct 7(3):481-486 (Pubitemid 8545988)
33. De Munck M, Moens D, Desmet W, Vandepitte D (2008) A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties. Comput Struct 86(10):1080-1092 (Pubitemid 351467114)
34. Der Kiureghian A, Zhang Y, Li CC (1994) Inverse reliability problem. J Eng Mech 120(5):1154-1159
35. Ditlevsen O (1978) Narrow reliability bounds for structural systems. Tech. Rep. 145, DCAMM (The Danish Center for Applied Mathematics and Mechanics)
36. Ditlevsen O, Madsen H (1996) Structural reliability methods. Wiley, Hoboken
37. Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225-233
38. Ellingwood B (2001) Earthquake risk assessment of building structures. Reliab Eng Syst Saf 74(3):251-262 (Pubitemid 33018666)
39. Enevoldsen I, Sørensen J (1993) Reliability-based optimization of series systems of parallel systems. J Struct Eng 119(4):1069-1084 (Pubitemid 23643744)
40. Enevoldsen I, Sørensen J (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169-196
41. Foschi R, Li H, Zhang J (2002) Reliability and performance-based design: A computational approach and applications. Struct Saf 24(2-4):205-218 (Pubitemid 34724824)
42. Freudenthal A (1956) Safety and the probability of structural failure. ASCE Trans 121:1337-1397
43. Gasser M, Schuëller G (1997) Reliability-based optimization of structural systems. Math Methods Oper Res 46(3):287-307 (Pubitemid 127601490)
44. Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Reading
45. Grandhi R, Wang L (1998) Reliability-based structural optimization using improved two-point adaptive nonlinear approximations. Finite Elem Anal Des 29(1):35-48
46. Haftka R, Gürdal Z (1992) Elements of structural optimization, 3rd edn. Kluwer, Dordrecht
47. Heer E, Yang J (1971) Optimization of structures based on fracture mechanics and reliability criteria. AIAA J 9(4):621-628
48. Hellevik S, Langen I, Sørensen J (1999) Cost optimal reliability based inspection and replacement planning of piping subjected to CO2 corrosion. Int J Pressure Vessels and Piping 76(8):527-538 (Pubitemid 29466693)
49. Hilton H, Feigen M (1960) Minimum weight analysis based on structural reliability. J Eerosp Sci 27(9):641-652
50. Hurtado J (2004) An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory. Struct Saf 26(3):271-293 (Pubitemid 38301093)
51. Hurtado J (2007) Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis. Struct Saf 29(1):2-15 (Pubitemid 44464124)
52. Jacobs J, Etman L, van Keulen F, Rooda J (2004) Framework for sequential approximate optimization. Struct Multidisc Optim 27(5):384-400
53. Jaynes E (1968) Prior probabilities. IEEE Trans Syst Sci Cybern 4(3):227-241
54. Jensen H (2005) Design and sensitivity analysis of dynamical systems subjected to stochastic loading. Comput Struct 83:1062-1075 (Pubitemid 40423307)
55. Jensen H, Catalan M (2007) On the effects of non-linear elements in the reliability-based optimal design of stochastic dynamical systems. Int J Non-Linear Mech 42(5):802-816 (Pubitemid 47016485)
56. Jensen H, Valdebenito M, Schuëller G (2008) An efficient reliabilitybased optimization scheme for uncertain linear systems subject to general Gaussian excitation. Comput Methods Appl Mech Eng 194(1):72-87
57. Jensen H, Valdebenito M, Schuëller G, Kusanovic D (2009) Reliability-based optimization of stochastic systems using line search. Comput Methods Appl Mech Eng 198(49-52):3915-3924
58. Jin R, Du X, Chen W (2003) The use of metamodeling techniques for optimization under uncertainty. Struct Multidisc Optim 25(2): 99-116
59. Johnson E, Proppe C, Spencer B Jr, Bergman L, Székely G, Schuëller G (2003) Parallel processing in computational stochastic dynamics. Probab Eng Mech 18(1):37-60
60. Józwiak S (1986) Minimum weight design of structures with random parameters. Comput Struct 23(4):481-485 (Pubitemid 16585206)
61. Kanda J, Ellingwood B (1991) Formulation of load factors based on optimum reliability. Struct Saf 9(3):197-210
62. Katafygiotis L, Cheung S (2006) Domain decomposition method for calculating the failure probability of linear dynamic systems subjected to Gaussian stochastic loads. J Eng Mech 132(5): 475-486
63. Katafygiotis L, Wang J (2009) Reliability analysis of wind-excited structures using domain decomposition method and line sampling. J Struct Eng Mech 32(1):37-51
64. Katafygiotis L, Zuev K (2007) Estimation of small failure probabilities in high dimensions by adaptive linked importance sampling. In: Papadrakakis M, Charmpis D, Lagaros N, Tsompanakis Y (eds) ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering (COMPDYN). Rethymno, Crete
65. Katafygiotis L, Zuev K (2008) Geometric insight into the challenges of solving high-dimensional reliability problems. Probab Eng Mech 23(2-3):208-218
66. Katafygiotis L, Zuev K (2009) Horseracing simulation algorithm for evaluation of small failure probabilities. In: Papadrakakis M, Kojic M, Papadopoulos V (eds) 2nd South-East European conference on computational mechanics (SEECCM 2009). Rhodes, Greece
67. Katafygiotis L, Moan T, Cheung S (2007) Auxiliary domain method for solving multi-objective dynamic reliability problems for nonlinear structures. Struct Eng Mech 25(3):347-363 (Pubitemid 46568798)
68. Kaymaz I, Marti K (2007) Reliability-based design optimization for elastoplastic mechanical structures. Comput Struct 85(10): 615-625 (Pubitemid 46428377)
69. van Keulen F, Vervenne K (2004) Gradient-enhanced response surface building. Struct Multidisc Optim 27(5):337-351
70. Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliabilitybased design optimization using a hybrid space with application to finite element analysis. Struct Multidisc Optim 24(3):233-245 (Pubitemid 35186131)
71. Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 220(4598):671-680
72. Koo H, Der Kiureghian A, Fujimura K (2005) Design-point excitation for non-linear random vibrations. Probab Eng Mech 20(2): 134-147
73. Koutsourelakis P (2008) Design of complex systems in the presence of large uncertainties: A statistical approach. Comput Methods Appl Mech Eng 197(49-50):4092-4103
74. Kupfer H, Freudenthal A (1977) Structural optimization and risk control. In: Kupfer H, Shinozuka M, Schuëller G (eds) Proceedings of the 2nd International Conference on Structural Safety and Reliability (ICOSSAR'77), Werner, Düsseldorf, Munich, pp 627-639
75. Kuschel N, Rackwitz R (1997) Two basic problems in reliability-based structural optimization. Math Methods Oper Res 46(3):309-333 (Pubitemid 127601491)
76. Kwak B, Lee T (1987) Sensitivity analysis for reliability-based optimization using an AFOSM method. Comput Struct 27(3): 399-406
77. Lee I, Choi K, Du L, Gorsich D (2008) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Mech Eng 198(1):14-27
78. Lee J, Kwak B (1995) Reliability-based structural optimal design using the Neumann expansion technique. Comput Struct 55(2):287-296
79. Lee JO, Yang YS, Ruy WS (2002) A comparative study on reliabilityindex and target-performance-based probabilistic structural design optimization. Comput Struct 80(3-4):257-269
80. Leite J, Topping B (1999) Parallel simulated annealing for structural optimization. Comput Struct 73(1-5):545-564 (Pubitemid 30517425)
81. Li H, Foschi R (1998) An inverse reliability method and its application. Struct Saf 20(3):257-270
82. Li W, Yang L (1994) An effective optimization procedure based on structural reliability. Comput Struct 52(5):1061-1067
83. Liang J, Mourelatos Z, Tu J (2008) A single-loop method for reliability-based design optimisation. Int J Prod Dev 5(1-2):76-92
84. Lind N (1976) Approximate analysis and economics of structures. ASCE J Struct Div 102(ST6):1177-1196
85. Liu P, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probab Eng Mech 1(2):105-112
86. Liu PL, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161-177
87. Madsen H, Torhaug R, Cramer E (1991) Probability-based cost benefit analysis of fatigue design, inspection and maintenance. In:Marine Structural Inspection, Maintenance and Monitoring Symposium. Society of Naval Architects and Marine Engineers, Arlington, Virginia
88. Marti K, Kaymaz I (2006) Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty. ZAMM 86(5):358-384 (Pubitemid 43751161)
89. Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335-341
90. Mínguez R, Castillo E (2009) Reliability-based optimization in engineering using decomposition techniques and FORMS. Struct Saf 31(3):214-223
91. Missoum S, Ramub P, Haftka R (2007) A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems. Comput Methods Appl Mech Eng 196(29- 30):2895-2906 (Pubitemid 46672755)
92. Moan T, Song R (2000) Implications of inspection updating on system fatigue reliability of offshore structures. J Offshore Mech Arct Eng 122(3):173-180
93. Moens D, Vandepitte D (2005) A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 194(12-16):1527-1555 (Pubitemid 40262941)
94. Mohsine A, Kharmanda G, El-Hami A (2006) Improved hybrid method as a robust tool for reliability-based design optimization. Struct Multidisc Optim 32(3):203-213 (Pubitemid 44157779)
95. Möller B, Beer M (2007) Engineering computation under uncertainty- capabilities of non-traditional models. Comput Struct 86(10):1024-1041
96. Moses F (1997) Problems and prospects of reliability-based optimization. Eng Struct 19(4):293-301 (Pubitemid 127405378)
97. Moses F, Kinser D (1967) Optimum structural design with failure probability constraints. AIAA J 5(6):1152-1158
98. Murthy P, Subramanian G (1968) Minimum weight analysis based on structural reliability. AIAA J 6(10):2037-2039
99. Neal R (2005) Estimating ratios of normalizing constants using linked importance sampling. Tech. Rep. No. 0511, Dept. of Statistics, University of Toronto
100. Nikolaidis E, Burdisso R (1988) Reliability based optimization: A safety index approach. Comput Struct 28(6):781-788 (Pubitemid 18624306)
101. Nocedal J, Wright S (1999) Numerical optimization. Springer, New York
102. Ormoneit D, White H (1999) An efficient algorithm to compute maximum entropy densities. Econom Rev 18:127-140
103. Papadrakakis M, Lagaros N (2002) Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 191(32):3491-3507 (Pubitemid 34811229)
104. Papadrakakis M, Lagaros N, Plevris V (2005) Design optimization of steel structures considering uncertainties. Eng Struct 27(9): 1408-1418 (Pubitemid 40841283)
105. PellissettiM(2009) Parallel processing in structural reliability. J Struct Eng Mech 32(1):95-126
106. PellissettiMF, Schuëller GI, Pradlwarter HJ, Calvi A, Fransen S, Klein M (2006) Reliability analysis of spacecraft structures under static and dynamic loading. Comput Struct 84(21):1313-1325
107. Petryna Y, Krätzig W (2005) Computational framework for long-term reliability analysis of RC structures. Comput Methods Appl Mech Eng 194(12-16):1619-1639 (Pubitemid 40262945)
108. Polak E (1997) Optimization: Algorithms and consistent approximations. Springer, New York
109. Pu Y, Das P, Faulkner D (1997) A strategy for reliability-based optimization. Eng Struct 19(3):276-282 (Pubitemid 127426381)
110. Rackwitz R (2001) Reliability analysis-a review and some perspectives. Struct Saf 23(4):365-395 (Pubitemid 34696460)
111. Rahman S, Wei D (2006) A univariate approximation at most probable point for higher-order reliability analysis. Int J Solids Struct 43(9):2820-2839 (Pubitemid 43374688)
112. Rahman S,Wei D (2008) Design sensitivity and reliability-based structural optimization by univariate decomposition. Struct Multidisc Optim 35(3):245-261 (Pubitemid 351207798)
113. Rahman S, Xu H (2004) A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Probab Eng Mech 19(4):393-408
114. Rajashekhar M, Ellingwood B (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3): 205-220
115. Ramu P, Qu X, Youn B, Haftka R, Choi K (2006) Inverse reliability measures and reliability-based design optimization. Int J Reliab Saf 1(1-2):187-205
116. Rao S (1980) Structural optimization by chance constrained programming techniques. Comput Struct 12(6):777-781 (Pubitemid 11460385)
117. Reddy M, Grandhi R, Hopkins D (1994) Reliability based structural optimization: A simplified safety index approach. Comput Struct 53(6):1407-1418
118. Royset J, Polak E (2004a) Implementable algorithm for stochastic optimization using sample average approximations. J Optim Theory Appl 122(1):157-184 (Pubitemid 39583428)
119. Royset J, Polak E (2004b) Reliability-based optimal design using sample average approximations. Probab Eng Mech 19(4):331-343
120. Royset J, Der Kiureghian A, Polak E (2001a) Reliability-based optimal design of series structural systems. J Eng Mech 127(6):607-614 (Pubitemid 32526711)
121. Royset J, Der Kiureghian A, Polak E (2001b) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73(3):213-221 (Pubitemid 32761536)
122. Royset J, Der Kiureghian A, Polak E (2006) Optimal design with probabilistic objective and constraints. J Eng Mech 132(1):107-118 (Pubitemid 43124781)
123. Schittkowski K (1983) On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function. Math Operforsch Stat Ser Optim 14:1-20
124. Schuëller G, Stix R (1987) A critical appraisal of methods to determine failure probabilities. Struct Saf 4(4):293-309 (Pubitemid 17633319)
125. Schuëller G, Pradlwarter H, Koutsourelakis P (2003) A comparative study of reliability estimation procedures for high dimensions using FE analysis. In: Turkiyyah G (ed) Electronic proceedings of the 16th ASCE engineering mechanics conference (CD-ROM). University of Washington, Seattle, USA
126. Schuëller G, Pradlwarter H, Koutsourelakis P (2004) A critical appraisal of reliability estimation procedures for high dimensions. Probab Eng Mech 19(4):463-474
127. Schuëller GI, Pradlwarter HJ, Beck J, Au S, Katafygiotis L, Ghanem R (2005) Benchmark study on reliability estimation in higher dimensions of structural systems-an overview. In: Soize C, Schuëller GI (eds) Structural dynamics EURODYN 2005- Proceedings of the 6th international conference on structural dynamics. Millpress, Rotterdam, pp 717-722
128. Silvern D (1963) Optimization of system reliability. AIAA J 1(12):2872-2873
129. Spall J (2003) Introduction to stochastic search and optimization. Estimation, simulation and control. Wiley, Hoboken
130. Sues R, Cesare M, Pageau S, Wu JYT (2001) Reliability-based optimization considering manufacturing and operational uncertainties. J Aerosp Eng 14(4):166-174 (Pubitemid 33073862)
131. Switzky H (1965) Minimum weight design with structural reliability. J Aircr 2(3):228-232
132. Taflanidis A, Beck J (2008a) An efficient framework for optimal robust stochastic system design using stochastic simulation. Comput Methods Appl Mech Eng 198(1):88-101
133. Taflanidis A, Beck J (2008b) Stochastic subset optimization for optimal reliability problems. Probab Eng Mech 23(2-3):324-338
134. Thierauf G, Cai J (1997) Parallel evolution strategy for solving structural optimization. Eng Struct 19(4):318-324 (Pubitemid 127405381)
135. Tu J, Choi K, Park Y (2001) Design potential method for robust system parameter design. AIAA J 39(4):667-677 (Pubitemid 32334883)
136. Umesha P, Venuraju M, Hartmann D, Leimbach K (2005) Optimal design of truss structures using parallel computing. Struct Multidisc Optim 29(4):285-297 (Pubitemid 40537595)
137. Valdebenito M, Schuëller G (2010) Efficient strategies for reliabilitybased optimization involving non linear, dynamical structures. Comput Struct (in press)
138. Valdebenito M, Pradlwarter H, Schuëller G (2010) The role of the design point for calculating failure probabilities in view of dimensionality and structural non linearities. Struct Saf 32(2): 101-111
139. Vanmarcke E (1973) Matrix formulation of reliability analysis and reliability-based design. Comput Struct 3(4):757-770
140. Winterstein S, Ude T, Cornell C, Bjerager P, Haver S (1994) Environmental parameters for extreme response: Inverse FORM with omission factors. In: Schuëller G, Shinozuka M, Yao J (eds) Proceedings of the 6th international conference on structural safety and reliability (ICOSSAR'93). A.A. Balkema, Rotterdam, pp 551-557
141. Wu Y (1994) Computational methods for efficient structural reliability and reliability sensitivity analysis. AIAA J 32(8):1717-1723
142. Wu YT, Millwater H, Cruse TA (1990) Advanced probabilistic structural analysis method for implicit performance functions. AIAA J 28(9):1663-1669
143. Xu H, Rahman S (2004) A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics. Int J Numer Methods Eng 61(12):1992-2019 (Pubitemid 39622519)
144. Yang JS, Nikolaidis E (1991) Design of aircraft wings subjected to gust loads-a safety index based approach. AIAA J 29(5):804-812 (Pubitemid 21651611)
145. Yang R, Gu L (2004) Experience with approximate reliability-based optimization methods. Struct Multidisc Optim 26(1-2):152-159
146. Youn B, Choi K, Park Y (2003) Hybrid analysis method for reliabilitybased design optimization. J Mech Des 125(2):221-232
147. Youn B, Choi K, Du L (2005) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidisc Optim 29(2):134-148 (Pubitemid 40536310)
148. Zhang J, Foschi R (2004) Performance-based design and seismic reliability analysis using designed experiments and neural networks. Probab Eng Mech 19(3):259-267
149. Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidisc Optim 31(3):190-200 (Pubitemid 43261432)
150. Zuev K (2009) Advanced stochastic simulation methods for solving high-dimensional reliability problems. Ph.D. thesis, The Hong Kong University of Science and Technology