Reliability-based optimization in engineering using decomposition techniques and FORMS

Structural Safety

Volumn 31, Issue 3, 2009, Pages 214-223

  Mínguez, Roberto ^a   Castillo, Enrique ^b  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

^b UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Benders' decomposition; Breakwater design; Civil engineering examples; Failure probability safety factor method; Sensitivity analysis

Indexed keywords

BREAKWATERS; CIVIL ENGINEERING; COST FUNCTIONS; COSTS; DESIGN; FAILURE ANALYSIS; OPTIMIZATION; PROBABILITY; PUMPS; RAILROAD PLANT AND STRUCTURES; RELIABILITY ANALYSIS; SAFETY FACTOR; SENSITIVITY ANALYSIS;

ARTIFICIAL VARIABLES; BENDERS' DECOMPOSITION; BI-LEVEL PROBLEMS; BREAKWATER DESIGN; CLASSICAL APPROACHES; CODE CONSTRAINTS; DECOMPOSITION METHODS; DECOMPOSITION SCHEMES; DECOMPOSITION TECHNIQUES; DESIGN VARIABLES; ENGINEERING WORKS; FAILURE PROBABILITIES; FAILURE-PROBABILITY SAFETY-FACTOR METHOD; FIRST-ORDER RELIABILITY METHODS; GLOBAL PROBLEMS; MIXED MODELS; OPTIMIZATION PROBLEMS; OPTIMIZATION PROCEDURES; RELIABILITY CALCULATIONS; RELIABILITY INDEXES; RELIABILITY-BASED OPTIMIZATIONS; STANDARD OPTIMIZATIONS; TOTAL COSTS;

QUALITY ASSURANCE;

EID: 61349145571     PISSN: 01674730     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.strusafe.2008.06.014     Document Type: Article

References (51)

1. Castillo E., Conejo A.J., Pedregal P., Garci{dotless}́a R., and Alguacil N. Building and solving mathematical programming models in engineering and science. Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts (2001), John Wiley & Sons Inc., New York
2. Melchers R.E. Structural reliability analysis and prediction. 2nd ed. (1999), John Wiley & Sons, New York
3. Ditlevsen O., and Madsen H.O. Structural reliability methods (1996), Wiley, Chichester, New York
4. Der Kiureghian A., and Thoft-Christensen P. Reliability and optimization of structural systems '90. Proceedings of the third IFIP WG 7.5 conference on reliability and optimization of structural systems. Lecture notes in engineering vol. 61 (1990), Springer Verlag, Berlin, Berkeley (CA)
5. Geyskens P., Der Kiureghian A., and Monteiro P. Bayesian model assessment: methods and case studies. In: Rackwitz R., and Thoft-Christensen P. (Eds). Proceedings of the fourth IFIP WG 7.5 conference 1991, Munich, Germany. Lecture notes in engineering vol. 76 (1992), Springer, Berlin 229-238
6. Sorensen J.D., and Faber M.H. Optimal inspection and repair strategies for structural systems. In: Rackwitz R., and Thoft-Christensen P. (Eds). Proceedings of the fourth IFIP WG 7.5 conference 1991, Munich, Germany. Lecture notes in engineering vol. 76 (1992), Springer, Berlin 383-394
7. Neuenhofer A., and Zilch K. Probabilistic validation of EC 2 partial safety-factors using full distribution reliability methods. In: Takamatsu-shi K. (Ed). Proceedings of the fifth IFIP WG 7.5 conference on reliability and optimization of structural systems. Lecture notes in engineering (1993), Springer, North-Holland, Amsterdam 197-294
8. Park G.J., Park Y.S., and Lee W.I. A study on the second-order approximation method for engineering optimization. In: Takamatsu-shi K. (Ed). Proceedings of the fifth IFIP WG 7.5 conference on reliability and optimization of structural systems. Lecture notes in engineering (1993), Springer, North-Holland, Amsterdam 213-220
9. Zhang Y., and Der Kiureghian A. Two improved algorithms for reliability analysis. In: Rackwitz G.A.R., and Borri A. (Eds). Proceedings of the 6th IFIP WG 7.5 working conference on reliability and optimization of structural systems. Reliability and optimization of structural systems (1994), Chapman & Hall 297-304
10. Polak E., Kirjner-Neto C., and Der Kiureghian A. Structural optimization with reliability constraint. In: Frangopol R.C.D., and Rackwitz R. (Eds). Proceedings of the seventh IFIP WG 7.5 working conference on reliability and optimization of structural systems. Reliability and optimization of structural systems (1996), Chapman & Hall 17-32
11. Royset J., Der Kiureghian A., and Polak E. Reliability-based optimal design: problem, formulations, algorithms and application. In: Maes M.A., and Huyse L. (Eds). Proceedings of the 11th IFIP WG 7.5 working conference on reliability and optimization of structural systems. Reliability and optimization of structural systems (2004), Banff, Canada 1-12
12. Enevoldsen I. Reliability-based structural optimization. Ph.D. thesis, University of Aalborg, Aalborg, Denmark; 1991.
13. Enevoldsen I., and Sorensen J.D. Reliability-based optimization in structural engineering. Struct Saf 15 (1994) 169-196
14. Frangopol D.M. Reliability-based optimum structural design. In: Sundarajan C. (Ed). Probabilistic structural mechanics handbook (1995), Chapmam & Hall, New York 352-387 [chapter 16]
15. Castillo E., and Sarabia J.M. Engineering analysis of extreme value data. J Waterw Port Coastal Ocean Eng 118 2 (1992) 129-146
16. Castillo E., Hadi A.S., Balakrishnan N., and Sarabia J.M. Extreme value and related models in engineering and science applications (2005), John Wiley & Sons, New York
17. R. Mínguez, Safety, reliability and sensitivity analysis in civil engineering works using decomposition techniques. Applications. Ph.D. thesis, University of Cantabria, Santander, Spain; 2003 [in Spanish].
18. Castillo E., Losada M., Mínguez R., Castillo C., and Baquerizo A. An optimal engineering design method that combines safety factors and failure probabilities: Application to rubble-mound breakwaters. J Waterw Port Coastal Ocean Eng ASCE 130 2 (2004) 77-88
19. Castillo E., Conejo A.J., Mínguez R., and Castillo C. An alternative approach for addressing the failure probability-safety factor method with sensitivity analysis. Reliab Eng Syst Saf 82 2 (2003) 207-216
20. Castillo C., Mínguez R., Castillo E., and Losada M. An optimal engineering design method with failure rate constraints and sensitivity analysis. Application to composite breakwaters. Coastal Eng 53 (2006) 1-25
21. Mínguez R., Castillo E., Castillo C., and Losada M. Optimal cost design with sensitivity analysis using decomposition techniques. Application to composite breakwaters. Struct Saf 28 (2006) 321-340
22. Conejo A.J., Castillo E., Mínguez R., and García-Bertrand R. Decomposition techniques in mathematical programming. Engineering and science applications (2006), Springer-Verlag, Berlin, Heidelberg, New York
23. Breitung K. Asymptotic approximations for multinormal integrals. J Eng Mech 100 3 (1984) 357-366
24. Tvedt L. Two second-order approximations to the failure probability. Der norske Veritas, Oslo; 1983. Veritas rep. rdiv/20-004083.
25. Der Kiureghian A., Lin H.Z., and Hwang S.J. Second order reliability approximations. J Eng Mech, ASCE 113 8 (1987) 1208-1225
26. Koyluoglu H.U., and Nielsen R.K. New approximations for SORM integrals. Struct Saf 13 (1994) 235-246
27. Castillo E., Sarabia J.M., Solares C., and Gómez P. Uncertainty analyses in fault trees and Bayesian networks using FORM/SORM methods. Reliab Eng Syst Saf 65 (1999) 29-40
28. Harbitz A. An efficient sampling method for probability of failure calculation. Struct Saf 3 2 (1986) 109-115
29. Shinozuka M. Stochastic methods in structural dynamics. Stochastic fields and their digital simulations. The Hague: Martinus Nijhoff; 1987.
30. Freudenthal A.M. Safety and the probability of structural failure. Transactions, ASCE 121 (1956) 1337-1397
31. Hasofer A.M., and Lind N.C. Exact and invariant second moment code format. J Eng Mech 100 EM1 (1974) 111-121
32. Rackwitz R., and Fiessler B. Structural reliability under combined load sequences. Comput Struct 9 (1978) 489-494
33. Hohenbichler M., and Rackwitz R. Non-normal dependent vectors in structural safety. J Eng Mech Div, ASCE 107 6 (1981) 1227-1238
34. Ditlevsen O. Principle of normal tail approximation. J Eng Mech Div, ASCE 107 6 (1981) 1191-1208
35. Rosenblatt M. Remarks on a multivariate transformation. Ann Math Stat 23 3 (1952) 470-472
36. Nataf A. Détermination des distribution de probabilités dont les marges sont données. CR Acad Sci 225 (1962) 42-43
37. Bazaraa M.S., Sherali H.D., and Shetty C.M. Nonlinear programming theory and algorithms. 2nd ed. (1993), John Wiley & Sons, New York
38. Benders J.F. Partitioning procedures for solving mixed-variable programming problems. Numer Math 4 (1962) 238-252
39. Mínguez R., Castillo E., and Hadi A.S. Solving the inverse reliability problem using decomposition techniques. Struct Saf 27 (2005) 1-23
40. Geoffrion A.M. Generalized benders decomposition. JOTA 10 4 (1972) 237-260
41. Enevoldsen I. Sensitivity analysis of reliability-based optimal solutions. J Eng Mech 120 1 (1994) 198-205
42. Sorensen J.D., and Enevoldsen I. Sensitivity analysis in reliability-based shape optimization. In: Topping B.H.V. (Ed). NATO ASI vol. 221 of E (1992), Kluwer Academic Publishers, Dordrecht, The Netherlands 617-638
43. Castillo E., Conejo A.J., Castillo C., Mínguez R., and Ortigosa D. A perturbation approach to sensitivity analysis in nonlinear programming. J Optimiz Theor Appl 128 1 (2006) 49-74
44. Castillo E., Conejo A.J., Mínguez R., and Castillo C. A closed formula for local sensitivity analysis in mathematical programming. Eng Optimiz 38 1 (2006) 93-112
45. Castillo E., Mínguez R., Ruíz-Terán A., and Fernández-Canteli A. Design of a composite beam using the probability-safety-factor method. Int J Numer Meth Eng 62 (2005) 1148-1182
46. Drud A. CONOPT: A system for large scale nonlinear optimization. Reference manual for CONOPT subroutine library. ARKI Consulting and Development A/S, Bagsvaerd, Denmark; 1996.
47. http://www.gams.com.
48. Rackwitz R. Reliability analysis a review and some perspectives. Struct Saf 23 (2001) 365-395
49. Der Kiureghian A., Haukaas T., and Fujimura K. Structural reliability software at the University of California, Berkeley. Struct Saf 28 (2006) 44-67
50. Pandey M.D. An effective approximation to evaluate multinormal integrals. Struct Saf 20 (1998) 51-67
51. Yuan X.X., and Pandey M.D. Analysis of approximations for multinormal integration in system reliability computation. Struct Saf 28 (2006) 361-377