Reliability-based structural optimization with probability and convex set hybrid models

Structural and Multidisciplinary Optimization

Volumn 42, Issue 1, 2010, Pages 89-102

  Kang, Zhan ^a   Luo, Yangjun ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Convex set; Hybrid model; Probability; Reliability; Structural optimization

Indexed keywords

BOUNDED UNCERTAINTY; CONVEX SET; DESIGN OPTIMIZATION PROBLEM; DESIGN PROBLEMS; DOUBLE-LOOP; HYBRID MODEL; LIMIT-STATE FUNCTION; LOAD UNCERTAINTY; MATHEMATICAL DEFINITIONS; MINIMIZATION PROBLEMS; NUMERICAL EXAMPLE; NUMERICAL TECHNIQUES; OPTIMALITY CONDITIONS; OPTIMIZATION PROBLEMS; PERFORMANCE MEASURE APPROACHES; RELIABILITY CONSTRAINTS; RELIABILITY INDEX; STRUCTURAL SYSTEMS;

CONVEX OPTIMIZATION; PROBABILITY; RELIABILITY; SET THEORY; SHAPE OPTIMIZATION; STRUCTURAL DESIGN; ULTRAHIGH MOLECULAR WEIGHT POLYETHYLENES;

STRUCTURAL OPTIMIZATION;

EID: 77952954183     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-009-0461-6     Document Type: Article

References (51)

1. PR Adduri RC Penmetsa 2007 Bounds on structural system reliability in the presence of interval variables Comput Struct 85 320 329 10.1016/j.compstruc. 2006.10.012 (Pubitemid 46135644)
2. FTK Au YS Cheng LG Tham GW Zeng 2003 Robust design of structures using convex models Comput Struct 81 2611 2619 10.1016/S0045-7949(03)00322-5
3. Ben-Haim Y, Elishakoff I (1990) Convex models of uncertainty in applied mechanics. Elsevier Science, Amsterdam
4. Berleant DJ, Ferson S, Kreinovich V, Lodwich WA (2005) Combining interval and probabilistic uncertainty: foundations, algorithms, challenges-an overview. In: Proceedings of the 4th international symposium on imprecise probabilities and their applications, Pittsburgh, Pennsylvania
5. HG Beyer B Sendhoff 2007 Robust optimization-a comprehensive survey Comput Methods Appl Mech Eng 196 3190 3218 1173.74376 10.1016/j.cma.2007.03.003 2330774 (Pubitemid 46780137)
6. Buckley JJ (2005) Fuzzy probabilities: new approach and applications. Springer, Berlin
7. Chen X, Hasselman TK, Neill DJ (1997) Reliability based structural design optimization for practical applications. In: Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference and exhibit, Kissimmee, FL, 7-10 April
8. G Cheng L Xu L Jiang 2006 A sequential approximate programming strategy for reliability-based structural optimization Comput Struct 84 1353 1367 10.1016/j.compstruc.2006.03.006
9. I Doltsinis Z Kang 2004 Robust design of structures using optimization methods Comput Methods Appl Mech Eng 193 2221 2237 1067.74554 10.1016/j.cma.2003.12.055 (Pubitemid 38503355)
10. X Du W Chen 2004 Sequential optimization and reliability assessment method for efficient probabilistic design ASME J Mech Des 126 225 233 10.1115/1.1649968
11. L Du KK Choi 2008 An inverse analysis method for design optimization with both statistical and fuzzy uncertainties Struct Multidisc Optim 37 107 119 10.1007/s00158-007-0225-0
12. L Du KK Choi BD Youn 2006 Inverse possibility analysis method for possibility-based design optimization AIAA J 44 11 2682 2690 10.2514/1.16546 (Pubitemid 44788065)
13. L Du KK Choi BD Youn D Gorsich 2006 Possibility-based design optimization method for design problems with both statistical and fuzzy input data J Mech Des 128 928 935 10.1115/1.2204972 (Pubitemid 44123182)
14. X Du A Sudjianto B Huang 2005 Reliability-based design with the mixture of random and interval variables J Mech Des 127 1068 1076 10.1115/1.1992510 (Pubitemid 41709564)
15. I Elishakoff 1995 Essay on uncertainties in elastic and viscoelastic structures: from A. M. Freudenthal's criticisms to modern convex modeling Comput Struct 56 871 895 0921.73004 10.1016/0045-7949(94)00499-S
16. Elishakoff I (1999) Are probabilistic and anti-optimization approaches compatible? In: Elishakoff I (ed) Whys and hows in uncertainty modelling: probability, fuzziness and anti-optimization. Springer, New York, pp 263-341
17. I Elishakoff P Colombi 1993 Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters Comput Methods Appl Mech Eng 104 2 187 209 0812.73036 10.1016/0045-7825(93)90197-6 1219636
18. MA Elseifi Z Gürdal E Nikolaidis 1999 Convex/probabilistic models of uncertainties in geometric imperfections of stiffened composite panels AIAA J 37 468 474 10.2514/2.757
19. I Enevoldsen JD Sørensen 1994 Reliability-based optimization in structural engineering Struct Saf 15 3 169 196 10.1016/0167-4730(94)90039-6
20. Frangopol DM, Corotis RB (1996) Reliability-based structural system optimization: state-of-the-art versus state-of-the-practice. In: Cheng FY (ed) Proceedings of the 12th conference on analysis and computation, Chicago. Analysis and computation. ASCE, New York, pp 67-76
21. JW Hall J Lawry 2004 Generation, combination and extension of random set approximations to coherent lower and upper probabilities Reliab Eng Syst Saf 85 89 101 10.1016/j.ress.2004.03.005
22. AM Hasofer NC Lind 1974 Exact and invariant second-moment code format ASCE J Eng Mech Div 100 1 111 121
23. ET Jaynes 1957 Information theory and statistical mechanics Phys Rev 108 171 197 10.1103/PhysRev.108.171 96414
24. C Jiang X Han GR Liu 2007 Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval Comput Methods Appl Mech Eng 196 4791 4800 1173.74364 10.1016/j.cma.2007.03.024 (Pubitemid 47423960)
25. DR Karanki HS Kushwaha AK Verma S Ajit 2009 Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment Risk Anal 29 5 662 675 10.1111/j.1539-6924.2009.01221.x
26. V Kreinovich G Xiang SA Starks, et al. 2006 Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity Reliab Comput 12 1385 3139 2278784
27. Kuschel N, Rackwitz R (2000) A new approach for structural optimization of series systems. In: Melchers RE, Stewart MG (ed) Applications of statistics and probability. Balkema, Rotterdam, pp 987-994
28. Lawrence C, Zhou JL, Tits AL (1997) User's guide for CFSQP version 2.5. Available at http://www.aemdesign.com
29. JO Lee S Yang WS Ruy 2002 A comparative study on reliability-index and target-performance-based probabilistic structural design optimization Comput Struct 80 257 269 10.1016/S0045-7949(02)00006-8 (Pubitemid 34222475)
30. J Liang ZP Mourelatos E Nikolaidis 2007 A single-loop approach for system reliability-based design optimization J Mech Des 129 1215 1225 10.1115/1.2779884 (Pubitemid 351188368)
31. Y Luo Z Kang Z Luo, et al. 2009 Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model Struct Multidisc Optim 39 297 310 10.1007/s00158-008-0329-1 2525066
32. Melchers RE (1999) Structural reliability analysis and prediction, 2nd edn. Wiley, Chichester
33. R Minguez E Castillo 2009 Reliability-based optimization in engineering using decomposition techniques and FORMS Struct Saf 31 214 223 10.1016/j.strusafe.2008.06.014
34. D Moens D Vandepitte 2005 A survey of non-probabilistic uncertainty treatment in finite element analysis Comput Methods Appl Mech Eng 194 1527 1555 1137.74443 10.1016/j.cma.2004.03.019 (Pubitemid 40262941)
35. Möller B, Beer M (2004) Fuzzy randomness: uncertainty in civil engineering and computational mechanics. Springer, Berlin
36. B Möller M Beer 2008 Engineering computation under uncertainty-capabilities of non-traditional models Comput Struct 86 1024 1041 10.1016/j.compstruc.2007.05.041 (Pubitemid 351471770)
37. ZP Mourelatos J Zhou 2005 Reliability estimation and design with insufficient data based on possibility theory AIAA J 43 8 1696 1705 10.2514/1.12044
38. A Neumaier A Pownuk 2007 Linear systems with large uncertainties, with applications to truss structures Reliab Comput 13 149 172 1117.65063 10.1007/s11155-006-9026-1 2297775 (Pubitemid 46122519)
39. CP Pantelides S Ganzerli 1998 Design of trusses under uncertain loads using convex models J Struct Eng 124 318 329 10.1061/(ASCE)0733-9445(1998)124: 3(318)
40. M Papadrakakis ND Lagaros 2002 Reliability-based structural optimization using neural networks and Monte Carlo simulation Comput Methods Appl Mech Eng 191 3491 3507 1101.74377 10.1016/S0045-7825(02)00287-6 (Pubitemid 34811229)
41. RC Penmetsa RV Grandhi 2002 Efficient estimation of structural reliability for problems with uncertain intervals Comput Struct 80 1103 1112 10.1016/S0045-7949(02)00069-X (Pubitemid 34772006)
42. Z Qiu I Elishakoff 1998 Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis Comput Methods Appl Mech Eng 152 361 372 0947.74046 10.1016/S0045-7825(96)01211-X
43. Z Qiu D Yang I Elishakoff 2008 Probabilistic interval reliability of structural systems Int J Solids Struct 45 2850 2860 1169.74578 10.1016/j.ijsolstr.2008.01.005
44. M Rosenblatt 1952 Remarks on a multivariate transformation Ann Math Stat 23 470 472 0047.13104 10.1214/aoms/1177729394 49525
45. JO Royset A Der Kiureghian E Polak 2001 Reliability-based optimal structural design by the decoupling approach Reliab Eng Syst Saf 73 213 221 10.1016/S0951-8320(01)00048-5 (Pubitemid 32761536)
46. GI Schuëller HA Jensen 2008 Computational methods in optimization considering uncertainties-an overview Comput Methods Appl Mech Eng 198 2 13 10.1016/j.cma.2008.05.004
47. C Soize 2001 Maximum entropy approach for modeling random uncertainties in transient elastodynamics J Acoust Soc Am 109 1979 1996 10.1121/1.1360716
48. J Tu KK Choi YH Park 1999 A new study on reliability-based design optimization J Mech Des 121 557 564 10.1115/1.2829499
49. LV Utkin IO Kozine 2005 Computing system reliability given interval-value characteristics of the components Reliab Comput 11 19 34 1075.65086 10.1007/s11155-005-5940-x 2147807 (Pubitemid 40537759)
50. T Vietor 1997 Stochastic optimization for mechanical structures Math Methods Oper Res 46 377 408 0896.90178 10.1007/BF01194862 1603083
51. BD Youn KK Choi L Du 2005 Enriched performance measure approach for reliability-based design optimization AIAA J 43 874 884 10.2514/1.6648