Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis

Structural and Multidisciplinary Optimization

Volumn 37, Issue 1, 2008, Pages 13-28

  Youn, Byeng D ^a   Xi, Zhimin ^a   Wang, Pingfeng ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Eigenvector dimension reduction; Probability analysis; Quality; Reliability; Sensitivity free

Indexed keywords

COVARIANCE MATRIX; CURVE FITTING; EIGENVALUES AND EIGENFUNCTIONS; FRUITS; GROUND SUPPORTS; IMAGE SEGMENTATION; INTEGRATION; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS; PROBABILITY; PROBABILITY DENSITY FUNCTION; QUALITY CONTROL; RANDOM PROCESSES; RANDOM VARIABLES; RELIABILITY; RELIABILITY ANALYSIS; SYSTEM STABILITY; WIRELESS TELECOMMUNICATION SYSTEMS;

COMPONENT RELIABILITIES; DIMENSION REDUCTIONS; DR METHODS; EIGEN VECTORS; EIGENVECTOR DIMENSION REDUCTION; ENGINEERING APPLICATIONS; HIGHLY NONLINEAR; MILDLY NONLINEAR SYSTEMS; MOVING LEAST SQUARES; NUMERICAL INTEGRATIONS; PEARSON SYSTEMS; PROBABILITY ANALYSES; PROBABILITY ANALYSIS; PROBABILITY DENSITIES; QUALITY; RANDOM INPUTS; RANDOM PARAMETERS; SAMPLING SCHEMES; SENSITIVITY-FREE; SINGULAR BEHAVIORS; STATISTICAL MOMENTS; SYSTEM RESPONSES; UNIVARIATE;

METHOD OF MOMENTS;

EID: 55849096638     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0210-7     Document Type: Article

References (26)

1. P Bjerager 1988 Probability integration by directional simulation J Eng Mech 114 1285 1302
2. CG Bucher 1988 Adaptive sampling-an iterative fast Monte Carlo procedure Struct Saf 5 119 126
3. Du X, Chen W (2002) Sequential optimization and reliability assessment method for efficient probabilistic design. Proceedings of the DETC-DAC34127 ASME Design Engineering Technical Conferences, Montreal, Canada, September 2002
4. S Engelund R Rackwitz 1993 A benchmark study on importance sampling techniques in structural reliability Struct Saf 12 255 276
5. AM Hasofer NC Lind 1974 Exact and invariant second-moment code format J Eng Mech 100 111 121
6. B Huang X Du 2006 Uncertainty analysis by dimension reduction integration and saddlepoint approximations J Mech Des 128 26 33
7. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions. Wiley, New York
8. DH Jung BC Lee 2002 Development of a simple and efficient method for robust optimization Int J Numer Methods Eng 53 2201 2215
9. Kleiber M, Hien TD (1992) The stochastic finite element method. Wiley, New York, NY
10. CY Lin WH Huang MC Jeng JL Doong 1997 Study of an assembly tolerance allocation model based on Monte Carlo simulation J Mater Process Technol 70 9 16
11. RE Melchers 1989 Importance sampling in structural systems Struct Saf 6 6 10
12. Myers RH, Montgomery DC (1995) Response surface methodology: process and product in optimization using designed experiments. Wiley & Sons, New York, NY, USA
13. Niederreiter H, Spanier J (2000) Monte Carlo and quasi-Monte Carlo methods. Springer, Berlin
14. R Rackwitz B Fiessler 1978 Structural reliability under combined random load sequences Comput Struct 9 489 494
15. S Rahman BN Rao 2001 A perturbation method for stochastic meshless analysis in elastostatics Int J Numer Methods Eng 50 1961 1991
16. S Rahman H Xu 2004 A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics Probab Eng Mech 19 393 408
17. Seo HS, Kwak BM (2003) An improved reliability analysis using design of experiments and an application to tolerance design. The 5th world congress of structural and multidisciplinary optimization, Lodo do Jesolo, Italy, May 19-23, 2003
18. IM Sobol 1998 On quasi-Monte Carlo integrations Math Comput Simul 47 103 112
19. P Varghese RN Braswell B Wang C Zhang 1996 Statistical tolerance analysis using FRPDF and numerical convolution Comput-Aided Des 28 9 723 732
20. Y-T Wu 1994 Computational methods for efficient structural reliability and reliability sensitivity analysis AIAA J 32 8
21. H Xu S Rahman 2004 A generalized dimension-reduction method for multidimensional integration in stochastic mechanics Int J Numer Methods Eng 61 1992 2019
22. F Yamazaki M Shinozuka 1988 Neumann expansion for stochastic finite element analysis J Eng Mech 114 1335 1354
23. BD Youn KK Choi 2004 A new response surface methodology for reliability-based design optimization Comput Struct 82 241 256
24. BD Youn KK Choi L Du 2004a Adaptive probability analysis using an enhanced hybrid mean value (HMV+) method J Struct Multidiscipl Optim 28 4 319 333
25. BD Youn KK Choi L Gu R-J Yang 2004b Reliability-based design optimization for crashworthiness of side impact J Struct Multidiscipl Optim 26 3-4 272 283
26. BD Youn KK Choi K Yi 2005 Performance moment integration for quality assessment in reliability-based robust design optimization Mechanics Based Design of Structures and Machines 33 185 213