An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

Reliability Engineering and System Safety

Volumn 97, Issue 1, 2012, Pages 1-13

  Guan, Xuefei ^a   He, Jingjing ^b   Jha, Ratneshwar ^a   Liu, Yongming ^b  

^a Clarkson University   (United States)

^b CLARKSON UNIVERSITY   (United States)

Author keywords

Bayesian; First order reliability method; FORM; Inverse FORM; Inverse reliability method; Laplace; Reliability updating

Indexed keywords

BAYESIAN; FIRST ORDER RELIABILITY METHODS; FORM; INVERSE FORM; INVERSE RELIABILITY; LAPLACE;

ALGORITHMS; APPROXIMATION THEORY; BAYESIAN NETWORKS; COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; FATIGUE CRACK PROPAGATION; INVERSE PROBLEMS; LAPLACE TRANSFORMS; MARKOV PROCESSES; RELIABILITY; ROBUSTNESS (CONTROL SYSTEMS); UNCERTAINTY ANALYSIS;

MONTE CARLO METHODS;

EID: 80054052547     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2011.09.008     Document Type: Article

References (50)

1. R. Melchers Structural reliability analysis and prediction 1999 John Wiley & Sons Ltd.
2. D. Brauer, and G. Brauer Reliability-centered maintenance IEEE Transactions on Reliability 36 2009 17 24
3. H. Madsen, S. Krenk, and N. Lind Methods of structural safety 1986 Prentice-Hall, Inc. Englewood Cliffs, NJ
4. O. Ditlevsen, and H. Madsen Structural reliability methods vol. 315 1996 Citeseer
5. R. Rackwitz Reliability analysis - a review and some perspectives Structural Safety 23 2001 365 395 (Pubitemid 34696460)
6. R. Rebba, and S. Mahadevan Computational methods for model reliability assessment Reliability Engineering & System Safety 93 2008 1197 1207 (Pubitemid 351418141)
7. M. Kalos, and P. Whitlock Monte Carlo methods 2008 Wiley-VCH
8. A. Gelman, and X. Meng Simulating normalizing constants: from importance sampling to bridge sampling to path sampling Statistical Science 13 1998 163 185 (Pubitemid 128466008)
9. J. Liu Metropolized independent sampling with comparisons to rejection sampling and importance sampling Statistics and Computing 6 1996 113 119 (Pubitemid 126724248)
10. C.G. Bucher, and U. Bourgund A fast and efficient response surface approach for structural reliability problems Structural Safety 7 1 1990 57 66 (Pubitemid 20647315)
11. G. Cai, and I. Elishakoff Refined second-order reliability analysis Structural Safety 14 1994 267 276
12. R. Zhang, and S. Mahadevan Integration of computation and testing for reliability estimation Reliability Engineering & System Safety 74 2001 13 21 (Pubitemid 32842220)
13. Y. Zhao, and T. Ono A general procedure for first/second-order reliability method (form/sorm) Structural Safety 21 1999 95 112 (Pubitemid 29432899)
14. A. Der Kiureghian, Y. Zhang, and C. Li Inverse reliability problem Journal of Engineering Mechanics 120 1994 1154 1159
15. A. Der Kiureghian, and T. Dakessian Multiple design points in first and second-order reliability Structural Safety 20 1998 37 49 (Pubitemid 128403470)
16. H. Li, and R. Foschi An inverse reliability method and its application Structural Safety 20 1998 257 270
17. X. Du, A. Sudjianto, and W. Chen An integrated framework for optimization under uncertainty using inverse reliability strategy Journal of Mechanical Design 126 2004 562
18. K. Saranyasoontorn, and L. Manuel Efficient models for wind turbine extreme loads using inverse reliability Journal of Wind Engineering and Industrial Aerodynamics 92 2004 789 804 (Pubitemid 38825812)
19. I. Lee, K. Choi, L. Du, and D. Gorsich Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems Computer Methods in Applied Mechanics and Engineering 198 2008 14 27
20. J. Cheng, J. Zhang, C. Cai, and R. Xiao A new approach for solving inverse reliability problems with implicit response functions Engineering Structures 29 2007 71 79 (Pubitemid 44767180)
21. Y. Xiang, and Y. Liu Application of inverse first-order reliability method for probabilistic fatigue life prediction Probabilistic Engineering Mechanics 26 2011 148 156
22. H. Hong Reliability analysis with nondestructive inspection Structural Safety 19 1997 383 395 (Pubitemid 127427640)
23. C. Papadimitriou, J. Beck, and L. Katafygiotis Updating robust reliability using structural test data Probabilistic Engineering Mechanics 16 2001 103 113 (Pubitemid 32874354)
24. T. Graves, M. Hamada, R. Klamann, A. Koehler, and H. Martz Using simultaneous higher-level and partial lower-level data in reliability assessments Reliability Engineering & System Safety 93 2008 1273 1279 (Pubitemid 351418137)
25. X. Wang, M. Rabiei, J. Hurtado, M. Modarres, and P. Hoffman A probabilistic-based airframe integrity management model Reliability Engineering & System Safety 94 2009 932 941
26. X. Guan, R. Jha, and Y. Liu Probabilistic fatigue damage prognosis using maximum entropy approach Journal of Intelligent Manufacturing 2009 1 9 10.1007/s10845-009-0341-3
27. L. Tierney, and J. Kadane Accurate approximations for posterior moments and marginal densities Journal of the American Statistical Association 81 1986 82 86
28. P. Gregory Bayesian logical data analysis for the physical sciences: a comparative approach with Mathematica support 2005 Cambridge University Press
29. J. Dennis Jr., D. Gay, and R. Walsh An adaptive nonlinear least-squares algorithm ACM Transactions on Mathematical Software (TOMS) 7 1981 348 368
30. J. More The LevenbergMarquardt algorithm: implementation and theory Numerical Analysis 1978 105 116
31. M. Powell A FORTRAN subroutine for solving systems of nonlinear algebraic equations Numerical Methods for Nonlinear Algebraic Equations 1970 115
32. H. Madsen Some experience with the RackwitzFiessler algorithm for the calculation of structural reliability under combined loading DIALOG-77 1977 Danish Engineering Academy Lyngby, Denmark 73 98
33. A. Hasofer, and N. Lind Exact and invariant second-moment code format Journal of the Engineering Mechanics Division 100 1974 111 121
34. R. Rackwitz, and B. Flessler Structural reliability under combined random load sequences Computers & Structures 9 1978 489 494 (Pubitemid 9397943)
35. A. Haldar, and S. Mahadevan Probability, reliability, and statistical methods in engineering design 2000 John Wiley & Sons Inc.
36. W. Hastings Monte Carlo sampling methods using Markov chains and their applications Biometrika 57 1970 97
37. A. Sudjianto, X. Du, and W. Chen SAE Transactions 114 2005 267 276
38. D. Virkler, B. Hillberry, and P. Goel The statistical nature of fatigue crack propagation Journal of Engineering Materials and Technology 101 1979 148
39. P. Paris, and F. Erdogan A critical analysis of crack propagation laws Journal of Basic Engineering 85 1963 528 534
40. Z. Kotulski On efficiency of identification of a stochastic crack propagation model based on virkler experimental data Archives of Mechanics 50 1998 829 848
41. X. Guan, R. Jha, and Y. Liu Model selection, updating, and averaging for probabilistic fatigue damage prognosis Structural Safety 33 2011 242 249
42. H. Lam Phase i iasc-asce structural health monitoring benchmark problem using simulated data Journal of Engineering Mechanics 130 2004 3
43. I.-A.S.T. Group, Asce structural health monitoring (shm) benchmark problem, Website, 1999. 〈 http://bc029049.cityu.edu.hk/asce.shm/phase1/ ascebenchmark.asp 〉.
44. P. Hess, D. Bruchman, I. Assakkaf, and B. Ayyub Uncertainties in material strength, geometric, and load variables ASNE Naval Engineers Journal 114 2002 139 165
45. A. Vrouwenvelder Developments towards full probabilistic design codes Structural Safety 24 2002 417 432 (Pubitemid 34724834)
46. B. Schmidt, and F. Bartlett Review of resistance factor for steel: data collection Canadian Journal of Civil Engineering 29 2002 98 108 (Pubitemid 34961530)
47. J. Luo, K. Ying, and J. Bai Savitzkygolay smoothing and differentiation filter for even number data Signal Processing 85 2005 1429 1434 (Pubitemid 40752327)
48. P. Baldi Gradient descent learning algorithm overview: a general dynamical systems perspective IEEE Transactions on Neural Networks 6 1995 182 195
49. G. Schuëller, and H. Pradlwarter Benchmark study on reliability estimation in higher dimensions of structural systems - an overview Structural Safety 29 2007 167 182 (Pubitemid 46336639)
50. I. Jolliffe Principal component analysis 2002 Wiley Online Library