To conduct a reliability analysis for mechanical components, it is necessary to consider the combined influence of strength deterioration and dynamic loads. An efficient method based on subset simulation is proposed in this paper to analyze time-variant reliability by considering the strength deterioration of mechanical components in a continuous system. A gamma process is used to describe the deterioration of system strength. A model for timevariant reliability considering strength deterioration is constructed for a continuous system. A representative example and tubular cantilever structure are assessed to demonstrate the efficiency and accuracy of the proposed method. The reliability probability examples were analyzed using a first-order reliability method and benchmark results for the proposed method were derived using direct Monte Carlo simulation (MCS). The results of the proposed method and MCS are consistent, indicating that the proposed method is an effective reliability analysis method for evaluating small failure probabilities in a continuous system subjected to strength deterioration and dynamic loads.
The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-019-00252-7
Xi-Nong En
,
Yi-Min Zhang
,
Xian-Zhen Huang
. Time-variant reliability analysis of a continuous system with strength deterioration based on subset simulation[J]. Advances in Manufacturing, 2019
, 7(2)
: 188
-198
.
DOI: 10.1007/s40436-019-00252-7
1. Castaldo P, Palazzo B, Mariniello A (2017) Effects of the axial force eccentricity on the time-variant structural reliability of agingcross-sections subjected to chloride-induced corrosion. Eng Struct 130:261-274
2. Huang X, Li Y, Zhang Y et al (2018) A new direct second-order reliability analysis method. Appl Math Model 55:68-80
3. Zhu SP, Huang HZ, Peng WW et al (2016) Probabilistic physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliab Eng Syst Saf 146:1-12
4. Mori Y, Ellingwood BR (1993) Reliability-based service-life assessment of aging concrete structures. J Struct Eng 119(5):1600-1621
5. Li CQ (1995) Computation of the failure probability of deteriorating structural systems. Comput Struct 56(6):1073-1079
6. Ciampoli M (1998) Time dependent reliability of structural systems subject to deterioration. Comput Struct 67(1-3):29-35
7. Li Q, Wang C, Ellingwood BR (2015) Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation. Struct Saf 52:132-141
8. Rice SO (1944) Mathematical analysis of random noise. Bell Syst Tech J 23(3):282-332
9. Andrieu-Renaud C, Sudret B, Lemaire M (2004) The PHI2 method:a way to compute time-variant reliability. Reliab Eng Syst Saf 84(1):75-86
10. Zhang XJ, Xie LY, Wu Y et al (2010) Modeling for time-variant reliability of mechanism. Adv Mater Res 118-120:621-624
11. Li CC, Kiureghian AD (1993) Optimal discretization of random fields. J Eng Mech 119(6):1136-1154
12. Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263-277
13. Au SK, Beck JL (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech 129(8):901-917
14. Vahdatirad MJ, Andersen LV, Ibsen LB et al (2014) Stochastic dynamic stiffness of a surface footing for offshore wind turbines:implementing a subset simulation method to estimate rare events. Soil Dyn Earthq Eng 65:89-101
15. Norouzi M, Nikolaidis E (2013) Integrating subset simulation with probabilistic re-analysis to estimate reliability of dynamic systems. Struct Multidiscip Optim 48(3):533-548
16. Song SF, Lu ZZ, Qiao HW (2009) Subset simulation for structural reliability sensitivity analysis. Reliab Eng Syst Saf 94(2):658-665
17. Bourinet JM, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343-353
18. Zuev KM, Beck JL, Au SK et al (2012) Bayesian post-processor and other enhancements of subset simulation for estimating failure probabilities in high dimensions. Comput Struct 92-93:283-296
19. Li HS, Ma YZ, Cao ZJ (2015) A generalized subset simulation approach for estimating small failure probabilities of multiple stochastic responses. Comput Struct 153:239-251
20. Wang Z, Mourelatos ZP, Li J et al (2014) Time-dependent reliability of dynamic systems using subset simulation with splitting over a series of correlated time intervals. J Mech Des 136(6):061008
21. Yu S, Wang ZL (2018) A novel time-variant reliability analysis method based on failure processes decomposition for dynamic uncertain structures. J Mech Des 140(5):051401
22. Yu S, Wang ZL, Meng DB (2018) Time-variant reliability assessment for multiple failure modes and temporal parameters. Struct Multidiscip Optim 58(4):1705-1717
23. Abdel-Hameed M (1975) A gamma wear process. IEEE Trans Reliab 24(2):152-153
24. Van Noortwijk JM (2009) A survey of the application of gamma processes in maintenance. Reliab Eng Syst Saf 94(1):2-21
25. Ellingwood BR, Mori Y (1993) Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants. Nucl Eng Des 142(2-3):155-166
26. Cinlar E, Osman E, Bazant ZP (1977) Stochastic process for extrapolating concrete creep. J Eng Mech Div 103(6):1069-1088
27. Hoffmans GJCM, Pilarczyk KW (1995) Local scour downstream of hydraulic structures. J Hydraul Eng 121(4):326-340
28. Van Noortwijk JM, Klatter HE (1999) Optimal inspection decisions for the block mats of the eastern-scheldt barrier. Reliab Eng Syst Saf 65:203-211
29. Papaioannou I, Betz W, Zwirglmaier K et al (2015) MCMC algorithms for subset simulation. Probab Eng Mech 41:89-103
30. Metropolis N, Rosenbluth AW, Rosenbluth MN et al (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087-1092
31. Zhao YG, Ono T (1999) A general procedure for first/secondorder reliability method (FORM/SORM). Struct Safe 21(2):95-112
32. Baumgärtner A, Binder K (1987) Applications of the Monte Carlo method in statistical physics. Springer, Berlin
33. Zhang YM, He XD, Liu QL et al (2005) Robust reliability design of banjo flange with arbitrary distribution parameters. J Press Vessel Technol 127(4):408-413
34. O'Connor AN (2011) Probability distributions used in reliability engineering. University of Maryland, Maryland
35. Bellman RE (1961) Adaptive control processes:a guided tour. Princeton University Press, New Jersey
36. International Organization for Standards (2006) ISO 6336-2-2006 calculation of load capacity of sour and helical gears-part 2:calculation of surface durability (pittings). International Organization for Standards, Switzerland
37. Au SK, Wang Y (2014) Engineering risk assessment with subset simulation. Wiley/Blackwell, New Jersey
38. Madsen HO, Krenk S, Lind N (1986) Methods of structural safety. Prentice Hall, New Jersey
39. Du XP, Chen W (1999) Towards a better understanding of modeling feasibility robustness in engineering design. J Mech Des 122(4):385-394
