A time-variant reliability analysis method for structural systems based on stochastic process discretization
Source abstract
Abstract
In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Reliability and Maintenance Optimization · Concrete Corrosion and Durability
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (45)
Show source-provided references
1. Adduri, P.R., Penmetsa, R.C.: System reliability analysis for mixed uncertain variables. Struct. Saf. 31(5), 375–382 (2009)10.1016/j.strusafe.2009.02.001 ↗
2. Adduri, P.R., Penmetsa, R.C., Grandhi, R.V.: Estimation of structural system reliability using fast Fourier transforms. In: Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany (2004)10.2514/6.2004-4341 ↗
3. Andrieu-Renaud, C., Sudret, B., Lemaire, M.: The PHI2 method: a way to compute time-variant reliability. Reliab. Eng. Syst. Saf. 84(1), 75–86 (2004)10.1016/j.ress.2003.10.005 ↗
4. Breitung, K.W.: Asymptotic approximation for multinormal integrals. ASCE J. Eng. Mech 110(3), 357–366 (1984)10.1061/(ASCE)0733-9399(1984)110:3(357) ↗
5. Breitung, K.W.: Asymptotic Approximations for Probability Integrals. Springer, Berlin (1994)10.1007/BFb0073538 ↗
6. Burgazzi, L.: About time-variant reliability analysis with reference to passive systems assessment. Reliab. Eng Syst. Saf. 93(11), 1682–1688 (2008)10.1016/j.ress.2008.01.002 ↗
7. Cornell, C.A.: Bounds on the reliability of structural systems. ASCE J. Struct. Div. 93(1), 171–200 (1967)10.1061/JSDEAG.0001577 ↗
8. Der Kiureghian, A.: The geometry of random vibrations and solutions by FORM and SORM. Probab. Eng. Mech. 15(1), 81–90 (2000)10.1016/S0266-8920(99)00011-9 ↗
9. Dey, A., Mahadevan, S.: Reliability estimation with time-variant loads and resistances. J. Struct. Eng. 126(5), 612–620 (2000)10.1061/(ASCE)0733-9445(2000)126:5(612) ↗
10. Ditlevsen, O.: Narrow reliability bounds for structural systems. J. Struct. Mech. 7(4), 453–472 (1979)10.1080/03601217908905329 ↗
11. Du, X.: Interval reliability analysis. In: ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, pp. 1103–1109 (2007)10.1115/DETC2007-34582 ↗
12. Engelung, S., Rackwitz, R., Lange, C.: Approximations of first passage times for differentiable processes based on higher order threshold crossings. Probab. Eng. Mech. 10(1), 53–60 (1995)10.1016/0266-8920(94)00008-9 ↗
13. Gao, H.X.: Applied Multivariate Methods for Data Analysts. Peking University Press, Beijing (2005)
14. Gupta, S., Pieter, V.G., Mahesh, P. Time-variant reliability analysis for series systems with log-normal vector response. In: Advances in Engineering Structures, Mechanics & Construction, Proceedings: Solid Mechanics & its Applications, Springer, New York (2006)10.1007/1-4020-4891-2_63 ↗
15. Hasofer, A.M., Lind, N.C.: Exact and invariant second-moment code format. ASME J. Eng. Mech. Div. 100(1), 111–121 (1974)10.1061/JMCEA3.0001848 ↗
16. Hohenbichler, M., Rackwitz, R.: Non-normal dependent vectors in structural safety. ASME J. Eng Mech. Div. 107(6), 1227–1238 (1981)10.1061/JMCEA3.0002777 ↗
17. Hohenbichler, M., Rackwitz, R.: First-order concepts in system reliability. Struct. Saf. 1(3), 177–188 (1983)10.1016/0167-4730(82)90024-8 ↗
18. Hu, Z., Du, X.P.: A sampling approach to extreme value distribution for time-dependent reliability analysis. ASME J. Mech. Des. 135(7), 071003 (2013)10.1115/1.4023925 ↗
19. Ibrahim, Y.: Observations on applications of importance sampling in structural reliability analysis. Struct. Saf. 9(4), 269–281 (1991)10.1016/0167-4730(91)90049-F ↗
20. Jiang, C., Li, W., Han, X., Liu, L.X., Le, P.H.: Structural reliability analysis based on random distributions with interval parameters. Comput. Struct. 89(23), 2292–2302 (2011)10.1016/j.compstruc.2011.08.006 ↗
21. Jiang, C., Han, X., Li, W.X., Liu, J., Zhang, Z.: A hybrid reliability approach based on probability and interval for uncertain structures. ASME J. Mech. Des. 134(3), 031001 (2012)10.1115/1.4005595 ↗
22. Jiang, C., Huang, X.P., Han, X., Zhang, D.Q.: A time-variant reliability analysis method based on stochastic process discretization. ASME J. Mech. Des. 136(9), 091009 (2014)10.1115/1.4027865 ↗
23. Jin, B.H.: System Reliability Engineering. National Defense Industry Press, Beijing (2004)
24. Kang, Z., Luo, Y.: Reliability-based structural optimization with probability and convex set hybrid models. Struct. Multidiscip. Optim. 42(1), 89–102 (2010)10.1007/s00158-009-0461-6 ↗
25. Karamchandani, A., Bjerager, P., Cornell, C.A. Adaptive importance sampling. ASCE Struct. Saf. Reliab. 855–862 (1989)
26. Li, C.C., Der Kiureghian, A.: Optimal discretization of random fields. J. Eng. Mech. 119(6), 1136–1154 (1993)10.1061/(ASCE)0733-9399(1993)119:6(1136) ↗
27. Li, J., Mourelatos, Z.P.: Time-dependent reliability estimation for dynamic problems using a niching genetic algorithm. ASME J. Mech. Des. 131(7), 071009 (2009)10.1115/1.3149842 ↗
28. Liu, P.L., Der Kiureghian, A.: Multivariate distribution models with prescribed marginals and covariances. Probab. Eng. Mech. 1(2), 105–112 (1986)10.1016/0266-8920(86)90033-0 ↗
29. Luo, Y., Kang, Z., Li, A.: Structural reliability assessment based on probability and convex set mixed model. Comput. Struct. 87(21), 1408–1415 (2009)10.1016/j.compstruc.2009.06.001 ↗
30. Mahadevan, S., Xiao, Q.: Time-variant reliability of brittle structural systems. ASCE J. Engrg. Mech. 121(3), 414–423 (1995)10.1061/(ASCE)0733-9399(1995)121:3(414) ↗
31. Melchers, R.E.: Importance sampling in structural systems. Struct. Saf. 6(1), 3–10 (1989)10.1016/0167-4730(89)90003-9 ↗
32. Melchers, R.E.: Structural Reliability Analysis and Prediction. Wiley, Chichester (1999)
33. Moses, F., Stahl, B.: Reliability analysis format for offshore structures. J. Petrol. Technol. 31(3), 347–354 (1979)10.2118/7203-PA ↗
34. Polidori, D.C., Beck, J.L., Papadimitriou, C.: New approximations for reliability integrals. ASCE J. Eng. Mech. 125(4), 466–475 (1999)10.1061/(ASCE)0733-9399(1999)125:4(466) ↗
35. Rackwitz, R., Flessler, B.: Structural reliability under combined random load sequences. Comput. Struct. 9(5), 489–494 (1978)10.1016/0045-7949(78)90046-9 ↗
36. Sheng, Z., Xie, S.Q., Pan, C.Y.: Probability Theory and Mathematical Statistics. Higher Education Press, Beijing (2008)
37. Siegert, A.J.F.: On the first passage time probability problem. Phys. Rev. 81(4), 617 (1951)10.1103/PhysRev.81.617 ↗
38. Son, Y.K., Savage, G.J.: Set theoretic formulation of performance reliability of multiple response time-variant systems due to degradations in system components. Qual. Reliab. Eng. Int. 23(2), 171–188 (2007)10.1002/qre.783 ↗
39. Song, S.F., Lu, Z.Z.: Markov chain-based line sampling method for reliability estimation of structural parallel system with multiple failure modes. J. Northw. Polytech. Univ. 26(2), 234–238 (2008)
40. Tang, L.K., Melchers, R.E.: Improved approximation for multinormal integral. Struct. Saf. 4(2), 81–93 (1986)10.1016/0167-4730(86)90024-X ↗
41. Wen, Y.K., Chen, Y.C.: System reliability under time varying loads: II. ASCE J. Eng. Mech. 115(4), 824–839 (1989)10.1061/(ASCE)0733-9399(1989)115:4(824) ↗
42. Wu, Y.T. An adaptive importance sampling method for structural system reliability analysis. Reliab. Technol. 217–231 (1992)
43. Zhang, M.: Structural Reliability Analysis: Methods and Programs. Science Press, Beijing (2009)
44. Zhang, J., Du, X.P.: Time-dependent reliability analysis for function generator mechanisms. ASME J. Mech. Des. 133(3), 031005 (2011)10.1115/1.4003539 ↗
45. Zhang, Y.M., Wen, B.C., Liu, Q.L.: First passage of uncertain single degree-of-freedom nonlinear oscillators. Comput. Meth. Appl. Mech. Eng. 165(1), 223–231 (1998)10.1016/S0045-7825(98)00042-5 ↗