Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An improved response surface method for reliability analysis of structures

  • Received : 2010.12.17
  • Accepted : 2012.03.13
  • Published : 2012.04.25
⟨ Previous Next ⟩

Abstract

This paper presents an algorithm for structural reliability with the response surface method. For this aim, an approach with three stages is proposed named as improved response surface method. In the algorithm, firstly, a quadratic approximate function is formed and design point is determined with First Order Reliability Method. Secondly, a point close to the exact limit state function is searched using the design point. Lastly, vector projected method is used to generate the sample points and Second Order Reliability Method is performed to obtain reliability index and probability of failure. Five numerical examples are selected to illustrate the proposed algorithm. The limit state functions of three examples (cantilever beam, highly nonlinear limit state function and dynamic response of an oscillator) are defined explicitly and the others (frame and truss structures) are defined implicitly. ANSYS finite element program is utilized to obtain the response of the structures which are needed in the reliability analysis of implicit limit state functions. The results (reliability index, probability of failure and limit state function evaluations) obtained from the improved response surface are compared with those of Monte Carlo Simulation, First Order Reliability Method, Second Order Reliability Method and Classical Response Surface Method. According to the results, proposed algorithm gives better results for both reliability index and limit state function evaluations.

Keywords

References

  1. ANSYS (2007), Swanson Analysis Systems Inc., Houston PA, USA.
  2. Ayyub, B.M. and Chia, C.Y. (1992), "Generalised conditional expectation for structural reliability assessment", Struct Saf, 11, 131-146. https://doi.org/10.1016/0167-4730(92)90005-8
  3. Ayyub, B.M. and McCuen, R.H. (1997), Probability, Statistics, & Reliability for Engineers, CRC Press, USA.
  4. Basaga, H.B. (2009), "An approach for reliability analysis of structures: improved response surface method", PhD Thesis, Karadeniz Technical University, Trabzon, Turkiye. (in Turkish)
  5. Bjerager, P. (1988), "Probability integration by directional simulation", J. Eng. Mech., 114(8), 1285-1301. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1285)
  6. Bucher, C.G. (1988), "Adaptive sampling-an iterative fast Monte Carlo procedure", Struct. Saf., 5(2), 119-126. https://doi.org/10.1016/0167-4730(88)90020-3
  7. Bucher, C.G. and Bourgund, U. (1990), "A fast and efficient response surface approach for structural reliability problems", Struct. Saf., 7(1), 57-66. https://doi.org/10.1016/0167-4730(90)90012-E
  8. Chen, J., Xu, Q., Li, J. and Fan, S. (2010), "Improved response surface method for anti-slide reliability analysis of gravity dam based on weighted regression", J. Zhejiang Univ.-Sc A., 11(6), 432-439. https://doi.org/10.1631/jzus.A0900709
  9. Das, P.K. and Zheng, Y. (2000), "Cumulative formation of response surface and its use in reliability analysis", Probab. Eng. Mech., 15, 309-315. https://doi.org/10.1016/S0266-8920(99)00030-2
  10. Faravelli, L. (1989), "Response surface approach for reliability analysis", J. Eng. Mech., 115(12), 2763-2781. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2763)
  11. Gavin, H.P. and Yau, S.C. (2008), "Higher order limit state functions in the response surface method for structural reliability analysis", Struct. Saf. 30, 162-179. https://doi.org/10.1016/j.strusafe.2006.10.003
  12. Gayton, N., Bourinet, J.M. and Lemaire, M. (2003), "CQ2RS: a new statistical approach to the response surface method for reliability analysis", Struct. Saf., 25, 99-121. https://doi.org/10.1016/S0167-4730(02)00045-0
  13. Gomes, H.M. and Awruch, A.M. (2004), "Comparison of response surface and neural network with other methods for structural reliability analysis", Struct. Saf., 26, 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5
  14. Kang, S.C., Koh, H.M. and Choo, J.F. (2010). "An efficient response surface method using moving least squares approximation for structural reliability analysis", Probab. Eng. Mech., 25(4), 365-371. https://doi.org/10.1016/j.probengmech.2010.04.002
  15. Kaymaz, I. and McMahon, C.A. (2005), "A response surface method based on weighted regression for structural reliability analysis", Probab. Eng. Mech., 20, 11-17. https://doi.org/10.1016/j.probengmech.2004.05.005
  16. Kim, S.H. and Na, S.W. (1997), "Response surface method using vector projected sampling points", Struct. Saf. 19(1), 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  17. Lee, S.H. and Kwak, B.M. (2006), "Response surface augmented moment method for efficient reliability analysis", Struct. Saf. 28, 261-272. https://doi.org/10.1016/j.strusafe.2005.08.003
  18. Melchers, R.E. (1990), "Search-based importance sampling", Struct. Saf., 9(2), 117-128. https://doi.org/10.1016/0167-4730(90)90003-8
  19. Melchers, R.E. (1999), Structural Reliability Analysis and Prediction, John Wiley & Sons, England.
  20. Myers, R.H. (1971), Response Surface Methodology, Allyn and Bacon, Boston.
  21. Rajashekhar, M.R. and Ellingwood, B.R. (1993), "A new look at the response surface approach for reliability analysis", Struct. Saf., 12(3), 205-220. https://doi.org/10.1016/0167-4730(93)90003-J
  22. Thoft-Christensen, P. and Baker, M.J. (1982), Structural Reliability Theory and Its Applications, Springer-Verlag, Berlin.
  23. Wong, S.M., Hobbs, R.E. and Onof, C. (2005), "An adaptive response surface method for reliability analysis of structures with multiple loading sequences", Struct. Saf., 27, 287-308. https://doi.org/10.1016/j.strusafe.2005.02.001
  24. Zheng, Y. and Das P.K. (2000), "Improved response surface method and its application to stiffened plate reliability analysis", Eng. Struct., 22, 544-551. https://doi.org/10.1016/S0141-0296(98)00136-9
  25. Zheng, Y., Fujimoto, Y. and Iwata, M. (1991), "An empirical fitting-adaptive approach to importance sampling in reliability analysis", J. Soc. Naval Arch. Japan, 171, 433-441.

Cited by

  1. A comparative study of three collocation point methods for odd order stochastic response surface method vol.45, pp.5, 2013, https://doi.org/10.12989/sem.2013.45.5.595
  2. A response surface method based on sub-region of interest for structural reliability analysis vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.587
  3. Analysis of structural dynamic reliability based on the probability density evolution method vol.45, pp.2, 2013, https://doi.org/10.12989/sem.2013.45.2.201
  4. An efficient method for reliable optimum design of trusses vol.21, pp.5, 2016, https://doi.org/10.12989/scs.2016.21.5.1069
  5. An efficient response surface method considering the nonlinear trend of the actual limit state vol.47, pp.1, 2013, https://doi.org/10.12989/sem.2013.47.1.045
  6. Reliability-based design optimization of structural systems using a hybrid genetic algorithm vol.52, pp.6, 2014, https://doi.org/10.12989/sem.2014.52.6.1099
  7. An efficient coupling of FORM and Karhunen–Loève series expansion vol.32, pp.1, 2016, https://doi.org/10.1007/s00366-015-0394-1
  8. An efficient simulation method for reliability analysis of systems with expensive-to-evaluate performance functions vol.55, pp.5, 2015, https://doi.org/10.12989/sem.2015.55.5.979
  9. Capabilities of stochastic response surface method and response surface method in reliability analysis vol.49, pp.1, 2014, https://doi.org/10.12989/sem.2014.49.1.111
  10. Structural reliability analysis using response surface method with improved genetic algorithm vol.62, pp.2, 2012, https://doi.org/10.12989/sem.2017.62.2.139
  11. Reliability analysis of laminated composite shells by response surface method based on HSDT vol.72, pp.2, 2012, https://doi.org/10.12989/sem.2019.72.2.203
  12. Finite element model updating of long-span cable-stayed bridge by Kriging surrogate model vol.74, pp.2, 2012, https://doi.org/10.12989/sem.2020.74.2.157
  13. Decomposable polynomial response surface method and its adaptive order revision around most probable point vol.76, pp.6, 2012, https://doi.org/10.12989/sem.2020.76.6.675
  14. An efficient reliability analysis strategy for low failure probability problems vol.78, pp.2, 2021, https://doi.org/10.12989/sem.2021.78.2.209
  15. An efficient particle swarm optimization-joint probability distribution optimization method for structural reliability analysis vol.235, pp.9, 2012, https://doi.org/10.1177/0954406220941559
  16. GNDO-SVR: An efficient surrogate modeling approach for reliability-based design optimization of concrete dams vol.35, pp.None, 2012, https://doi.org/10.1016/j.istruc.2021.11.048