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KSCE Journal of Civil Engineering

, Volume 23, Issue 9, pp 4063–4074 | Cite as

The Estimation of Reliability Probability of Structures based on Improved Iterative Response Surface Methods

  • Yanxu WeiEmail author
  • Guangchen Bai
  • Lukai Song
  • Bin Bai
Structural Engineering
  • 28 Downloads

Abstract

Response surface method (RSM) provides an efficient way to performance reliability analysis for structures. However, the locations of samples are very important due to its great influence on computational accuracy and efficiency of RSM for reliability analysis. To further improve computational accuracy and efficiency of RSM, new methods of selecting samples are proposed based on a new starting center point, 2n + 1 directions and a linear interpolation. The objective of the new methods is to find samples which are close to limit state function (LSF) around design point, thus the fitting precision of response surface function (RSF) to LSF can be improved, and a quadratic polynomial without cross terms is employed as the RSF in each iteration. Then improved iterative RSMs are formed. Two mathematical examples and a truss structure are employed to demonstrate the accuracy and efficiency of the proposed RSMs. Results show that the proposed RSMs can improve the fitting precision of RSF to LSF and achieve more accurate results with relatively high efficiency.

Keywords

response surface method reliability analysis samples new starting center point linear interpolation 

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Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant no. 51575024 and 11772011).

References

  1. Alibrandi, U., Alani, A. M., and Ricciardi, G. (2015). “A new sampling strategy for SVM-based response surface for structural reliability analysis.” Probabilistic Engineering Mechanics, Vol. 41, pp. 1–12, DOI:  https://doi.org/10.1016/j.probengmech.2015.04.001.CrossRefGoogle Scholar
  2. Allaix, D. L. and Carbone, V. I. (2011). “An improvement of the response surface method.” Structural Safety, Vol. 33, No. 2, pp. 165–172, DOI:  https://doi.org/10.1016/j.strusafe.2011.02.001.CrossRefGoogle Scholar
  3. Bjerager, P. (1988). “Probability integration by directional simulation.” Journal of Engineering Mechanics, Vol. 114, No. 8, pp. 1285–1302, DOI:  https://doi.org/10.1061/(asce)0733-9399(1988)114:8(1285).CrossRefGoogle Scholar
  4. Blatmana, G. and Sudret, B. (2010). “An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis.” Probabilistic Engineering Mechanics, Vol. 25, No. 2, pp. 183–197, DOI:  https://doi.org/10.1016/j.probengmech.2009.10.003.CrossRefGoogle Scholar
  5. Bucher, C. G. and Bourgund, U. (1990). “A fast and efficient response surface approach for structural reliability problems.” Structural Safety, Vol. 7, No. 1, pp. 57–66, DOI:  https://doi.org/10.1016/0167-4730(90)90012-E.CrossRefGoogle Scholar
  6. Cheng, J., Li, Q. S., and Xiao, R. C. (2008). “A new artificial neural network-based response surface method for structural reliability analysis.” Probabilistic Engineering Mechanics, Vol. 23, No. 1, pp. 51–63, DOI:  https://doi.org/10.1016/j.probengmech.2007.10.003.CrossRefGoogle Scholar
  7. Duprat, F. and Sellier, A. (2006). “Probabilistic approach to corrosion risk due to carbonation via an adaptive response surface method.” Probabilistic Engineering Mechanics, Vol. 21, No. 3, pp. 207–216, DOI:  https://doi.org/10.1016/j.probengmech.2005.11.001.CrossRefGoogle Scholar
  8. Elhewy, A. H., Mesbahi, E., and Pu, Y. (2006). “Reliability analysis of structures using neural network method.” Probabilistic Engineering Mechanics, Vol. 21, No. 1, pp. 44–53, DOI:  https://doi.org/10.1016/j.probengmech.2005.07.002.CrossRefGoogle Scholar
  9. Gavin, H. P. and Yau, S. C. (2008). “High-order limit state functions in the response surface method for structural reliability analysis.” Structural Safety, Vol. 30, No. 2, pp. 162–179, DOI:  https://doi.org/10.1016/j.strusafe.2006.10.003.CrossRefGoogle Scholar
  10. Gayton, N., Bourinet, J. M., and Lemaire, M. (2003). “CQ2RS: A new statistical approach to the response surface method for reliability analysis.” Structural Safety, Vol. 25, No. 1, pp. 99–121, DOI:  https://doi.org/10.1016/S0167-4730(02)00045-0.CrossRefGoogle Scholar
  11. Goswami, S., Ghosh, S., and Chakraborty, S. (2016). “Reliability analysis of structures by iterative improved response surface method.” Structural Safety, Vol. 60, pp. 56–66, DOI:  https://doi.org/10.1016/j.strusafe.2016.02.002.CrossRefGoogle Scholar
  12. Guan, X. L. and Melchers, R. E. (2001). “Effect of response surface parameter variation on structural reliability estimates.” Structural Safety, Vol. 23, No. 4, pp. 429–444, DOI:  https://doi.org/10.1016/S0167-4730(02)00013-9.CrossRefGoogle Scholar
  13. Hadidi, A., Azar, B. F., and Rafiee, A. (2017). “Efficient response surface method for high-dimensional structural reliability analysis.” Structural Safety, Vol. 41, pp. 15–27, DOI:  https://doi.org/10.1016/j.strusafe.2017.03.006.CrossRefGoogle Scholar
  14. Hasofer, A. M. and Lind, N. C. (1974). “Exact and invariant second moment code format.” Journal of Engineering Mechanics, ASCE, Vol. 100, No. 1, pp. 111–121, DOI:  https://doi.org/10.1016/S0022-460X(74)80150-1.Google Scholar
  15. 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.” Probabilistic Engineering Mechanics, Vol. 25, No. 4, pp. 365–371, DOI:  https://doi.org/10.1016/j.probengmech.2010.04.002.CrossRefGoogle Scholar
  16. Kaymaz, I. and Chris, A. M. (2005). “A response surface method based on weighted regression for structural reliability analysis.” Probabilistic Engineering Mechanics, Vol. 20, No. 1, pp. 11–17, DOI:  https://doi.org/10.1016/j.probengmech.2004.05.005.CrossRefGoogle Scholar
  17. Kim, S. and Na, S. (1997). “Response surface method using vector projected sampling points.” Structural Safety, Vol. 19, No. 1, pp. 3–19, DOI:  https://doi.org/10.1016/S0167-4730(96)00037-9.CrossRefGoogle Scholar
  18. Kiureghian, D. A., Lin, H. Z., and Hwang, S. J. (1987). “Second-order reliability approximations.” Journal of Engineering Mechanics, Vol. 113, No. 8, pp. 1208–1225, DOI:  https://doi.org/10.1061/(asce)0733-9399(1987)113:8(1208).CrossRefGoogle Scholar
  19. Kumar, A., Chakrabarti, A., Bhargava, P., and Chowdhury, R. (2015). “Probabilistic failure analysis of laminated sandwich shells based on higher order zigzag theory.” Journal of Sandwich Structures & Materials, Vol. 17, No. 5, pp. 546–561, DOI:  https://doi.org/10.1177/1099636215577368.CrossRefGoogle Scholar
  20. Li, X., Li, X. B., and Su, Y. H. (2016). “A hybrid approach combining uniform design and support vector machine to probabilistic tunnel stability assessment.” Structural Safety, Vol. 61, pp. 22–42, DOI:  https://doi.org/10.1016/j.strusafe.2016.03.001.CrossRefGoogle Scholar
  21. Liu, P. L. and Kiureghian, D. A. (1991). “Optimization algorithms for structural reliability.” Structural Safety, Vol. 9, No. 3, pp. 161–177, DOI:  https://doi.org/10.1016/0167-4730(91)90041-7.CrossRefGoogle Scholar
  22. Nguyen, X. S., Sellier, A., Duprat, F., and Pons, G. (2009). “Adaptive response surface method based on a double weighted regression technique.” Probabilistic Engineering Mechanics, Vol. 24, No. 2, pp. 135–143, DOI:  https://doi.org/10.1016/j.probengmech.2008.04.001.CrossRefGoogle Scholar
  23. Rackwitz, R. and Flessler, B. (1978). “Structural reliability under combined random load sequences.” Computers & Structures, Vol. 9, No. 5, pp. 489–494, DOI:  https://doi.org/10.1016/0045-7949(78)90046-9.CrossRefzbMATHGoogle Scholar
  24. Rajashekhar, M. R. and Ellingwood, B. R. (1993). “A new look at the response surface approach for reliability analysis.” Structural Safety, Vol. 12, No. 3, pp. 205–220, DOI:  https://doi.org/10.1016/0167-4730(93)90003-j.CrossRefGoogle Scholar
  25. Richard, B., Cremona, C., and Adelaide, L. (2012). “A response surface method based on support vector machines trained with an adaptive experimental design.” Structural Safety, Vol. 39, pp. 14–21, DOI:  https://doi.org/10.1016/j.strusafe.2012.05.001.CrossRefGoogle Scholar
  26. Roussouly, N., Petitjean, F., and Salaun, M. (2013). “A new adaptive response surface method for reliability analysis.” Probabilistic Engineering Mechanics, Vol. 32, pp. 103–105, DOI:  https://doi.org/10.1016/j.probengmech.2012.10.001.CrossRefGoogle Scholar
  27. Shayanfar, M. A., Barkhordari, M. A., and Roudak, M. A. (2017). “An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method.” Communications in Nonlinear Science and Numerical Simulation, Vol. 47, pp. 223–237, DOI:  https://doi.org/10.1016/j.cnsns.2016.11.021.CrossRefGoogle Scholar
  28. Song, L. K., Bai, G. C., and Fei, C. W. (2019). “Probabilistic LCF life assessment for turbine discs with DC strategy-based wavelet neural network regression.” International Journal of Fatigue, Vol. 119, 204–219, DOI:  https://doi.org/10.1016/j.ijfatigue.2018.10.005.CrossRefGoogle Scholar
  29. Song, L. K., Wen, J., Fei, C. W., and Bai, G. C. (2018). “Distributed collaborative probabilistic design of multi-failure structure with fluid-structure interaction using fuzzy neural network of regression.” Mechanical Systems and Signal Processing, Vol. 104, pp. 72–86, DOI:  https://doi.org/10.1016/j.ymssp.2017.09.039.CrossRefGoogle Scholar
  30. Wang, Z. Q., Broccardo, M., and Kiureghian, A. D. (2016). “An algorithm for finding a sequence of design points in reliability analysis.” Structural Safety, Vol. 58, pp. 52–59, DOI:  https://doi.org/10.1016/j.strusafe.2015.09.004.CrossRefGoogle Scholar
  31. Wei, Y. X., Bai, G. C., Wang, B. W., and Bai, B. (2018). “Reliability Analysis on structures based on a modified iterative response surface method.” Mathematical Problems in Engineering, DOI:  https://doi.org/10.1155/2018/8794160.
  32. Zhao, W. T. and Qiu, Z. P. (2013). “An efficient response surface method and its application to structural reliability and reliability based optimization.” Finite Elements in Analysis and Design, Vol. 67, pp. 34–42, DOI:  https://doi.org/10.1016/j.finel.2012.12.004.CrossRefGoogle Scholar

Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  1. 1.School of Energy and Power EngineeringBeihang UniversityBeijingChina
  2. 2.State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHeBei University of TechnologyTianjinChina

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