International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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The hybrid uncertain neural network method for mechanical reliability analysis

  • Peng, Wensheng (School of Reliability and Systems Engineering, Beihang University) ;
  • Zhang, Jianguo (School of Reliability and Systems Engineering, Beihang University) ;
  • You, Lingfei (School of Reliability and Systems Engineering, Beihang University)
  • Received : 2015.06.04
  • Accepted : 2015.12.04
  • Published : 2015.12.30
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Abstract

Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.

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References

  1. Hurtado, J. E. and Alvarez, D. A., "The encounter of interval and probabilistic approaches to structural reliability at design point", Applied Mechanics and Engineering, Vol. 225, 2012, pp. 74-94.
  2. Hurtado, J. E., "Assessment of reliability intervals under input distributions with uncertain parameters", Prababilistic Engineering Mechanics, Vol. 32, 2013, pp. 80-92. https://doi.org/10.1016/j.probengmech.2013.01.004
  3. Ni,Z. and Qiu,Z.P. "Hybrid probabilistic fuzzy and nonprobabilistic model of structural reliability", Computers & Industrial Engineering, Vol. 58, 2010, pp. 463-467. https://doi.org/10.1016/j.cie.2009.11.005
  4. Jiang ,C.,Long, X. Y.,Han,X. et al, "Probability-interval hybrid reliability analysis for cracked structures existing epistemic uncertainty", Engineering Fracture Mechanics, Vol. 112-113, 2013, pp.148-164. https://doi.org/10.1016/j.engfracmech.2013.10.009
  5. Wang, J. and Qiu, Z. P., "The reliability analysis of probabilistic and interval hybrid structural system", Applied Mathematical Modelling, Vol. 34, 2010, pp. 3648-3658. https://doi.org/10.1016/j.apm.2010.03.015
  6. Zhu, L. P. and Elishakoff, I., "Hybrid probabilistic and convex modeling of excitation and response of periodic structures", Mathematical Problems in Engineering, Vol. 2, No. 2, pp. 143-163, 1996. https://doi.org/10.1155/S1024123X96000282
  7. Qiu, Z. P., Yang, D. and Elishakoff, I., "Probabilistic interval reliability of structural systems", International Journal of Solids and Structures, Vol. 45, No. 10, 2008, pp. 2850-2860. https://doi.org/10.1016/j.ijsolstr.2008.01.005
  8. Guo, S. X. and Lu, Z. Z., "Hybrid probabilistic and nonprobabilistic model of structural reliability", Chinese J Mech Strength, Vol. 24, No. 4, 2002, pp. 524-526.
  9. Cheng, Y. S., Zhong, Y. X. and Zeng, G. W., "Structural robust design based on hybrid probabilistic and nonprobabilistic models", Chinese Journal of Computational Mechanics, Vol. 22, No. 4, 2005, pp. 501-505.
  10. Kang, Z. and Luo YJ., "Reliability-based structural optimization with probability and convex set hybrid models", Struct Multidisc Optim, Vol. 42, 2010, pp. 89-102. https://doi.org/10.1007/s00158-009-0461-6
  11. Luo, YJ., Kang, Z. and Li, A., "Structural reliability assessment based on probability and convex set mixed model". Comput Struct, Vol. 87, 2009, pp. 1408-15. https://doi.org/10.1016/j.compstruc.2009.06.001
  12. Jiang, C., Li, W.X. and Han,X., et al., "Structural reliability analysis based on random distributions with interval parameters", Computer and Structures, Vol. 89, 2011, pp. 2292-2302. https://doi.org/10.1016/j.compstruc.2011.08.006
  13. Du, X. P., Sudjianto, A. and Huang, B. Q., "Reliabilitybased design with the mixture of random and interval variables", in ASME 2003 design engineering technical conference and computers and information in engineering conference (DETC2003), Chicago, Illinois, USA, 2005.
  14. Du,X.P., "Interval reliability analysis", inASME 2007 design engineering technical conference and computers and information in engineering conference (DETC2007), Las Vegas, Nevada, USA, 2007.
  15. Guo, J. and Du, X. P., "Reliability sensitivity analysis with random and interval variables", International journal for numerical methods in engineering, Vol. 78, 2009, pp. 1585-161. https://doi.org/10.1002/nme.2543
  16. Lu, Z. Z., Feng, Y. W. and Yue, Z. F., "A advanced interval-truncation approach and non-probabilistic reliability analysis based on interval analysis", Chinese Journal of Computational Mechanics, Vol.19, No.3, 2002, pp. 260-264.
  17. Zhao, M. H., Jiang, C. and Cao, W. G., "Nonprobabilistic reliability analysis of retaining walls based on interval theory", Chinese Journal of Geotechnical Engineering, Vol.30, No. 4, 2008, pp. 467-472.
  18. Zou, T. F., Cai, M. and Shu, X., "Response surface methodology and improved interval analysis method-For analyzing uncertainty in accident reconstruction". Forensic Science International222, 2012, pp. 306-312. https://doi.org/10.1016/j.forsciint.2012.07.007
  19. Jiang, T., Chen, J. J. and Xu, Y. L.,"A semi-analytic method for calculating non-probabilistic reliability index based on interval models". Applied Mathematical Modelling, Vo. 31, 2007, pp. 1362-1370. https://doi.org/10.1016/j.apm.2006.02.013
  20. Koduru, S. D. and Haukaas, T., "Feasibility of FORM in the finite element reliability analysis". Structural Safety, Vol. 32, No. 2, 2010, pp. 145-153. https://doi.org/10.1016/j.strusafe.2009.10.001
  21. Eldred, M. S., Swiler, L. P. and Tang, G., "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation" Reliability engineering and system safety, Vol.96, 2011, pp. 1092-1113. https://doi.org/10.1016/j.ress.2010.11.010
  22. Harsheel R. Shah, Serhat Hosder, and Tyler Winter, "A mixed uncertainty quantification approach with evidence theory and stochastic expansions". 16th AIAA Nondeterministic Approaches conference, AIAA page2014-0298, national harbor, Maryland.
  23. Angel Urbina, Sankaran Mahadevan, and Thomas L. Paez., "Quatification of margins and uncertainties of complex systems in the presence of aleatoric and epstemic uncertainty". Reliability engineering and system safety, Vol. 96, 2011, pp. 1114-1125. https://doi.org/10.1016/j.ress.2010.08.010
  24. Zhao, Y. G., and Ono, T., "Moment methods for structural reliability". Structural Safety, Vol. 23, No. 1, 2001, pp. 47-75. https://doi.org/10.1016/S0167-4730(00)00027-8
  25. Ren, Y. and Bai, G. C., "New Neural Network Response Surface Methods for Reliability Analysis". Chinese Journal of Aeronautics, Vol. 24, 2011, pp. 25-31. https://doi.org/10.1016/S1000-9361(11)60004-6
  26. Yan, P. F. and Zhang, C. S., Artificial neural networks and evolutionary computing 2nd ed., Tsinghua University Press, Beijing, China, 2005.
  27. Herbert, M. G. and Armando, M. A., "Comparison of response surface and neural network with other methods for structural reliability analysis". Structural Safety, Vol. 26, 2004, pp. 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5
  28. Deng, J., Gu, D. S., Li, X. B. and Yue, Z. Q., "Structural reliability analysis for implicit performance functions using artificial neural network". Structural Safety, Vol. 27, 2005, pp. 25-48. https://doi.org/10.1016/j.strusafe.2004.03.004
  29. Bai, Y. C., Han, X., Jiang, C. and Bi, R.G., "A responsesurface-based structural reliability analysis method by using non-probability convex model", Applied Mathematical Modelling, Vol. 38, 2014, pp. 3834-3847 https://doi.org/10.1016/j.apm.2013.11.053
  30. Gong, Q., Zhang, J.G., TC. L. and W, C. C., "Neural Networks Combined with Importance Sampling Techniques for Reliability Evaluation of Explosive Initiating Device". Chinese Journal of Aeronautics, Vol. 25, 2012, pp. 208-215. https://doi.org/10.1016/S1000-9361(11)60380-4
  31. Han, X., Jiang, C., Liu, L.X., Liu, J. and Long, X. Y., "Response-surface-based structural reliability analysis with random and interval mixed uncertainties", Science China Technological Sciences, Vol. 57, 2014, pp. 1322-1334. https://doi.org/10.1007/s11431-014-5581-6
  32. Zhang, Y. and der Kiureghian, A., "Two improved algorithms for reliability analysis", reliability and optimization of structural systems, Proceedings of the Sixth IFIP WG7.5 Working Conferences on Reliability and Optimization of Structural Systems, Assisi, Italy.

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