Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Failure Probability Calculation Method Using Kriging Metamodel-based Importance Sampling Method

크리깅 근사모델 기반의 중요도 추출법을 이용한 고장확률 계산 방안

  • Received : 2016.10.04
  • Accepted : 2017.01.13
  • Published : 2017.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.

마르코프체인 시뮬레이션으로 추출한 점을 기반으로 커널 밀도함수를 구성하고 중요도 추출함수로 가정하였다. 크리깅 근사모델은 한계상태식 근방에서 상세히 구성되었다. 고장확률은 크리깅 근사모델에 대해 중요도 추출법을 수행하여 계산하였다. 커널 밀도함수가 한계상태식의 근방에서 더 많은 점을 추출할 수 있도록 기존의 방법을 개선하였다. 커널 밀도함수의 파라메터를 찾기 위한 안정적인 수치계산 방안이 제시된다. 크리깅 근사모델의 불확실성으로 인해 계산된 고장확률이 변경될 가능성을 계산하여, 크리깅 근사모델의 완성도를 평가하였다.

Keywords

References

  1. Bichon, B. J., Eldred, M. S., Swiler, L. P., Mahadevan, S. and McFarland, M., 2008, "Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions," AIAA Journal, Vol. 46, No. 10, pp. 2459-2468. https://doi.org/10.2514/1.34321
  2. Au, S. K. and Beck, J. L., 1999, "A New Adaptive Importance Sampling Scheme for Reliability Calculations," Structural Safety, Vol. 21, pp. 135-158. https://doi.org/10.1016/S0167-4730(99)00014-4
  3. Bucher, C. G. and Bourgund, U., 1990, "A Fast and Efficient Response Surface Approach for Structural Reliability Problems," Structural Safety, Vol. 7, pp. 75-66.
  4. Kim, S.-H. and Na, S.-W., 1997, "Response Surface Method using Vector Projected Sampling Points," Structural Safety, Vol. 19, No. 1, pp. 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  5. Jerome Sacks, Susannah B. Schiler and William J. Welch, 1989, "Designs for Computer Experiments," Technometrics, Vol. 31, No. 1, pp. 41-47. https://doi.org/10.1080/00401706.1989.10488474
  6. Ju, B.-H., 2008, "Reliability Based Design Optimization Using a Kriging Metamodel and a Moment Method," Korea Advanced Institute of Science and Technology.
  7. Santner, T. J., Williams, B. J. and William, I. N., 2003, "The Design and Analysis of Computer Experiments," Springer, Chapter 2-4.
  8. Echard, B., Gayton, N. and Lemaire, M., 2011, "AKMCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation," Structural Safety, Vol. 33, pp. 145-154. https://doi.org/10.1016/j.strusafe.2011.01.002
  9. Dubourg, V., Sudret, B. and Deheeger, F., 2013, "Metamodel-based Importance Sampling for Structural Reliability Analysis," Probabilistic Engineering Mechanics, Vol. 33, pp. 47-57. https://doi.org/10.1016/j.probengmech.2013.02.002
  10. Cadini, F., Santos, F. and Zio, E., 2014, "An Improved Adaptive Kriging-based Importance Technique for Sampling Multiple Failure Regions of Low Probability," Reliability Engineering and System Safety, Vol. 131, pp. 109-117. https://doi.org/10.1016/j.ress.2014.06.023
  11. Zhao, H., Yue, Z., Liu, Y., Gao, Z. and Zhang, Y., 2015, "An Efficient Reliability Method Combining Adaptive Importance Sampling and Kriging Metamodel," Applied Mathematical Modelling, Vol. 39, pp. 1853-1866. https://doi.org/10.1016/j.apm.2014.10.015
  12. Cho, T.-M., Ju, B.-H., Jung, D.-H. and Lee, B.-C., 2006, "Reliability Estimation Using Two-Staged Kriging Metamodel and Genetic Algorithm," Trans. Korean Soc. Mech. Eng. A, Vol. 30, No. 9, pp. 1116-1123. https://doi.org/10.3795/KSME-A.2006.30.9.1116
  13. Meggiolaro, M. A. and Castro, J. T. P., 2004, "Statistical Evaluation of Strain-life Fatigue Crack Initiation Predictions," International Journal of Fatigue, Vol. 26, pp. 463-476. https://doi.org/10.1016/j.ijfatigue.2003.10.003