- Volume 41 Issue 5
DOI QR Code
Failure Probability Calculation Method Using Kriging Metamodel-based Importance Sampling Method
크리깅 근사모델 기반의 중요도 추출법을 이용한 고장확률 계산 방안
- Lee, Seunggyu (Korea Aerospace Research Institue) ;
- Kim, Jae Hoon (Dept. of Mechanical Engineering, Chungnam Nat'l Univ.)
- Received : 2016.10.04
- Accepted : 2017.01.13
- Published : 2017.05.01
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.
Importance Sampling;Markov Chain Simulation;Kernel Density;Kriging Metamodel
- 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
- 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
- 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.
- 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
- 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
- Ju, B.-H., 2008, "Reliability Based Design Optimization Using a Kriging Metamodel and a Moment Method," Korea Advanced Institute of Science and Technology.
- Santner, T. J., Williams, B. J. and William, I. N., 2003, "The Design and Analysis of Computer Experiments," Springer, Chapter 2-4.
- 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
- 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
- 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
- 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
- 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
- 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