한국안전학회지 (Journal of the Korean Society of Safety)

  • 제35권3호
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  • Pages.49-57
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  • 2020
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  • 1738-3803(pISSN)
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  • 2383-9953(eISSN)
한국안전학회 (The Korean Society of Safety)
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동적 신뢰성 해석 기법의 수치 안정성에 관하여

On the Numerical Stability of Dynamic Reliability Analysis Method

  • 이도근 (한경대학교 토목안전환경공학과) ;
  • 옥승용 (한경대학교 사회안전시스템공학부)
  • Lee, Do-Geun (Department of Civil, Safety and Environmental Engineering, Hankyong National University) ;
  • Ok, Seung-Yong (Department of Civil, Safety and Environmental Engineering & Construction Engineering Research Institute, Hankyong National University)
  • 투고 : 2020.03.19
  • 심사 : 2020.05.12
  • 발행 : 2020.06.30
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초록

In comparison with the existing static reliability analysis methods, the dynamic reliability analysis(DyRA) method is more suitable for estimating the failure probability of a structure subjected to earthquake excitations because it can take into account the frequency characteristics and damping capacity of the structure. However, the DyRA is known to have an issue of numerical stability due to the uncertainty in random sampling of the earthquake excitations. In order to solve this numerical stability issue in the DyRA approach, this study proposed two earthquake-scale factors. The first factor is defined as the ratio of the first earthquake excitation over the maximum value of the remaining excitations, and the second factor is defined as the condition number of the matrix consisting of the earthquake excitations. Then, we have performed parametric studies of two factors on numerical stability of the DyRA method. In illustrative example, it was clearly confirmed that the two factors can be used to verify the numerical stability of the proposed DyRA method. However, there exists a difference between the two factors. The first factor showed some overlapping region between the stable results and the unstable results so that it requires some additional reliability analysis to guarantee the stability of the DyRA method. On the contrary, the second factor clearly distinguished the stable and unstable results of the DyRA method without any overlapping region. Therefore, the second factor can be said to be better than the first factor as the criterion to determine whether or not the proposed DyRA method guarantees its numerical stability. In addition, the accuracy of the numerical analysis results of the proposed DyRA has been verified in comparison with those of the existing first-order reliability method(FORM), Monte Carlo simulation(MCS) method and subset simulation method(SSM). The comparative results confirmed that the proposed DyRA method can provide accurate and reliable estimation of the structural failure probability while maintaining the superior numerical efficiency over the existing methods.

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참고문헌

  1. A. Der Kiureghian, "The Geometry of Random Vibrations and Solutions by FORM and SORM", Probabilistic Engineering Mechanics, Vol. 15, No. 1, pp. 81-90, 2000. https://doi.org/10.1016/S0266-8920(99)00011-9
  2. H. Koo, A. Der Kiureghian and K. Fujimura, "Design-Point Excitation for Non-linear Random Vibrations", Probabilistic Engineering Mechanics, Vol. 20, No. 2, pp. 136-147, 2005. https://doi.org/10.1016/j.probengmech.2005.04.001
  3. K. Fujimura and A. Der Kiureghian, "Tail-equivalent Linearization Method for Nonlinear Random Vibration", Probabilistic Engineering Mechanics, Vol. 22, No. 1, pp. 63-76, 2007. https://doi.org/10.1016/j.probengmech.2006.08.001
  4. S. -Y. OK, "FORM-based Structure Reliability Analysis of Dynamical Active Control System", J. Korean Soc. Saf., Vol. 28, No. 1, pp. 74-80, 2013. https://doi.org/10.14346/JKOSOS.2013.28.1.074
  5. S. -M. Kim, S. -Y. Ok and J. Song, "Multi-Scale Dynamic System Reliability Analysis of Actively-Controlled Structures under Random Stationary Ground Motions", KSCE Journal of Civil Engineering, Vol. 23, No. 3, pp. 1259-1270, 2019. https://doi.org/10.1007/s12205-019-1584-y
  6. S. -M. Kim and S. -Y. OK, "Dynamic Response based Reliability Analysis of Structure with Passive Damper -Part 1: Assessment of Member Failure Probability", J. Korean Soc. Saf., Vol. 31, No. 4, pp. 90-96, 2016. https://doi.org/10.14346/JKOSOS.2016.31.4.90
  7. S. -M. Kim and S. -Y. OK, "Dynamic Response based Reliability Analysis of Structure with Passive Damper -Part 2: Assessment of System Failure Probability", J. Korean Soc. Saf., Vol. 31, No. 5, pp. 95-101, 2016. https://doi.org/10.14346/JKOSOS.2016.31.5.95
  8. J. Chun, J. Song and G. H. Paulino, "Structural Topology Optimization under Constraints on Instantaneous Failure Probability", Structural and Multidisciplinary Optimization, Vol. 53, Issue. 4, pp. 773-799, 2016. https://doi.org/10.1007/s00158-015-1296-y
  9. A. K. Chopra, "Dynamics of Structures-Theory and Applications to Earthquake Engineering", 1995.
  10. A. Der Kiureghian, "First- and Second-order Reliability Methods", Engineering Design Reliability Handbook, Edited by E. Nikolaidis, D. M. Ghiocel & S. Singhal, CRC Press, Boca Raton, FL, Chapter 14, 2005.
  11. N. Metropolis and S. Ulam, "The Monte Carlo Method", Journal of the American Statistical Association, Vol. 44, No. 247, pp. 335-341, 1949. https://doi.org/10.1080/01621459.1949.10483310
  12. A. Genz, "Numerical Computation of Multivariate Normal Probabilities", Journal of Computational and Graphical Statistics, Vol. 1, No. 2, pp. 141-149, 1992. https://doi.org/10.2307/1390838
  13. W. H. Kang and J. Song, "Evaluation of Multivariate Normal Integrals for General Systems by Sequential Compounding", Structural Safety, Vol. 32, No. 1, pp. 35-41, 2010. https://doi.org/10.1016/j.strusafe.2009.06.001
  14. J. H. Chun, J. H. Song and G. H. Paulino, "Parameter Sensitivity of System Reliability Using Sequential Compounding Method", Structural Safety, Vol. 55, pp. 26-36, 2015. https://doi.org/10.1016/j.strusafe.2015.02.001
  15. W.-S. Park and S.-Y. OK, "Reliability Analysis of Stowage System of Container Crane Using Subset Simulation with Markov Chain Monte Carlo Sampling", J. Korean Soc. Saf., Vol. 32, No. 3, pp. 54-59, 2017. https://doi.org/10.14346/JKOSOS.2017.32.3.54
  16. S. -K. An and J. L. Beck, "Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation", Probabilistic Engineering Mechanics, Vol. 16, No. 4, pp. 263-277, 2001. https://doi.org/10.1016/S0266-8920(01)00019-4
  17. A. Der Kiureghian, "A Coherency Model for Spatially Varying Ground Motions", Earthquake Engineering and Structural Dynamics, Vol. 25, No. 1, pp. 99-111, 1996. https://doi.org/10.1002/(SICI)1096-9845(199601)25:1<99::AID-EQE540>3.0.CO;2-C
  18. R. W. Clough and J. Penzien, "Dynamics of Structure", 1993.