Journal of the Korean Society of Safety (한국안전학회지)

The Korean Society of Safety (한국안전학회)
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On the Numerical Stability of Dynamic Reliability Analysis Method

동적 신뢰성 해석 기법의 수치 안정성에 관하여

  • 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)
  • 이도근 (한경대학교 토목안전환경공학과) ;
  • 옥승용 (한경대학교 사회안전시스템공학부)
  • Received : 2020.03.19
  • Accepted : 2020.05.12
  • Published : 2020.06.30
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Abstract

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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References

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