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Fast Dynamic Reliability Estimation Approach of Seismically Excited SDOF Structure

지진하중을 받는 단자유도 구조물의 신속한 동적 신뢰성 추정 방법

  • Lee, Do-Geun (Department of Civil, Safety and Environmental Engineering, Hankyong National University) ;
  • Ok, Seung-Yong (School of Social Safety System Engineering & Construction Engineering Research Institute, Hankyong National University)
  • 이도근 (한경대학교 토목안전환경공학과) ;
  • 옥승용 (한경대학교 사회안전시스템공학부)
  • Received : 2020.08.21
  • Accepted : 2020.09.25
  • Published : 2020.10.31

Abstract

This study proposes a fast estimation method of dynamic reliability indices or failure probability for SDOF structure subjected to earthquake excitations. The proposed estimation method attempts to derive coefficient function for correcting dynamic effects from static reliability analysis in order to estimate the dynamic reliability analysis results. For this purpose, a total of 60 cases of structures with various characteristics of natural frequency and damping ratio under various allowable limits were taken into account, and various types of approximation coefficient functions were considered as potential candidate models for dynamic effect correction. Each reliability index was computed by directly performing static and dynamic reliability analyses for the given 60 cases, and nonlinear curve fittings for potential candidate models were performed from the computed reliability index data. Then, the optimal estimation model was determined by evaluating the accuracy of the dynamic reliability analysis results estimated from each candidate model. Additional static and dynamic reliability analyses were performed for new models with different characteristics of natural frequency, damping ratio and allowable limit. From these results, the accuracy and numerical efficiency of the optimal estimation model were compared with the dynamic reliability analysis results. As a result, it was confirmed that the proposed model can be a very efficient tool of the dynamic reliability estimation for seismically excited SDOF structure since it can provide very fast and accurate reliability analysis results.

Keywords

References

  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", Journal of Korean Society of Safety, 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", Journal of Korean Society of Safety, Vol. 31, No. 5, pp. 95-101, 2016. https://doi.org/10.14346/JKOSOS.2016.31.5.95
  8. D. -G. Lee and S. -Y. Ok, "On the Numerical Stability of Dynamic Reliability Analysis Method", J. Korean Soc. Saf., Vol. 35, No. 3, pp. 49-57, 2020. https://doi.org/10.14346/JKOSOS.2020.35.3.49
  9. 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.
  10. K. Kanai, "Semi-empirical Formula for the Seismic Characterisrics of the Ground", Bulletin of the Earthquake Researche Instutute, University of Tokyo, Vol. 35, No. 2, pp. 309-325, 1957.
  11. H. Tajimi, "A Statistical Method of Determining the Maximim Response of a Building Structure during an Earthquake", Proceeding of 2nd world Conference on Earthquake Engineering, Tokyo, Japan, Vol. 2, pp. 781-897, 1960.
  12. J. Chun, J. Song and G. H. Paulino, "Structural Topology Optimization under Constraints on Instantaneous Failure Probability", Structural and Multidisciplinary Optimization, Vol. 53, No. 4, pp. 773-799, 2016. https://doi.org/10.1007/s00158-015-1296-y
  13. A. K. Chopra, "Dynamics of structure - Theory and Applications to Earthquake Engineering", 3rd ed., Pearson Prentice Hall, 2007.
  14. D. -G. Lee, "A Study on Dynamic Effect Correction of Static Reliability Analysis", Master Thesis, Hankyong National University.
  15. MOLIT, Korean Design Standard, KDS 17 00 00 : 2018, http://www.kcsc.re.kr.
  16. N. Satake, K. Suda, T. Arakawa, A. Sasaki and Y. Tamura, "Damping Evaluation Using Full-Scale Data of Buildings in Japan", Journal of Structural Engineering, ASCE, Vol. 129, No. 4, pp. 470-477, 2003. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:4(470)
  17. A. V. Papageorgiou and C. J. Gantes, "Equivalent Modal Damping Ratios for Concrete/Steel Mixed Structures", Computers and Structures, Vol. 88, pp. 1124-1136, 2010. https://doi.org/10.1016/j.compstruc.2010.06.014
  18. T. F. Coleman and Y. Li, "An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds", SIAM Journal on Optimization, Vol. 6, pp. 418-445, 1996. https://doi.org/10.1137/0806023
  19. T. F. Coleman and Y. Li, "On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds", Mathematical Programming, Vol. 67, N0. 2, pp. 189-224, 1994. https://doi.org/10.1007/BF01582221