Journal of the Earthquake Engineering Society of Korea (한국지진공학회논문집)

Earthquake Engineering Society of Korea (한국지진공학회)
권호 표지
DOI QR코드

DOI QR Code

Optimal design of nonlinear seismic isolation system by a multi-objective optimization technique integrated with a stochastic linearization method

추계학적 선형화 기법을 접목한 다목적 최적화기법에 의한 비선형 지진격리시스템의 최적설계

  • 곽신영 (서울대학교 건설환경공학부) ;
  • 옥승용 (서울대학교 BK21 안전하고 지속가능한 사회기반건설사업단) ;
  • 고현무 (서울대학교 건설환경공학부)
  • Published : 2010.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper proposes an optimal design method for the nonlinear seismic isolated bridge. The probabilities of failure at the pier and the seismic isolator are considered as objective functions for optimal design, and a multi-objective optimization technique is employed to efficiently explore a set of multiple solutions optimizing mutually-conflicting objective functions at the same time. In addition, a stochastic linearization method is incorporated into the multi-objective optimization framework in order to effectively estimate the stochastic responses of the bridge without performing numerous nonlinear time history analyses during the optimization process. As a numerical example to demonstrate the efficiency of the proposed method, the Nam-Han river bridge is taken into account, and the proposed method and the existing life-cycle-cost based design method are both applied for the purpose of comparing their seismic performances. The comparative results demonstrate that the proposed method not only shows better seismic performance but also is more economical than the existing cost-based design method. The proposed method is also proven to guarantee improved performance under variations in seismic intensity, in bandwidth and in the predominant frequency of the seismic event.

본 논문에서는 비선형 지진격리교량의 최적 설계 방법을 제시하였다. 최적설계를 위한 목적함수로는 교각과 지진격리장치의 파괴확률을 고려하였으며, 상충하는 두 목적함수를 동시에 최적화하는 다수의 해를 효율적으로 검색하고자 유전자 알고리즘에 기반한 다목적 최적화기법을 도입하였다. 또한, 최적화 과정에서 요구되는 다수의 비선형 시간이력해석을 수행하지 않고도 교량의 확률적 응답을 효율적으로 예측할 수 있는 추계학적 선형화 방법을 접목하였다. 제시하는 방법의 효율성을 검증하기 위한 수치 예로서 실제 교량인 남한강교를 고려하였고, 제안하는 방법과 기존 비선형 시간이력해석을 이용한 생애주기비용 기반 설계법을 각각 적용하여 내진성능을 비교하였다. 내진성능을 비교한 결과, 제시하는 방법이 기존의 비용에 기반한 최적설계보다 우수한 성능 및 경제성을 보임을 검증하였다. 또한, 다양한 지진하중에 대해서도 제안된 방법이 보다 개선된 성능을 보임을 확인하였다.

Keywords

References

  1. Kunde, M.C., and Jangid, R.S., “Seismic behavior of isolated bridges: A-state-of-the-art review,” Electronic Journal of Structural Engineering, Vol. 3, No. 3, 140-170, 2003.
  2. Marano, G.C., and Sgobba, S., “Stochastic energy analysis of seismic isolated bridges,” Soil Dynamics and Earthquake Engineering, Vol. 27, No. 8, 759-773, 2007. https://doi.org/10.1016/j.soildyn.2006.12.001
  3. Jangid, R.S., “Equivalent linear stochastic seismic response of isolated bridges,” Journal of Sound and Vibration, Vol. 309, No. 3-5, 805-822, 2007. https://doi.org/10.1016/j.jsv.2007.07.071
  4. 고현무, 송준호, “사용기간비용 최소화에 의한 지진격리 교량의 경제성 평가,” 대한토목학회 논문집, 대한토목학회, 제 19권, 제 I-4호, 539-550, 1999.
  5. 함대기, 고현무, 하동호, 송준호, “교각의 비선형 거동을 고려한 지진격리 교량의 경제성 평가,” 대한토목학회 학술발표대회 논문집, 대한토목학회, 589-592, 1999.
  6. 고현무, 함대기, 신정환, “교각 및 지진격리장치의 비선형성을 고려한 지진격리교량의 손상평가 및 LCC 최적설계,” 한국지진공학회 추계학술발표대회 논문집, 한국지진공학회, 344-351, 2003.
  7. Ok, S.-Y., Song, J., and Park, K.-S., “Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method,” Engineering Structures, Vol. 30, No. 5, 1240-1249, 2008. https://doi.org/10.1016/j.engstruct.2007.07.019
  8. Bouc, R., “Forced vibration of mechanical system with hysteresis,” Proceeding of 4th conference on Nonlinear Oscillation, Prague Czechoslovakia., 1967.
  9. Wen, Y.K., “Method for random vibration of hysteretic system,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. 2, 249-263, 1976.
  10. Kanai, K., “Semi-empirical formula for the seismic characteristics of the ground,” Bulletin of the Earthquake Research Institute, University of Tokyo, Vol. 35, No. 2, 309-325, 1957.
  11. Tajimi, H., “A statistical method of determining the maximum response of a building structure during an earthquake,” Proceeding of 2nd world conference on Earthquake Engineering, Tokyo, Japan, Vol. 2, 781-897, 1960.
  12. Jennings, P.C., “Periodic response of a general yielding structure,” Journal of the Engineering Mechanics Division, ASCE, Vol. 90, No. 2, 131-163, 1964.
  13. Iwan, W.D., “A distributed-element model for hysteresis and its steady-state dynamic response,” Journal of Applied Mechanics, Transactions of the ASME, Vol. 33, No. 4, 893-900, 1966. https://doi.org/10.1115/1.3625199
  14. Kaul, M.K., and Penzien, J., “Stochastic analysis of yielding offshore towers,” Journal of the Engineering Mechanics Division, ASCE, Vol. 100, No. 5, 1025-1038, 1974.
  15. Bazant, Z.P., Krizek, R.J., and Shieh, C.L., “Hysteretic endochronic theory for sand,” Journal of the Engineering Mechanics Division, ASCE, Vol. 109, No. 4, 1073-1095, 1983. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:4(1073)
  16. Casciati, F., “Nonlinear stochastic dynamics of large structural systems by equivalent linearization,” Proceeding of 5th International Conference on Application of Statics and Probability in Soil and Structure Engineering, ICASP5, Vancouver, B.C., Canada, 1987.
  17. Thyagarajan, R.S., and Iwan, W.D., “Performance characteristics of a widely used hysteretic model in structural dynamics,” Proceeding of 4th U.S. National Conference on Earthquake Engineering, Palm Springs, California, 1990.
  18. Wen Y.K., and Eliopoulos, D., “Method for nonstationary random vibration of inelastic structures,” Probabilistic Engineering Mechanics, Vol. 9, No. 1-2, 115-123, 1994. https://doi.org/10.1016/0266-8920(94)90035-3
  19. Sasani, M., and Popov, E.P., “Seismic energy dissipators for RC panels: analytical studies,” Journal of Engineering Mechanics, ASCE, Vol. 127, No. 8, 835-843, 2001. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:8(835)
  20. Constantinou, M.C., and Tadjbakhsh, I.G., “Hysteretic dampers in base isolation: random approach,” Journal of Structural Engineering, ASCE, Vol. 111, No. 4, 705-721, 1985. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(705)
  21. Yang, J.N., Li, Z., and Vongchavalitkul, S., “Stochastic hybrid control of hysteretic structures,” Probabilistic Engineering Mechanics, Vol 9, No. 1-2, 125-133, 1994. https://doi.org/10.1016/0266-8920(94)90036-1
  22. Hurtado, J.E., and Barbat, A.H., “Improved stochastic linearization method using mixed distributions,” Structural Safty, Vol. 18, No. 1, 49-62, 1996. https://doi.org/10.1016/0167-4730(96)00017-3
  23. Song, J., and Der Kiureghian, A., “Generalized Bouc-Wen model for highly asymmetric hysteresis,” Journal of Engineering Mechanics, Vol. 132, No. 6, 610-618, 2006. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:6(610)
  24. Barber, T.T., and Wen, Y.K., “Random vibration of hysteretic, degrading systems,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. 6, 1069-1087, 1981.
  25. Wen, Y.K., “Equivalent linearization for hysteretic systems under random excitation,” Journal of Applied Mechanics, Transactions of the ASME, Vol. 47, No. 1, 150-154, 1980. https://doi.org/10.1115/1.3153594
  26. Skinner, R.I., Tyler, R.G., Heine, A.J., and Robinson, W.H., “Hysteretic dampers for the protection of structures from Earthquakes,” Bulletin of New Zealand National Society for Earthquake Engineering, Vol. 13, No. 1, 21-33, 1981.
  27. Wong. C.W., Ni, Q.Y., and Lau, S.L., "Steady-state oscillation of hysteretic differential model. I: response analysis," Journal of Engineering Mechanics, ASCE, Vol. 120, No. 11, 2271-2298, 1994. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:11(2271)
  28. Atalik, T.S., and Utku, S., “Stochastic linearization of multidegree-of-freedom nonlinear systems,” Earthquake Engineering and Structural Dynamics, Vol. 4, No. 3, 411-420. 1976. https://doi.org/10.1002/eqe.4290040408
  29. Nigam, N.C., Introduction to random vibration, MIT Press, Cambridge, 1983.
  30. Lin, Y.K., Probabilistic theory of structural dynamics, McGraw-Hill, New York, NY, 1967.
  31. Song, J., Seismic response and reliability of electrical substation equipment and systems, Ph.D. Thesis, University of California, Berkeley, 2004.
  32. 양영순, 서용석, 이재옥, 구조 신뢰성 공학, 서울대학교출판부, 서울, 159-198, 1999.
  33. Marano, G.C., Greco, R., Trentadue, F., and Chiaia, B., “Constrained reliability-based optimization of linear tuned mass dampers for seismic control,” International Journal of Solids and Structures, Vol. 44, No. 22-23, 7370-7388, 2007. https://doi.org/10.1016/j.ijsolstr.2007.04.012
  34. Vanmarcke, E.H., “Properties of spectral moments with application to random vibration,” Journal of the Engineering Mechanics Division, ASCE, Vol. 98, No. 2, 425-446, 1972.
  35. Vanmarcke, E.H., “On the distribution of the first passage time for normal stationary random process,” Journal of Applied Mechanics, ASME, Vol. 43, 215-220, 1975.
  36. Rice, S.O., “Mathematical analysis of random noise,” Bell System Technology Journal, Vol. 23, 282-332, 1944. https://doi.org/10.1002/j.1538-7305.1944.tb00874.x
  37. Rice, S.O., “Mathematical analysis of random noise,” Bell System Technology Journal, Vol. 24, 46-156, 1945. https://doi.org/10.1002/j.1538-7305.1945.tb00453.x
  38. Song, J., and Der Kiureghian, A., “Joint first-passage probability and reliability of systems under stochastic excitation,” Journal of Engineering Mechanics, Vol. 132, No. 1, 65-77, 2006. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:1(65)
  39. Fonseca, C.M., and Fleming, P.J., “Genetic algorithms for multi-objective optimization: formulation, discussion and generalization,” Proceedings of 5th International conference on Genetic Algorithms, Morgan Kauffman, San Mateo, California, 416-423, 1993.
  40. Horn, J., Nafploitis, N., and Goldberg, D.E., “A niched Pareto genetic algorithm for multi-objective optimization,” Proceedings of 1st IEEE Conference on Evolutionary Computation, IEEE Service Center, Piscataway, New Jersey, 82-87, 1994.
  41. Srinavas, N., and Deb, K., “Multi-objective function optimization using non-dominated sorting genetic algorithms,” Evolutionary Computation, Vol. 2, No. 3, 221-248, 1994. https://doi.org/10.1162/evco.1994.2.3.221
  42. 고현무, 하동호, 옥승용, 이선영, 류효선, “중약진지역 특성을 고려한 실규모 지진격리교량의 동적실험,” 대한토목학회 논문집, 대한토목학회, 제25권, 제6A호, 1043-1051, 2005.
  43. 한국도로교통협회, 도로교 설계기준, 대한민국, 2005.
  44. Ok, S.-Y., Song, J., and Park, K.-S., “Development of optimal design formula for bi-tuned mass dampers using multiobjective optimization,” Journal of Sound and Vibration, Vol. 322, No. 1-2, 60-77, 2009. https://doi.org/10.1016/j.jsv.2008.11.023
  45. Der Kiureghian, A., “Structural response to stationary excitation,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. 6, 1195-1213, 1980.
  46. 옥승용, 박관순, 송준호, 고현무, “목표신뢰성을 만족하는 구조물-감쇠기 복합시스템의 다목적 통합최적설계,” 한국지진공학회 논문집, 한국지진공학회, 제12권, 제2호, 9-22, 2008. https://doi.org/10.5000/EESK.2008.12.2.009