Browse > Article
http://dx.doi.org/10.5000/EESK.2010.14.2.001

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

Kwag, Shin-Young (서울대학교 건설환경공학부)
Ok, Seung-Yong (서울대학교 BK21 안전하고 지속가능한 사회기반건설사업단)
Koh, Hyun-Moo (서울대학교 건설환경공학부)
Publication Information
Journal of the Earthquake Engineering Society of Korea / v.14, no.2, 2010 , pp. 1-13 More about this Journal
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.
Keywords
Nonlinear seismic isolation system; Stochastic llinearization method; Multi-objective optimization technique; Genetic algorithm; Failure probability;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
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.   DOI   ScienceOn
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.   DOI   ScienceOn
4 고현무, 송준호, “사용기간비용 최소화에 의한 지진격리 교량의 경제성 평가,” 대한토목학회 논문집, 대한토목학회, 제 19권, 제 I-4호, 539-550, 1999.
5 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.
6 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.   DOI   ScienceOn
7 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.   DOI   ScienceOn
8 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.   DOI   ScienceOn
9 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.   DOI   ScienceOn
10 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.   DOI   ScienceOn
11 Nigam, N.C., Introduction to random vibration, MIT Press, Cambridge, 1983.
12 Lin, Y.K., Probabilistic theory of structural dynamics, McGraw-Hill, New York, NY, 1967.
13 Song, J., Seismic response and reliability of electrical substation equipment and systems, Ph.D. Thesis, University of California, Berkeley, 2004.
14 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.
15 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.
16 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.
17 Rice, S.O., “Mathematical analysis of random noise,” Bell System Technology Journal, Vol. 23, 282-332, 1944.   DOI
18 한국도로교통협회, 도로교 설계기준, 대한민국, 2005.
19 Srinavas, N., and Deb, K., “Multi-objective function optimization using non-dominated sorting genetic algorithms,” Evolutionary Computation, Vol. 2, No. 3, 221-248, 1994.   DOI
20 고현무, 하동호, 옥승용, 이선영, 류효선, “중약진지역 특성을 고려한 실규모 지진격리교량의 동적실험,” 대한토목학회 논문집, 대한토목학회, 제25권, 제6A호, 1043-1051, 2005.
21 양영순, 서용석, 이재옥, 구조 신뢰성 공학, 서울대학교출판부, 서울, 159-198, 1999.
22 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.   DOI   ScienceOn
23 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.   DOI   ScienceOn
24 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.   DOI   ScienceOn
25 Der Kiureghian, A., “Structural response to stationary excitation,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. 6, 1195-1213, 1980.
26 옥승용, 박관순, 송준호, 고현무, “목표신뢰성을 만족하는 구조물-감쇠기 복합시스템의 다목적 통합최적설계,” 한국지진공학회 논문집, 한국지진공학회, 제12권, 제2호, 9-22, 2008.   과학기술학회마을   DOI   ScienceOn
27 함대기, 고현무, 하동호, 송준호, “교각의 비선형 거동을 고려한 지진격리 교량의 경제성 평가,” 대한토목학회 학술발표대회 논문집, 대한토목학회, 589-592, 1999.
28 고현무, 함대기, 신정환, “교각 및 지진격리장치의 비선형성을 고려한 지진격리교량의 손상평가 및 LCC 최적설계,” 한국지진공학회 추계학술발표대회 논문집, 한국지진공학회, 344-351, 2003.   과학기술학회마을
29 Bouc, R., “Forced vibration of mechanical system with hysteresis,” Proceeding of 4th conference on Nonlinear Oscillation, Prague Czechoslovakia., 1967.
30 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.
31 Jennings, P.C., “Periodic response of a general yielding structure,” Journal of the Engineering Mechanics Division, ASCE, Vol. 90, No. 2, 131-163, 1964.
32 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.   DOI
33 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.
34 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.   DOI
35 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.
36 Hurtado, J.E., and Barbat, A.H., “Improved stochastic linearization method using mixed distributions,” Structural Safty, Vol. 18, No. 1, 49-62, 1996.   DOI   ScienceOn
37 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.   DOI   ScienceOn
38 Wen, Y.K., “Method for random vibration of hysteretic system,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. 2, 249-263, 1976.
39 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.
40 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.   DOI   ScienceOn
41 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.   DOI
42 Rice, S.O., “Mathematical analysis of random noise,” Bell System Technology Journal, Vol. 24, 46-156, 1945.   DOI
43 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.   DOI   ScienceOn
44 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.
45 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.
46 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.