Subset Simulation and its Application to Seismic Risk Based on Dynamic Analysis
Publication: Journal of Engineering Mechanics
Volume 129, Issue 8
Abstract
A method is presented for efficiently computing small failure probabilities encountered in seismic risk problems involving dynamic analysis. It is based on a procedure recently developed by the writers called Subset Simulation in which the central idea is that a small failure probability can be expressed as a product of larger conditional failure probabilities, thereby turning the problem of simulating a rare failure event into several problems that involve the conditional simulation of more frequent events. Markov chain Monte Carlo simulation is used to efficiently generate the conditional samples, which is otherwise a nontrivial task. The original version of Subset Simulation is improved by allowing greater flexibility for incorporating prior information about the reliability problem so as to increase the efficiency of the method. The method is an effective simulation procedure for seismic performance assessment of structures in the context of modern performance-based design. This application is illustrated by considering the failure of linear and nonlinear hysteretic structures subjected to uncertain earthquake ground motions. Failure analysis is also carried out using the Markov chain samples generated during Subset Simulation to yield information about the probable scenarios that may occur when the structure fails.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ang, G. L., Ang, A. H.-S., and Tang, W. H.(1992). “Optimal importance-sampling density estimator.” J. Eng. Mech., 118(6), 1146–1163.
Atkinson, G. M., and Silva, W.(2000). “Stochastic modeling of California ground motions.” Bull. Seismol. Soc. Am., 90(2), 255–274.
Au, S. K. (2001). “On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment.” PhD thesis in Civil Engineering, EERL Rep. No. 2001-02, California Institute of Technology, Pasadena, Calif., available at 〈http://www.ntu.edu.sg/home/cskau〉.
Au, S. K., and Beck, J. L.(1999). “A new adaptive importance sampling scheme.” Struct. Safety, 21, 135–158.
Au, S. K., and Beck, J. L.(2001a). “Estimation of small failure probabilities in high dimensions by subset simulation.” Probab. Eng. Mech., 16(4), 263–277.
Au, S. K., and Beck, J. L.(2001b). “First-excursion probabilities for linear systems by very efficient importance sampling.” Probab. Eng. Mech., 16, 193–207. Software available at 〈http://www.ntu.edu.sg/home/cskau〉.
Au, S. K., and Beck, J. L.(2002). “Importance sampling in high dimensions.” Struct. Safety, 25(2), 139–163.
Au, S. K., Papadimitriou, C., and Beck, J. L.(1999). “Reliability of uncertain dynamical systems with multiple design points.” Struct. Safety, 21, 113–133.
Beck, J. L., and Au, S. K.(2002). “Bayesian updating of structural models and reliability using Markov Chain Monte Carlo simulation.” J. Eng. Mech., 128(4), 380–391.
Boore, D. M.(1983). “Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra.” Bull. Seismol. Soc. Am., 73(6), 1865–1894.
Boore, D. M., and Joyner, W. B.(1997). “Site amplifications for generic rock sites.” Bull. Seismol. Soc. Am., 87(2), 327–341.
Brune, J. N.(1971a). “Correction.” J. Geophys. Res., 76, 5002.
Brune, J. N.(1971b). “Techonic stress and spectra of seismic shear waves from earthquakes.” J. Geophys. Res., 75, 4997–5009.
Bucher, C. G.(1988). “Adaptive sampling-An iterative fast Monte Carlo procedure.” Struct. Safety, 5, 119–126.
Cornell, C. A. (1996). “Reliability-based earthquake-resistant design: the future.” Proc., 11th World Conf. on Earthquake Engineering, International Association of Earthquake Engineering, Acapulco, Mexico.
Cox, R. T. (1961). The algebra of probable inference, Johns Hopkins, Baltimore.
Der Kiureghian, A., and Dakessian, T.(1998). “Multiple design points in first and second-order reliability.” Struct. Safety, 20, 37–49.
Engelund, S., and Rackwitz, R.(1993). “A benchmark study on importance sampling techniques in structural reliability.” Struct. Safety, 12, 255–276.
Fishman, G. S. (1996). Monte Carlo: Concepts, algorithms, and applications, Springer-Verlag, New York.
Freudenthal, A. M.(1947). “The safety of structures.” Trans. Am. Soc. Civ. Eng., 112, 125–180.
Freudenthal, A. M.(1956). “Safety and the probability of structural failure.” Trans. Am. Soc. Civ. Eng., 121, 1337–1397.
Freudenthal, A. M., Garrelts, J. M., and Shinozuka, M.(1966). “The analysis of structural safety.” J. Struct. Div., ASCE, 92(1), 267–325.
Gutenberg, B., and Richter, C.(1958). “Earthquake magnitude, intensity and acceleration.” Bull. Seismol. Soc. Am., 62(2), 105–145.
Hammersley, J. M., and Handscomb, D. C. (1964). Monte-Carlo methods, Methuen, London.
Hanks, T. C., and Kanamori, H.(1979). “A moment magnitude scale.” J. Geophys. Res. B, 84, 2348–2350.
Hanks, T. C., and McGuire, R. K.(1981). “The character of high-frequency of strong ground motion.” Bull. Seismol. Soc. Am., 71(6), 2071–2095.
Hastings, W. K.(1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, 57, 97–109.
Kanamori, H.(1977). “The energy release in great earthquakes.” J. Geophys. Res., 82, 2981–2987.
Karsan, I. D., and Jirsa, J. O.(1969). “Behavior of concrete under compressive loadings.” J. Struct. Div., ASCE, 95(12), 2543–2563.
Kent, D. C., and Park, R.(1971). “Flexural members with confined concrete.” J. Struct. Div., ASCE, 97(7), 1969–1990.
Kramer, S. L. (1996). Geotechnical earthquake engineering, Prentice-Hall, Englewood Cliffs, New Jersey.
Melchers, R. E.(1989). “Importance sampling in structural systems.” Struct. Safety, 6, 3–10.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., and Teller, A. H.(1953). “Equations of state calculations by fast computing machines.” J. Chem. Phys., 21(6), 1087–1092.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S.(1997). “Asymptotic expansions for reliabilities and moments of uncertain dynamic systems.” J. Eng. Mech., 123(12), 1219–1229.
Rubinstein, R. Y. (1981). Simulation and the Monte-Carlo method, Wiley, New York.
Schuëller, G. I., Pradlwarter, H. J., and Pandey, M. D. (1993). “Methods for reliability assessment of nonlinear systems under stochastic dynamic loading—A review.” Proc., EURODYN’93, Balkema, The Netherlands, 751–759.
Schuëller, G. I., and Stix, R.(1987). “A critical appraisal of methods to determine failure probabilities.” Struct. Safety, 4, 293–309.
Structural Engineers Association of California (SEAOC 1995). (2000). “Vision 2000: Performance based seismic engineering of buildings.” Technical Rep., Structural Engineers Association of California, Sacramento, Calif.
Silverman, B. W. (1986). Density estimators, Chapman and Hall, New York.
Wen, Y. K. (2000). “Reliability and performance based design.” Proc., 8th ASCE Specialty Conf. on Probabilitic Mechanics and Structural Reliability, ASCE, Notre Dame, Ind.
Information & Authors
Information
Published In
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Jan 7, 2002
Accepted: Nov 21, 2002
Published online: Jul 15, 2003
Published in print: Aug 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.