Multi-scale Dynamic System Reliability Analysis of Actively-controlled Structures under Random Stationary Ground Motions
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This paper proposes a multi-scale dynamic system reliability analysis approach to assess the failure probability of an actively-controlled structure subject to random stationary ground motions. The proposed approach employs a multi-scale hierarchical framework where a lower-scale system reliability analyses compute the failure probabilities of the structural members during the earthquakes and a higher-scale system reliability analysis computes the failure probability of the structural system based on results of the lower-scale analyses. The multi-scale framework facilitates the system reliability analysis of the large-sized complex system by decomposing the complex system into the manageable-sized subsystems. It also enables us to deal with statistical dependence both in spatial and temporal senses through the decomposition of the reliability analysis in space and time aspects. In these regards, the proposed approach performs a reliability analysis with the dynamic responses in time domain. This dynamic reliability analysis approach can consider uncertainties in system parameters and earthquake excitations simultaneously. In addition, the peak response over a time duration is used to describe the limit state of the structural system, which provides a more realistic measure of the failure probability of a structural system than instantaneous probability. In order to demonstrate the proposed approach, a 3-story shear-type building equipped with an optimal active control device is considered. The control performance under uncertainties is investigated through the reliability assessment by the proposed approach and the Monte Carlo Simulation (MCS) approach, respectively. The numerical study also investigates the influence of the uncertainties in the system parameters and the earthquake excitations on the system failure probability. The results of the numerical examples demonstrate that the proposed approach can efficiently estimate the system reliability and the failure probability of an actively-controlled structure.
Keywordsdynamic reliability system reliability analysis multi-scale approach active control system uncertainty probabilistic performance assessment
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- Burl, J. B. (1998). Linear optimal control: H 2 and H ∞ methods, Addison-Wesley Longman, Inc.Google Scholar
- Der Kiureghian, A. (2005). “First- and second-order reliability methods.” Engineering Design Reliability Handbook, E. Nikoaidis, D. M. Ghuicel, and S. Singhal, Eds., Chapter 14, CRC Press, Boca Raton, FL, USA.Google Scholar
- Ditlevsen, O. D. and Madsen, H. O. (1996). Structural reliability methods, Wiley, New York, NY, USA.Google Scholar
- Genz, A. (1992). “Numerical computation of multivariate normal probabilities.” Journal of Computational and Graphical Statistics, Vol. 1, No. 2, pp. 141–149, DOI: 10.1080/10618600.1992.10477010.Google Scholar
- Housner, G. W., Bergman, L. A., Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri, S. F., Skelton, R. E., Soong, T. T., Spencer, B. F. Jr., and Yao, J. T. P. (1997). “Structural control: Past, present, and future.” Journal of Engineering Mechanics, Vol. 123, No. 9, pp. 897–971, DOI: 10.1061/(ASCE)0733-9399(1997)123:9(897).CrossRefGoogle Scholar
- Kanai, K. (1957). “Semi-empirical formula for the seismic characteristics of the ground.” Bulletin of the Earthquake Research Institute, Vol. 35, No. 2, pp. 309–325.Google Scholar
- Song, J. and Ok, S. Y. (2010). “Multi-scale system reliability analysis of lifeline networks under earthquake hazards.” Earthquake Engineering and Structural Dynamics, Vol. 39, No. 3, pp. 259–279, DOI: 10.1002/eqe.938.Google Scholar
- Spencer, B. F. Jr, and Sain, M. K. (1997). “Controlling buildings: A new frontier in feedback.” IEEE Control Systems Magazine on Emerging Technology, Vol. 17, No. 6, pp. 19–35, DOI: 10.1109/37.642972.Google Scholar
- Tajimi, H. (1960). “A statistical method of determining the maximum response of a building structure during an earthquake.” Proceeding of 2nd world conference on Earthquake Engineering, pp. 781–897.Google Scholar