Abstract
An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that constants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.
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References
He J. New development of research on first passage problems [J]. Journal of Earthquake Engineering and Engineering Vibration, 2006, 26(5): 55–60 (in Chinese).
Johnson N L, Kotz S. Continuous univariate distribution-1 [M]. Boston: Houghton Mifflin Company; 1970.
Zhao Y G, Ono T. Third-moment standardization for structural reliability analysis [J]. Journal of Structural Engineering, 2000, 126(6): 724–732.
Winterstein S R. Nonlinear vibration models for extremes and fatigue [J]. Journal of Engineering Mechanics, 1988, 114(10): 1772–1790.
He J. Monte Carlo simulation of first passage time of structures excited by non-Gaussian loads [J]. Journal of Vibration and Shock, 2007, 26(3): 59–61 (in Chinese).
Langley R S. A first passage approximation for normal stationary random processes [J]. Journal of Sound and Vibration, 1988, 122(2): 261–275.
He J, Zhao Y G. First passage times of stationary non-Gaussian structural responses [J]. Journal of Computers and Structures, 2007, 85(7–8): 431–436.
Zhou D, Ma J, Zhu Z Y. Wind vibration study of long-span steel arch structure of Beijin Capital International Airport [J]. Journal of Shanghai Jiaotong University (Science), 2005, 10(4): 429–435.
Naess A. The response statistics of non-linear, secondorder transformations to Gaussian loads [J]. Journal of Sound and Vibration, 1987, 115(1): 103–129.
Schuëller G I, Shinozuka M. Stochastic Methods in Structural Dynamics [M]. Dordrecht: Martinus Nijhoff Publishers; 1987.
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Foundation item: the National Natural Science Foundation of China (No. 50478017)
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He, J., Zhou, YJ. & Kou, XJ. First passage probability of structures under non-Gaussian stochastic behavior. J. Shanghai Jiaotong Univ. (Sci.) 13, 400–403 (2008). https://doi.org/10.1007/s12204-008-0400-5
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DOI: https://doi.org/10.1007/s12204-008-0400-5