Outcrossings from Convex Polyhedrons for Nonstationary Gaussian Processes
Publication: Journal of Engineering Mechanics
Volume 119, Issue 11
Abstract
This technical note concerns the estimation of the outcrossing rate of nonstationary Gaussian vector processes from a convex polyhedral limit-state surface enclosing the origin. The theoretically most attractive approach for this type of problem in time-dependent structural reliability analysis is to employ the concept of first-passage probability in stochastic-process theory. Because the use of the generalized Rice formula poses some difficulty, the outcrossing problem is formulated in another way; i.e., using the original Rice formula directly. This situation allows the multidimensional integral to be reduced to a one-dimensional integral. This then allows the formulation (which applies also to smooth nonstationary processes) to be extended to time-dependent domain boundaries. An example is given to illustrate the method.
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References
1.
Ditlevsen, O. (1981). Uncertainty modeling. McGraw‐Hill Book Co., Inc., New York, N.Y.
2.
Ditlevsen, O. (1983). “Gaussian outcrossings from safe convex polyhedrons.” J. Engrg. Mech., ASCE, 109(1), 127–148.
3.
Ditlevsen, O., and Bjerager, P. (1986). “Methods of structural systems reliability.” Struct. Safety, 3(3 + 4), 195–229.
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Melchers, R. E. (1987). Structural reliability analysis and prediction. John Wiley and Sons, New York, N.Y.
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Melchers, R. E. (1992). “Load space formulation for time‐dependent structural reliability.” J. Engrg. Mech., ASCE, 118(5), 853–870.
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Copyright © 1993 American Society of Civil Engineers.
History
Received: Mar 11, 1992
Published online: Nov 1, 1993
Published in print: Nov 1993
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