Abstract
Several methods for the calculation of first excursion probabilities of Gaussian processes are discussed. Two of them are based on factorial moments of the number of crossings into the failure region including a new method based on a Gram-Charlier series expansion. Numerical methods for the evaluation of factorial moments are investigated. On the basis of these methods two examples are studied. The examples show that the new method converges faster towards the exact solution than Rice’s “in- and exclusion” series. However, it is difficult to establish when bounds are obtained. Further it is shown that for engineering applications the Poisson assumption as modified by Ditlevsen such that the initial conditions are taken into account provide excellent results in almost all cases.
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© 1994 Springer-Verlag, Berlin Heidelberg
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Engelund, S., Rackwitz, R., Lange, C. (1994). Improved Bounds on First-Passage Times for Scalar Gaussian Processes. In: Spanos, P.D., Wu, YT. (eds) Probabilistic Structural Mechanics: Advances in Structural Reliability Methods. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85092-9_10
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DOI: https://doi.org/10.1007/978-3-642-85092-9_10
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