Importance sampling for randomly excited dynamical systems |
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Authors: | M Macke C Bucher |
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Institution: | Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99421 Weimar, Germany |
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Abstract: | An importance sampling technique for linear and non-linear dynamical systems subjected to random excitations is presented. Applying a transformation of probability measures, controls are introduced in the system of Itô stochastic differential equations such that the sample trajectories can be influenced in a predetermined way. As is shown, there exist controls resulting in unbiased zero-variance estimators. However, these optimal controls are in general not accessible and have to be replaced by sub-optimal ones derived from an optimization procedure analogous to the first order reliability method known from time-invariant problems. The efficiency of the proposed Monte Carlo simulation technique is demonstrated by estimating first-passage probabilities of typical oscillators under external white-noise excitation. |
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