In this paper the use of the Girsanov transformaiton as a means of obtaining an importance sampling procedures for estiamting first-passage failure probabilities of some linear dynamical systems is investigated. It has already been verified that the method seems to be acurate and very efficient for certain dynamical systems, but its general applicability, within its intrinsic limitations, is still an unsettled problem. It will be demonstrated that while the importance sampling procedure works reasonably well also for hte dynamic systems studied in this paper, it may in some cases lead to a certain bias in the estimation of th failure probability. To comply with the use of the Girsanov transformation, the discussion is limited to reliability problems that can be formulated in terms of the dynamic response obtained from the solution of an Ito stochastic differnetial equation. Specifically, it is assumed that the reliability problem can be formulated as a first-passage time failure occurring when the response process exits a safe domain.
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