Girsanov Transformation–Based Reliability Modeling and Testing of Actively Controlled Structures

Abstract

The problem of estimation of the time-variant reliability of actively controlled structural dynamical systems under stochastic excitations is considered. Monte Carlo simulations, reinforced with Girsanov transformation–based sampling variance reduction, are used to tackle the problem. In this approach, the external excitations are biased by an additional artificial control force. The conflicting objectives of the two control forces—one designed to reduce structural responses and the other to promote limit-state violations (but to reduce sampling variance)—are noted. The control for variance reduction is fashioned after design-point oscillations based on a first-order reliability method. It is shown that for structures that are amenable to laboratory testing, the reliability can be estimated experimentally with reduced testing times by devising a procedure based on the ideas of the Girsanov transformation. Illustrative examples include studies on a building frame with a magnetorheologic damper–based isolation system subject to nonstationary random earthquake excitations.