A variance reduction technique for Monte Carlo simulation of randomly exicted non-linear dynamic systems is presented. Modeling the structural response by a system of Ito stochastic differnetial equations, the drift term is changed according to a minimization criterion for the variance ofthe estimator of the system response by applying the measurement transformaiton method (Girsanov transformation). Solving the coresponding Bellman equation, it can be shown that--at least theoretically--unbiased zero-variance estiamtors of functionals of the system response can be constructed. Applying approximate solution techniques as e.g. equivalent linearization or cumulant-neglect closure, sub-optimal estimators can be established. The efficiency of the mehtod is demonstrated by calcualting the trasient response characteristics of oscillators under external white noise excitation with conservative hardening and hysteretic softening restoring forces.
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