Efficient Extreme Value Prediction for Nonlinear Beam Vibrations using Measured Random Response Histories

摘要: Predicted extreme exceedance probabilities associated withexperimental measurements of highly non-linear clamped-clamped beamvibrations driven by band-limited white-noise, are compared using twodifferent approaches for application to short data sets. The firstapproach uses response history calibrate a discretedynamic model Markov moment method appropriately matched toextreme value prediction via finite element solution theFokker?Planck (FPK) equation. dynamic is obtained theWoinowsky?Krieger equation with added empirical damping. Stationary FPKsolutions used obtain mean crossing rates, and the purpose ofextreme prediction, crossings assumed be independent. Thesecond approach Weissman type I asymptotic estimator, justifiedby use Hasofer?Wang hypothesis test. Both methods comparedwith from long experiments in which dependence between values excluded. Thepaper shows that exploiting estimator forwardpredictive mode, very accurate can obtainedfrom relatively small amounts measured data. calibrated modelbased predictions consistently error as result non-linearcoupling effects not included ? this coupling isimplicitly accounted predictions.