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

journal contribution
posted on 2023-06-07, 22:48 authored by Julian DunneJulian Dunne, M Ghanbari
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 measurements to calibrate a discretedynamic model using a Markov moment method appropriately matched toextreme value prediction via finite element solution of theFokker¿Planck (FPK) equation. The dynamic model is obtained via theWoinowsky¿Krieger equation with added empirical damping. Stationary FPKsolutions are used to obtain mean crossing rates, and for the purpose ofextreme value prediction, crossings are assumed to be independent. Thesecond approach uses a Weissman type I asymptotic estimator, justifiedby use of the Hasofer¿Wang hypothesis test. Both methods are comparedwith exceedance probabilities obtained using data from long experiments in which dependence between extreme values is excluded. Thepaper shows that by exploiting the Weissman estimator in a forwardpredictive mode, very accurate exceedance probabilities can be obtainedfrom relatively small amounts of measured data. The calibrated modelbased predictions are consistently in error as a result of non-linearcoupling effects not included in the model ¿ this coupling isimplicitly accounted for in the Weissman predictions.


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  • Published


Nonlinear Dynamics







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  • Engineering and Design Publications


This invited paper uses asymptotic extreme value theory for structural reliability assessment. The method is useful for integrity analysis of aerospace structures and vibro-acoustic analysis of vehicle structures. Since 2003, the method has been under further development within CDH-AG (a German-based CAE supplier to the automotive industry such as Audi, Toyota, and Nissan) and is being incorporated into CDHs Vibro-Acoustic Optimisation package. The method gives a 100-fold speed improvement on simulations which take 250 CPU hours on HP Itanium, IBM Power 5, and NEC Itanium servers. Contact: Dr. L. Huang, Special Applications Department, CDH AG. Email:

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