A structural dynamic reliability updating method and analysis based on Bayesian theorem

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (12) : 29-34.

LIU Pei1,2

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Abstract

An approach based on Bayesian theorem and structural vibration test data is presented for reliability updating. The approach takes account of uncertainties of the excitation, structural model and its parameters. Structural model parameters are identified based on the vibration test data and Bayesian parameter identification method. According to Laplace asymptotic approximation, dynamic reliability obtained by design conditions is updated. Reliabilities of a truss structure subjected to dynamic random loading are calculated for three cases. Only the uncertainty of the loading is considered for the first case. The uncertainties of the loading and the prior probability distribution of model parameters are considered for the second case. The uncertainties of the loading and the updated probability distribution of model parameters are considered for the third case. Natural frequencies and mode shapes of the actual structure and the updated model are compared. Discussions about the updated reliabilities are made. Results show that the updated failure probability of the tested DOF agrees well with the actual value compared with the deterministic nominal models. The updated failure probability of untested DOFs may deviate from the actual values. Increasing tested DOFs may have no effect on the updated failure probability.

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Bayesian theorem / dynamic reliability / parameter identification / failure probability / updated probability distribution

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LIU Pei1,2. A structural dynamic reliability updating method and analysis based on Bayesian theorem[J]. Journal of Vibration and Shock, 2015, 34(12): 29-34

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