4. Bayesian Uncertainty Quantification and Propagation in Nonlinear Structural Dynamics

A Bayesian uncertainty quantification and propagation (UQ&P) framework is presented for identifying nonlinear models of dynamic systems using vibration measurements of their components. The measurements are taken to be either response time histories or frequency response functions of linear and nonlinear components of the system. For such nonlinear models, stochastic simulation algorithms are suitable Bayesian tools to be used for identifying system and uncertainty models as well as perform robust prediction analyses. The UQ&P framework is applied to a small scale experimental model of a vehicle with nonlinear wheel and suspension components. Uncertainty models of the nonlinear wheel and suspension components are identified using the experimentally obtained response spectra for each of the components tested separately. These uncertainties, integrated with uncertainties in the body of the experimental vehicle, are propagated to estimate the uncertainties of output quantities of interest for the combined wheel-suspension-frame system. The computational challenges are outlined and the effectiveness of the Bayesian UQ&P framework on the specific example structure is demonstrated.