Mechanical and Civil Engineering Seminar

Bayesian inference is used in engineering science for quantifying and propagating uncertainties in system simulations making use of experimental data from system or component tests. The Bayesian tools are mainly Laplace methods of asymptotic approximation and stochastic simulation algorithms, requiring a moderate to very large number of system re-analyses to be performed over the space of uncertain parameters. Computational demands may become excessive, depending on the model complexity, the time required to perform a simulation, and the number of model runs.

This lecture will cover selected theoretical and computational developments of a Bayesian Uncertainty Quantification (UQ) framework for structural dynamics. Available formulations for developing the likelihood assume that the prediction errors between model predictions and measurements are spatially and temporally uncorrelated. The importance of the correlation structure and correlation length of the prediction errors will first be addressed. Then computationally efficient techniques will be presented to handle, within the Bayesian UQ framework, large-order finite element models of hundreds of thousands or millions degrees of freedom, and localized nonlinear actions activated during system operation. Such techniques include (a) parameterization-consistent component mode synthesis methods to drastically reduce the model size, (b) surrogate models to substantially speed up computations, avoiding full system re-analyses, and (c) parallel versions of asymptotic approximations and Markov Chain Monte Carlo algorithms to efficiently distribute the computations in available multi-core CPUs. Applications will be mainly focused on finite element model updating, structural health monitoring and updating reliability of civil infrastructure using vibration measurements.