Application Of Bayesian Belief Nets For Modeling Uncertainty In Structural Dynamics

The quality of modeling and performance prediction for any structural system is affected and limited by an inherent presence of various sources of uncertainty. To date, uncertainty has been usually quantified by means of uncertainty propagation techniques (e.g. Monte Carlo simulations), where a statistical realization of the system's input parameters is propagated through a (usually) numerical model to construct the statistics of the system's outputs. This approach works well for sensitivity studies, but some limitations arise when data is available at the output level (as in the case of experiments) or at some intermediate stage within the analysis. The primary objective of this paper is to investigate the feasibility of using Bayesian Belief Networks (BBN) to model multi-directional uncertainty propagation in a process where experimental data can be introduced as evidence. The problem under consideration has the objective of estimating the modal parameters of a structural system with uncertain parameters. The estimation is based on a model of the system, but it is assumed that a limited set of experimental data may be available on input or output parameters. The procedure is first applied to the simple case of a beam structure, for which a number of natural frequencies are evaluated in the presence of uncertainty. Next, it is extended to the estimation of modal quantities of a turbine engine bladed disk sector, which provides the motivation for these investigations.