Stochastic model updating in structural dynamics

Although finite element modelling has become very sophisticated, there are still features of structures, such as joints, that are difficult to model. Measurements of a physical structure often show poor correlation to the model, and uncertain parameters in the model may be estimated from the experimental data. This is model updating. Model updating using measurements on a single structure are well developed, and the two critical issues are deciding how a finite element model should be parameterized and estimating the unknown parameters from the resulting ill-conditioned equations. A lack of understanding of these issues will lead to updated models without physical meaning. This paper considers methods to quantify parametric uncertainty in finite element models using measured data from multiple, nominally identical, structures. The variability in seemingly identical test structures may arise from many sources including geometric tolerances and the manufacturing process. The probability density distributions (for example, Gaussian) of the uncertain parameters are selected, and parameters specified to represent these distributions (for example mean and covariance). The uncertain parameter distributions are propagated through the finite element model using Monte-Carlo analysis to provide multiple sets of predicted results. The resulting output statistics may be used to produce the objective function that is minimized in the model updating procedure. For example, the maximum likelihood method gives the parameter distribution most likely to give the measured outputs. The approach is demonstrated on a simple example.