Selection of modelling parameters for stochastic model updating

In structural dynamics, the adjustment of a set of modelling parameters based on the minimization of the discrepancy between experimental and model responses is known as model updating. In the context of stochastic model updating, the selection of a set of updating parameters from the modelling ones is very important, both in terms of computational efficiency and of the accuracy of the solution of this stochastic inverse problem. One can find in the literature several approaches to model updating. A simple expression was developed for covariance matrix correction in stochastic model updating and by its use one may observe the relevance of choosing the correct set of updating parameters. One may conclude that if the updating parameters are correctly chosen, then the covariance matrix of the outputs is correctly reconstructed, but when the updating parameters are wrongly chosen is found that the responses covariance matrix is generally not reconstructed accurately, although the reconstructing of the responses mean values is accurate. Hence, the selection of updating parameters is developed by assessing the contribution of each candidate parameter to the responses covariance matrix, thereby enabling the selection of updating parameters to ensure that both the responses mean values and covariance matrix are reconstructed by the updated model. It is shown that the scaled output covariance matrix may be decomposed to allow the contributions of each candidate parameter to be assessed. Numerical examples are given to illustrate this theory.