Application of the Perturbation Method With Parameter Weighting Matrix Assignments for Estimating Variability in a Set of Nominally Identical Welded Structures

A perturbation method is employed in this paper and the problem of model updating in the presence of uncertainty due to manufacturing variability is addressed. Statistical properties of experimental data are considered and updating parameters are treated as random variables. The perturbation equations are used for estimation of means and covariances of updating parameters. The perturbation formulation is included and two approaches of parameter weighting matrix assignments are explained. Results from one of the approaches demonstrate good correlation between the predicted mean natural frequencies and their measured data, but poor correlation is obtained between the predicted and measured covariances of the outputs. In another approach, different parameter weighting matrices are assigned to the means and covariances updating equations. Results from the latter approach are in very good agreement with the experimental data and excellent correlation between the predicted and measured covariances of the outputs is achieved.