Parameter selection and stochastic model updating using perturbation methods with parameter weighting matrix assignment

Parameterisation in stochastic problems is a major issue in real applications. In addition, complexity of test structures (for example, those assembled through laser spot welds) is another challenge. The objective of this paper is two-fold: (1) stochastic uncertainty in two sets of different structures (i.e., simple flat plates, and more complicated formed structures) is investigated to observe how updating can be adequately performed using the perturbation method, and (2) stochastic uncertainty in a set of welded structures is studied by using two parameter weighting matrix approaches. Different combinations of parameters are explored in the first part; it is found that geometrical features alone cannot converge the predicted outputs to the measured counterparts, hence material properties must be included in the updating process. In the second part, statistical properties of experimental data are considered and updating parameters are treated as random variables. Two weighting approaches are compared; results from one of the approaches are in very good agreement with the experimental data and excellent correlation between the predicted and measured covariances of the outputs is achieved. It is concluded that proper selection of parameters in solving stochastic updating problems is crucial. Furthermore, appropriate weighting must be used in order to obtain excellent convergence between the predicted mean natural frequencies and their measured data.

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