Updating of a Model and its Uncertainties Utilizing Dynamic Test Data

Abstract

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. Using a Bayesian probabilistic formulation, 6the updated "posterior" probability distribution of the uncertain parameters is obtained and it is found that for a large number of data points it is very peaked at some "optimal" values of the parameters. These optimal parameters can be obtained by minimizing a positive-definite measure-of-fit function. This paper focuses on the identifiability of the optimal parameters. The problem of finding the whole set of optimal models that have the same output at the observed degrees of freedom for a given input is resolved for the first time, by presenting an algorithm which methodically and efficiently searches the parameter space. Also, a simplified expression is given for the weighting coefficients associated with each optimal model which are involved in the probability distribution for the predicted response.