Bayesian modal updating using ambient data

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian probabilistic approach is followed to obtain not only the most probable (optimal) values but also the probability distribution of the updated modal parameters. This is very important when one plans to use these estimates for further processing, such as for updating the theoretical finite-element model of the structure, because it provides a rational basis for weighting differently the errors of the various modal parameters, the errors being the differences between the theoretical and identified values of these parameters. The approach is introduced here for a SDOF system. Under the assumption of white noise excitation the statistical properties of an estimator of the spectral density are presented. Based on these statistical results expressions for the updated probability density function (PDF) of the modal parameters are derived. The optimal values of the parameters are the ones at which the updated PDF is maximized. Numerical examples using simulated data are presented to demonstrate the approach.