Bayesian modal updating by use of ambient data

The problem of identification of the modal parameters of a structural model by using measured ambient response time histories is addressed. A Bayesian probabilistic framework for modal updating is adopted, which allows one to obtain not only the optimal (most probable) values of the updated modal parameters but also their uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite-element model based on modal estimates. A new probabilistic approach is proposed that uses the statistical properties of an estimator of the spectral density to obtain expressions for the updated probability density function (PDF) of the modal parameters. The proposed approach is first introduced for single-degree-of-freedom systems and then extended for multiple-degree-of-freedom systems. It is found that the updated PDF can be well approximated by a Gaussian distribution centered at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method