This thesis mainly focuses on two problems: The first one is to update the modal parameters of linear structures and their associated uncertainties by utilizing ambient dynamic response data following a Bayesian probabilistic framework. Another issue is how to select the optimal location of sensors....[ Read more ]

This thesis mainly focuses on two problems: The first one is to update the modal parameters of linear structures and their associated uncertainties by utilizing ambient dynamic response data following a Bayesian probabilistic framework. Another issue is how to select the optimal location of sensors.

In the first part of this thesis (Chapter 2 - Chapter 4), the problem of identification of the modal parameters of linear structural models using measured ambient response time histories is addressed. Three Bayesian probabilistic frameworks for modal updating are introduced which allow one to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties, calculated from their joint probability distribution. Each of these chapters is corresponding to a different approach. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with a subsequent step of updating the theoretical finite element model based on the modal estimates. These three new approaches will be referred to as Bayesian fast Fourier transform approach (BFFTA), Bayesian spectral density approach (BSDA) and Bayesian Time-domain approach (BTDA). 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 methods.

Another issue addressed in this thesis is for making decisions regarding the optimal location of sensors for modal/model identification. Uncertainties are quantified using probability distributions, and the Bayesian spectral density approach is utilized for deriving appropriate expressions for the updated probability density function (PDF) of the modal/model parameters based on measured ambient response time histories. The optimal sensor configuration is selected as the one that minimizes the information entropy which is a unique measure of the uncertainties in the modal/model parameters. The information entropy measure is also extended to handle large uncertainties expected in the pre-test nominal model of a structure. Genetic algorithms are well-suited for solving the resulting discrete optimization problem. In experimental design, the proposed information entropy can be used to design cost-effective modal/model experiments by comparing and evaluating the benefits from placing additional sensors on the structure in relation to the improvement in the quality of the modal/model parameters identification.