UBC Theses and Dissertations
Probabilistic assessment of damage states using dynamic response parameters Quiroz, Laura Maria
To acknowledge and account for the uncertainties present in civil engineering applications is an area of major importance and of continuing research interest. This Thesis focuses on an application of Bayes' inference rule to evaluate the probability of damage in structures, using measured modal parameters and a set of possible damage states. The hypothesis is that observed changes in dynamic characteristics are due to damage accumulation over time. The main objective is to identify the most likely damage scenario from a set of previously defined damage states. These are characterized in terms of vectors, θi, the components of which are the parameters, θij, that are associated with the stiffness contribution, Kj, from each substructure undergoing damage. These stiffness matrices are uncertain as a result of random geometric and material properties. For different combinations of the damage parameters and realizations of the random variables, the modal parameters are calculated solving the basic eigenvalue problem. The results are used to calculate the statistics of the parameters given a specific damage state, the likelihood functions, as these are needed to calculate the probability of a given a set of measurements given a damage state. Each damage state Di is associated with a prior probability P(Di). In order to calculate its posterior probability, given a set of measurements, a Bayesian updating is implemented, in which the prior probability is updated by means of the likelihood functions, f(r|Di), which represent the probability density function of the modal parameter, r, given the damage state, Di. This Thesis discusses the effectiveness of the approach in identifying a particular damage state referred to as damage scenario. It is shown that measurement of multiple modal parameters is required to identify, quickly and with confidence, a given damage state. The discussion also considers the effect of error in the measurements, and the number of repeated measurements that are required to achieve a substantial confidence as to the presence of a particular damage state. Ranking of the estimated probabilities, after a set of measurements, offers guidance to the engineer as when and where to conduct a direct inspection of the structure.
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