Abstract
A probabilistic method is presented for identifying the dynamic soil-foundation stiffnesses of building structures. It is based on model updating of a Timoshenko beam resting on sway and rocking springs, which respectively represent the superstructure and the soil-foundation system. Unlike those previously employed for this particular problem, the proposed method is a Bayesian one, which accounts for the prevailing uncertainties due to modeling and measurement errors. As such, it yields the probability distribution of the system parameters as opposed to average/deterministic values. In this approach, the joint probability density function of the parameters that control the flexible-base Timoshenko beam model, together with the fundamental natural frequency and mode shape of the system, forms the prior distribution. Using Bayes' theorem, a posterior distribution is obtained by updating the prior distribution with a sparsely measured mode shape and frequency. The most probable realizations of the system parameters are then determined by maximizing the posterior distribution. For this purpose, first- and second-order derivatives of the objective function are analytically computed via direct differentiation. The proposed method is verified using a synthetic example. Additionally, sensitivity analyses are carried out on both the system parameters and standard deviations of the sources of error. Subsequently, the proposed method is applied to real-life data recorded at the Millikan Library building, which is located at the California Institute of Technology campus in Pasadena, California, and the results are compared with a previous deterministic study.
Published Version
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