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Bayesian identification of soil‐foundation stiffness of building structures
Author(s) -
ShirzadGhaleroudkhani Nima,
Mahsuli Mojtaba,
Ghahari S. Farid,
Taciroglu Ertugrul
Publication year - 2018
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.2090
Subject(s) - bayes' theorem , probability density function , timoshenko beam theory , stiffness , sensitivity (control systems) , mode (computer interface) , probability distribution , probabilistic logic , bayesian inference , joint probability distribution , mathematics , engineering , posterior probability , beam (structure) , algorithm , bayesian probability , structural engineering , computer science , statistics , electronic engineering , operating system
Summary 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.