Bayesian identification of soil‐foundation stiffness of building structures

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 t...

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Published in:	Structural control and health monitoring Vol. 25; no. 3; pp. e2090 - n/a
Main Authors:	Shirzad‐Ghaleroudkhani, Nima, Mahsuli, Mojtaba, Ghahari, S. Farid, Taciroglu, Ertugrul
Format:	Journal Article
Language:	English
Published:	Pavia John Wiley & Sons, Inc 01.03.2018
Subjects:	Bayesian analysis Bayesian updating Buildings dynamic stiffness Mathematical models Model updating Objective function Parameter sensitivity Probabilistic methods Probability density functions Probability distribution Sensitivity analysis Soil dynamics Soils soil‐structure interaction Springs (elastic) Statistical analysis Stiffness system identification Timoshenko beam United States > US California
ISSN:	1545-2255, 1545-2263
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Abstract	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.
AbstractList	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. 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.
Author	Ghahari, S. Farid Shirzad‐Ghaleroudkhani, Nima Taciroglu, Ertugrul Mahsuli, Mojtaba
Author_xml	– sequence: 1 givenname: Nima surname: Shirzad‐Ghaleroudkhani fullname: Shirzad‐Ghaleroudkhani, Nima organization: Sharif University of Technology – sequence: 2 givenname: Mojtaba orcidid: 0000-0001-7192-0881 surname: Mahsuli fullname: Mahsuli, Mojtaba email: mahsuli@sharif.edu organization: Sharif University of Technology – sequence: 3 givenname: S. Farid orcidid: 0000-0002-3847-5277 surname: Ghahari fullname: Ghahari, S. Farid organization: University of California – sequence: 4 givenname: Ertugrul orcidid: 0000-0001-9618-1210 surname: Taciroglu fullname: Taciroglu, Ertugrul organization: University of California
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Snippet	Summary A probabilistic method is presented for identifying the dynamic soil‐foundation stiffnesses of building structures. It is based on model updating of a... Summary A probabilistic method is presented for identifying the dynamic soil-foundation stiffnesses of building structures. It is based on model updating of a...
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SubjectTerms	Bayesian analysis Bayesian updating Buildings dynamic stiffness Mathematical models Model updating Objective function Parameter sensitivity Probabilistic methods Probability density functions Probability distribution Sensitivity analysis Soil dynamics Soils soil‐structure interaction Springs (elastic) Statistical analysis Stiffness system identification Timoshenko beam
Title	Bayesian identification of soil‐foundation stiffness of building structures
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