Updating Models and Their Uncertainties. I: Bayesian Statistical Framework

Beck, James L.; Katafygiotis, Lambros S.

doi:10.1061/(asce)0733-9399(1998)124:4(455)

Cited by 1,241 publications

(876 citation statements)

References 20 publications

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“…Many works have been published in this field and a state-of-the-art can be found, for instance, in [1,2,3,4,5,6,7,8,9,10,11]. Nevertheless, the parametric probabilistic approach does not allow the modeling uncertainties to be taken into account (see for instance [12,13]). …”

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

“…The Bayesian method then allows a posterior probability distribution to be constructed from the optimal prior probability distribution and the experimental data. Many works have been published in the literature (see for instance textbooks on the Bayesian method such as [59,60,61,62] and papers devoted to the use of the Bayesian method in the context of uncertain mechanical and dynamical systems such as [12,128,129,130,131,132,133]. We will use such a Bayesian approach in Sections 4.6 and 6.…”

Section: Identification Of the Stochastic Model Of Random Variables Imentioning

confidence: 99%

“…Concerning modeling uncertainties induced by modeling errors, it is today well understood that the prior and posterior stochastic models of the uncertain parameters of the computational model are not sufficient and do not have the capability to take into account modeling uncertainties in the context of computational mechanics (see for instance [12,13,14,15]). Two main methods can be used to take into account modeling uncertainties (modeling errors).…”

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

“…Two main methods can be used to take into account modeling uncertainties (modeling errors). (i) The first one consists in introducing a stochastic model of the output-predictionerror, considered as a noise, which is the difference between the real system output and the computational model output [12]. In this approach, the modeling errors and the measurements errors are simultaneously taken into account and cannot really be separately identified.…”

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

“…Such a prior stochastic model can then be used to study the propagation of uncertainties through the mechanical system which is analyzed. If experimental data are available for the mechanical system, then they can be used (1) to identify the parameters of the prior stochastic model [29] using, for instance, the maximum likelihood method [57,58] or (2) to construct a posterior stochastic model [12] using, for instance, the Bayesian method (see for instance [59,60,61,62,58]). …”

Section: Types Of Representation For the Stochastic Modeling Of Uncermentioning

confidence: 99%

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Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

139

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

Section: Identification Of the Stochastic Model Of Random Variables Imentioning

confidence: 99%

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

Section: Types Of Representation For the Stochastic Modeling Of Uncermentioning

confidence: 99%

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Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

139

106

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Identification of linear structural systems using earthquake-induced vibration data

Luş

Betti

Longman

1999

Earthquake Engng. Struct. Dyn.

132

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This paper addresses the issue of system identi"cation for linear structural systems using earthquake induced time histories of the structural response. The proposed methodology is based on the Eigensystem Realization Algorithm (ERA) and on the Observer/Kalman "lter IDenti"cation (OKID) approach to perform identi"cation of structural systems using general input}output data via Markov parameters. The e$ciency of the proposed technique is shown by numerical examples for the case of eight-storey building "nite element models subjected to earthquake excitation and by the analysis of the data from the dynamic response of the Vincent-Thomas cable suspension bridge (Long Beach, CA) recorded during the Whittier and the Northridge earthquakes. The e!ects of noise in the measurements and of inadequate instrumentation are investigated. It is shown that the identi"ed models show excellent agreement with the real systems in predicting the structural response time histories when subjected to earthquake-induced ground motion.

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Bayesian probabilistic damage detection of a reinforced-concrete bridge column

Sohn

Law

2000

Earthquake Engng. Struct. Dyn.

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SUMMARYA Bayesian probabilistic approach for damage detection has been proposed for the continuous monitoring of civil structures (Sohn H, Law KH. Bayesian probabilistic approach for structure damage detection. Earthquake Engineering and Structural Dynamics 1997; 26: 1259}1281). This paper describes the application of the Bayesian approach to predict the location of plastic hinge deformation using the experimental data obtained from the vibration tests of a reinforced-concrete bridge column. The column was statically pushed incrementally with lateral displacements until a plastic hinge is fully formed at the bottom portion of the column. Vibration tests were performed at di!erent damage stages. The proposed damage detection method was able to locate the damaged region using a simpli"ed analytical model and the modal parameters estimated from the vibration tests, although (1) only the "rst bending and "rst torsional modes were estimated from the experimental test data, (2) the locations where the accelerations were measured did not coincide with the degrees of freedom of the analytical model, and (3) there existed discrepancies between the undamaged test structure and the analytical model. The Bayesian framework was able to systematically update the damage probabilities when new test data became available. Better diagnosis was obtained by employing multiple data sets than just by using each test data set separately.

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Updating Models and Their Uncertainties. I: Bayesian Statistical Framework

Cited by 1,241 publications

References 20 publications

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Identification of linear structural systems using earthquake-induced vibration data

Bayesian probabilistic damage detection of a reinforced-concrete bridge column

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