Inversion of probabilistic structural models using measured transfer functions

Arnst, Maarten; Clouteau, Didier; Bonnet, Marc

doi:10.1016/j.cma.2007.08.011

Cited by 26 publications

(20 citation statements)

References 55 publications

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“…In practice, such an assumption does not hold for dynamical systems which are considered in this paper and then, the statistical dependence is very important. As it can be seen in [2], [3], the use of Eq. (37) instead of Eq.…”

Section: Standard Methodsmentioning

confidence: 99%

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

Soize

Capiez‐Lernout

Durand

et al. 2008

Computer Methods in Applied Mechanics and Engineering

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We present a methodology to perform the identification and validation of complex uncertain dynamical systems using experimental data, for which uncertainties are taken into account by using the nonparametric probabilistic approach. Such a probabilistic model of uncertainties allows both model uncertainties and parameter uncertainties to be addressed by using only a small number of unknown identification parameters. Consequently, the optimization problem which has to be solved in order to identify the unknown identification parameters from experiments is feasible. Two formulations are proposed. The first one is the mean-square method for which a usual differentiable objective function and an unusual non-differentiable objective function are proposed. The second one is the maximum likelihood method coupling with a statistical reduction which leads us to a considerable improvement of the method. Three applications with experimental validations are presented in the area of structural vibrations and vibroacoustics.

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Section: Standard Methodsmentioning

confidence: 99%

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

Soize

Capiez‐Lernout

Durand

et al. 2008

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…The choice of that level of fluctuation can be made by comparison with experiments [63][64][65]. It can also be performed by comparison with numerical results conducted with an appropriate choice of the parametric probabilistic model [66,67].…”

Section: Nonparametric Approachmentioning

confidence: 99%

Probabilistic impedance of foundation: Impact of the seismic design on uncertain soils

Cottereau

Clouteau

Soize³

2008

Earthq Engng Struct Dyn

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SUMMARYIn the linear seismic design of buildings, the (deterministic) substructure method is a customary and efficient approach. However, the existence of spatial variability in the parameters of the mechanical model of the soil, as well as parametric errors, calls for the use of probabilistic approaches in order to provide a reliable design of the structure. The construction of probabilistic models of the soil impedance matrix provides a natural path to such approaches within the context of the substructure method. Two main techniques are described in this paper: a parametric one, typically using the stochastic finite element method, and a nonparametric one, which was introduced more recently. The latter is explored more specifically, and the possibilities it offers in terms of seismic design are presented. In particular, it is shown that it allows for the estimation of quantiles of the quantities of interest, rather than confidence intervals, which lead to highly conservative design.

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“…Such MCMC method can be developed in introducing a stochastic dissipative Hamiltonian system such as introduced in [75] and in [25,26]. Concerning the experimental identification of the parameters of the prior probability distributions of random matrices introduced by the nonparametric probabilistic approach of uncertainties in computational mechanics, we refer the reader to [5,6,7,8,23,24,32,33,36,74,76,78]. The statistical inverse methods and the Bayesian inference approach to inverse problems have received a particular attention [9,11,12,25,26,27,35,45,48,79,87,88,90].…”

Section: Uncertainty Quantification and Identification Of The Stochasmentioning

confidence: 99%

Bayesian posteriors of uncertainty quantification in computational structural dynamics for low-and medium-frequency ranges

Soize

2013

Computers & Structures

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To cite this version:Christian Soize. Bayesian posteriors of uncertainty quantification in computational structural dynamics for low-and medium-frequency ranges. Computers and Structures, Elsevier, 2013, 126 (-) AbstractThe paper is devoted to the modeling and identification of uncertainties in computational structural dynamics for low-and medium-frequency ranges. A complete methodology is presented for the identification procedure. The first eigenfrequencies are used to quantify the uncertainties in the low-frequency band while the frequency response functions are used to quantify the uncertainties in the medium-frequency band. The system-parameter uncertainties are taken into account with the parametric probabilistic approach. The model uncertainties are taken in to account with the nonparametric probabilistic approach. The posterior stochastic model of systemparameter uncertainties is identified using the Bayes method.

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Inversion of probabilistic structural models using measured transfer functions

Cited by 26 publications

References 55 publications

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation

Probabilistic impedance of foundation: Impact of the seismic design on uncertain soils

Bayesian posteriors of uncertainty quantification in computational structural dynamics for low-and medium-frequency ranges

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