Stochastic Modeling of Structural Uncertainty/Variability from Ground Vibration Modal Test Data

Avalos, Javier; Mignolet, Marc P.; Swenson, Eric D.; Lindsley, Ned

doi:10.2514/1.c031546

Cited by 14 publications

(5 citation statements)

References 13 publications

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“…It should be noted that, in [2], the authors have proposed an alterna-tive solution to take into account mode crossings and mode veerings in the identification of the hyperparameters of a SCM. Their solution consists in projecting the experimental mode shapes in the modal basis of the NCM and in letting the eigenfrequencies unchanged.…”

Section: Initializationmentioning

confidence: 99%

“…These parameters can be related to material properties (Young's modulus, mass density, and so on), geometry (CAD, thickness, area moments of inertia, and so on) and boundary conditions. (2) The second step consists in performing a sensitivity analysis of the quantities of interest with respect to the parameters in order to select the most-sensitive parameters which have to be updated (see for instance [6,15]). (3) The third step consists in updating the most-sensitive parameters using experimental data.…”

Section: Introductionmentioning

confidence: 99%

“…These hyperparameters have to be identified using experimental data and realizations of the SCM. Several types of observation can be used in order to perform such an identification and the choice depends on the quantities of interest for the developed SCM (see for instance, [34,35,19,22,23] for model-parameter uncertainties, and [45,46,12,13,5,2,49] for both model-parameter uncertainties and model uncertainties). For example, if the computational model is devoted to the prediction of responses in the low-frequency band of analysis and if the resonances are relatively well-separated, then the modal quantities (eigenfrequencies, mode shapes) are suitable observations.…”

Section: Introductionmentioning

confidence: 99%

“…For example, if the computational model is devoted to the prediction of responses in the low-frequency band of analysis and if the resonances are relatively well-separated, then the modal quantities (eigenfrequencies, mode shapes) are suitable observations. In a random context and for the low-frequency dynamical analysis, the eigenfrequencies can be used if a one-to-one correspondence can be constructed between the computational modes and the experimental modes [45,5,2]. This means that the experimental variability and the randomness in the SCM should not induce mode crossing phenomena or mode veering phenomena (see [36,37,33]) for the experimental modes and for the computed stochastic modes.…”

Section: Introductionmentioning

confidence: 99%

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Model identification in computational stochastic dynamics using experimental modal data

Batou¹,

Soize²,

Audebert³

2015

Mechanical Systems and Signal Processing

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International audienceThis paper deals with the identification of a stochastic computational model using experimental eigenfrequencies and mode shapes. In presence of randomness, it is difficult to construct a one-to-one correspondence between the results provided by the stochastic computational model and the experimental data because of the random modes crossing and veering phenomena that may occurs from one realization to another one. In this paper, this correspondence is constructed by introducing an adapted transformation for the computed modal quantities. Then the transformed computed modal quantities can be compared with the experimental data in order to identify the parameters of the stochastic computational model. The methodology is applied to a booster pump of thermal units for which experimental modal data have been measured on several sites

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Section: Initializationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model identification in computational stochastic dynamics using experimental modal data

Batou¹,

Soize²,

Audebert³

2015

Mechanical Systems and Signal Processing

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“…In fact, one can show that of the [20]) to further reduce the modal information to the skew coefficients…”

Section: Measurements and Maximum Likelihood Parameter Estimationmentioning

confidence: 99%

Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

Avalos

Richter

Wang

et al. 2012

Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts a and B

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This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural 2 frequencies and mode shape information of the beams around their final clamped-clamped state.To validate these concepts, three simulated, computational experiments were conducted within Nastran to produce populations of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The three experiments differed from each other by the nature of the clamping condition in the in-plane direction. One experiment assumed a no-slip condition (zero in-plane displacement), another a perfect slip (no in-plane force), while the third one invoked friction. The first two experiments gave distributions of frequencies with similar features while the latter one yielded a strong deterministic dependence of the frequencies on each other, a situation observed and explained recently and thus not considered further here. Then, the application of the stochastic modeling concepts to the no-slip simulated data was carried out and led to a good matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process.These results strongly suggest the applicability of the proposed stochastic model.

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Random Matrix Models and Nonparametric Method for Uncertainty Quantification

Soize¹

2015

Handbook of Uncertainty Quantification

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This paper deals with the fundamental mathematical tools and the associated computational aspects for constructing the stochastic models of random matrices that appear in the nonparametric method of uncertainties and in the random constitutive equations for multiscale stochastic modeling of heterogeneous materials. The explicit construction of ensembles of random matrices, but also the presentation of numerical tools for constructing general ensembles of random matrices are presented and can be used for high stochastic dimension. The developments presented are illustrated for the nonparametric method for multiscale stochastic modeling of heterogeneous linear elastic materials and for the nonparametric stochastic models of uncertainties in computational structural dynamics.

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Stochastic Modeling of Structural Uncertainty/Variability from Ground Vibration Modal Test Data

Cited by 14 publications

References 13 publications

Model identification in computational stochastic dynamics using experimental modal data

Model identification in computational stochastic dynamics using experimental modal data

Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

Random Matrix Models and Nonparametric Method for Uncertainty Quantification

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