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

Soize, Christian

doi:10.1016/j.compstruc.2013.03.020

Cited by 21 publications

(8 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following simple example [205] shows the capability of the generalized probabilistic approach to take into account uncertainties that occur at two different scales (for instance, for vibrations in the low-and in the medium-frequency ranges) in a computational model by using the Bayes method. This method allows for updating the stochastic model of an uncertain model parameter whose statistical fluctuations induce significant effects for the first scale (for instance, for the low-frequency band) and in presence of model uncertainties induced by the modeling errors for which the statistical fluctuations induce significant effects for the second scale (for instance, for the medium-frequency band).…”

Section: Simple Example Showing the Capability Of The Generalized Promentioning

confidence: 99%

Uncertainty Quantification

Soize

2017

Interdisciplinary Applied Mathematics

124

View full text Add to dashboard Cite

show abstract

Section: Simple Example Showing the Capability Of The Generalized Promentioning

confidence: 99%

Uncertainty Quantification

Soize

2017

Interdisciplinary Applied Mathematics

124

View full text Add to dashboard Cite

show abstract

“…In the material model, the error can be approximated using a stochastic process. 3,12,18 Thus, the sources of uncertainty in the elastomers that are considered in this study are as follows:…”

Section: Sources Of Uncertainties In Elastomersmentioning

confidence: 99%

Variability analysis of vibrational responses in a passenger car considering the uncertainties of elastomers

Kwon

Lee

2015

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

Passenger cars have many elastomeric joints that are used to reduce the vibration transmission from the source to the cabin structure. In the design stage, the dynamic characteristics of the elastomeric joints are optimally determined in order to satisfy the design goals for interior noise and vibration. However, the material properties of the elastomeric joints have large variations due to production variability. In addition, operational conditions, e.g. environmental temperature, vary according to the locations of the car. As a result, the vibrational comfort of a passenger car exhibits large variations. In this paper, the amount of vibration fluctuation due to uncertain elastomeric joint parameters is estimated using a statistical approach. First, the dynamic characteristics of the elastomers are described using the fractional derivative model. The uncertainties of the fractional derivative model parameters of the elastomers are characterized using a statistical calibration approach based on specimen test data. Then, a finite element model for the elastomers and the passenger car structure are constructed in order to calculate the vibrational response. In order to estimate the variability of the vibrational response due to the uncertainties of the elastomers, uncertainty propagation analyses are conducted using the eigenvector dimension reduction (EDR) method. The operational conditions such as temperature are also included in the variability analysis. The performance of the EDR method is assessed through comparing the estimated response distribution with that of the Monte Carlo simulation (MCS) method in a simplified structure. The variability analysis results demonstrate that the vibrational response variation due to the uncertainties of the elastomers can be efficiently predicted using the proposed method. The proposed variability analysis procedure could be an effective tool in the design stage for quality control of passenger car comfort.

show abstract

“…erein, structural model updating [18,19] is more convenient than other methods and recommendable for the complex structure due to large number of DOFs in the finite element model. Moreover, among various model updating methods, Bayesian inference is a very popular probabilistic identification method, which has been widely used in both linear and nonlinear structures [20][21][22][23][24][25][26][27]. Compared with the deterministic method based on optimization, Bayesian method can more flexibly deal with modelling uncertainties and measurement noise.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Shen

Liu

Zang

et al. 2021

Shock and Vibration

View full text Add to dashboard Cite

Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

show abstract

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

Cited by 21 publications

References 76 publications

Uncertainty Quantification

Uncertainty Quantification

Variability analysis of vibrational responses in a passenger car considering the uncertainties of elastomers

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Contact Info

Product

Resources

About