scholarly journals An Updating Method for Structural Dynamics Models with Uncertainties

2008 ◽  
Vol 15 (3-4) ◽  
pp. 245-256 ◽  
Author(s):  
B. Faverjon ◽  
P. Ladevèze ◽  
F. Louf
Keyword(s):  
Structural Dynamics ◽  
Polynomial Chaos ◽  
Error Estimator ◽  
Chaos Expansion ◽  
Finite Element Analyses ◽  
Industrial Structures ◽  
Stochastic Problems ◽  
Constitutive Relation Error ◽  
Dynamics Models

One challenge in the numerical simulation of industrial structures is model validation based on experimental data. Among the indirect or parametric methods available, one is based on the “mechanical” concept of constitutive relation error estimator introduced in order to quantify the quality of finite element analyses. In the case of uncertain measurements obtained from a family of quasi-identical structures, parameters need to be modeled randomly. In this paper, we consider the case of a damped structure modeled with stochastic variables. Polynomial chaos expansion and reduced bases are used to solve the stochastic problems involved in the calculation of the error.

scholarly journals Error Estimation of Polynomial Chaos Approximations in Transient Structural Dynamics

2020 ◽  
Vol 17 (10) ◽  
pp. 2050003
Author(s):  
T. D. Dao ◽  
Q. Serra ◽  
S. Berger ◽  
E. Florentin
Keyword(s):  
Structural Dynamics ◽  
Polynomial Chaos ◽  
Approximation Error ◽  
Chaos Expansion ◽  
Reference Solution ◽  
Challenging Problem ◽  
Random Parameters ◽  
Testing Dataset ◽  
Stochastic Framework

Usually, within stochastic framework, a testing dataset is used to evaluate the approximation error between a surrogate model (e.g., a polynomial chaos expansion) and the exact model. We propose here another method to estimate the quality of an approximated solution of a stochastic process, within the context of structural dynamics. We demonstrate that the approximation error is governed by an equation based on the residue of the approximate solution. This problem can be solved numerically using an approximated solution, here a coarse Monte Carlo simulation. The developed estimate is compared to a reference solution on a simple case. The study of this comparison makes it possible to validate the efficiency of the proposed method. This validation has been observed using different sets of simulations. To illustrate the applicability of the proposed approach to a more challenging problem, we also present a problem with a large number of random parameters. This illustration shows the interest of the method compared to classical estimates.

scholarly journals Robust control of PGD-based numerical simulations

2012 ◽  
Author(s):  
Ludovic Chamoin ◽  
Pierre Ladevèze
Keyword(s):  
Robust Control ◽  
Numerical Simulations ◽  
Error Estimation ◽  
Constitutive Relation ◽  
Numerical Solutions ◽  
Error Estimator ◽  
Error Sources ◽  
Adaptive Procedures ◽  
Constitutive Relation Error

In this paper, we develop an error estimator that enables to control effectively the quality of numerical solutions obtained using proper generalised decomposition. The method is based on the Constitutive Relation Error and the construction of associated admissible fields. It takes all error sources (discretisations, truncation of the modal representation, etc.) into account and can be used, introducing adjoint-based techniques, for goal-oriented error estimation. Furthermore, specific indicators can be derived to split error contributions and thus drive adaptive procedures in an optimal manner.

scholarly journals Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3370
Author(s):  
Hesham AbdelFattah ◽  
Amnah Al-Johani ◽  
Mohamed El-Beltagy
Keyword(s):  
Porous Media ◽  
Correlation Function ◽  
Polynomial Chaos ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Chaos Expansion ◽  
Stochastic Problem ◽  
First Order ◽  
Stochastic Problems ◽  
Exponential Correlation Function

Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem.

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