Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Evolutionary computation: toward a new philosophy of machine intelligence
Evolutionary computation: toward a new philosophy of machine intelligence
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
SIAM Journal on Scientific Computing
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
SIAM Journal on Scientific Computing
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
Journal of Computational Physics
Optimization under worst case constraints--a new global multimodel search procedure
Structural and Multidisciplinary Optimization
Hi-index | 31.46 |
This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology.