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Author Soize, Christian ♦ Farhat, Charbel
Source Hyper Articles en Ligne (HAL)
Content type Text
Publisher Wiley
File Format PDF
Language English
Subject Keyword probabilistic learning ♦ model-form uncertainties ♦ nonparametric probabilistic method ♦ model reduction ♦ uncertainty quantification ♦ machine learning ♦ spi ♦ math ♦ Engineering Sciences [physics] ♦ Engineering Sciences [physics]/Mechanics [] ♦ Mathematics [math]/Probability [math.PR] ♦ Mathematics [math]/Statistics [math.ST]
Abstract Recently, a novel, nonparametric, probabilistic method for modeling and quantifying model-form uncertainties in nonlinear computational mechanics was proposed. Its potential was demonstrated through several uncertainty quantification (UQ) applications in vibration analysis and nonlinear computational structural dynamics. This method, which relies on projection-based model order reduction in order to achieve computational feasibility, exhibits a vector-valued hyperparameter in the probability model of the random reduced-order basis and associated stochastic, projection-based reduced-order model. It identifies this hyperparameter by formulating a statistical inverse problem grounded in target quantities of interest and solving the corresponding nonconvex optimization problem. For many practical applications however, this identification approach is computationally intensive. For this reason, this paper presents a faster, predictor-corrector approach for determining the appropriate value of the vector-valued hyperparameter that is based on a probabilistic learning on manifolds. It also demonstrates the computational advantages of this alternative identification approach through the UQ of two three-dimensional, nonlinear, structural dynamics problems associated with two different configurations of a MEMS device.
ISSN 00295981
Educational Use Research
Learning Resource Type Article
Publisher Date 2019-01-01
e-ISSN 10970207
Journal International Journal for Numerical Methods in Engineering
Volume Number 117
Issue Number 7
Page Count 25
Starting Page 819
Ending Page 843