Random matrix theory for modeling uncertainties in computational mechanics

By Christian Soize. 2005

306 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3461cccc8ae37b936dfd1bfa58f0d091cb840063

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In Civil and Structural Engineering

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems (2008, methodology): “A probabilistic approach that does include both parameter and model uncertainty has recently been devised (Soize, [3-5]) and applied/validated (see [6] for a review) on a variety of dynamic problems involving linear structures with possible additional local nonlinearities.”
Construction of a probabilistic model for impedance matrices (2007, background): “The identification from experimental results is left to be discussed in a future paper, and the choice of the dispersion parameters is not presented here as it has been described in other publications [19,20].”
Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2006, methodology): “[74,75,81], we introduced the ensemble SG of the random matrices [Gn], defined on a probability space (Θ, T , P )with values in!+n ( ), whose probability distribution was constructed by using the entropy optimization principle [65,34,36,37]”
A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics (2005, methodology): “[25] introduces (1) two additional sets of random matrices useful for fluid-structure interaction problems in the field of elastoacoustics and (2) a methodology for performing the experimental identification of the non-parametric probabilistic approach.”
Probabilistic model identification of the bit–rock-interaction-model uncertainties in nonlinear dynamics of a drill-string (2010, methodology): “In Ritto et al. (2009), a probabilistic model has been proposed for the bit-rock interaction model, whose uncertainties are modeled using the nonparametric probabilistic approach (Soize (2001, 2005, 2010)).”
Non-linear dynamics of a drill-string with uncertain model of the bit–rock interaction (2009, methodology): “Taking into account the above available information and using the Maximum Entropy Principle [26, 27, 28] yield the following probability density function of [Gb] [17], p[Gb]([Gb]) = (1)M2 (R)([Gb])CGb det([Gb]) 3 (1−δ2) 2δ2 exp { − 3 2δ2 tr([Gb]) } , (46)”
Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition (2007, background): “These random matrices are usually not obtained from a finite-dimensional representation of a partial differential operator, and in a number of interesting cases, closed-form expressions of the statistical moments and probability density functions of their eigenvalues and eigenvectors are available [”