A nonparametric model of random uncertainties for reduced matrix models in structural dynamics

By Christian Soize. 2000

572 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/026bc5bfa18800f1621b729ff2c200bfe66496e4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity (2012, methodology): “All details concerning the construction of this proba bility model can be found in [17,18].”
Construction of a probabilistic model for impedance matrices (2007, methodology): “It was originally developped in linear structural dynamics [12,13] with applications in vibrations and transient elastodynamics, and was extended to nonlinear dynamical systems [14] and to the medium frequency range [15].”
Uncertainty analysis of complex structural systems (2009, background): “A different random matrix solution for uncertainty propagation has been proposed in [52, 53, 54, 55], where a so called non-parametric approach is suggested.”
A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models (2017, background): “However, it does not take into account neither the model uncertainties induced by modeling errors introduced during the construction of a -parametric HDM (model form uncertainties) nor those due to model reduction [27, 29, 38].”
Random uncertainties model in dynamic substructuring using a nonparametric probabilistic model (2003, methodology): “It is proved (Soize 2000 and 2001) that this constraint yields E{‖[G]−1‖2F } +∞.”
Probabilistic model identification of the bit–rock-interaction-model uncertainties in nonlinear dynamics of a drill-string (2010, methodology): “The nonparametric probabilistic approach (Soize (2000, 2010)) is used.”
Random matrix theory for modeling uncertainties in computational mechanics (2005, methodology): “(2) The second ensemble SE of random matrices, herein called the the positive-definite ensemble, has been constructed in [28,29], simultaneously with SG.”
A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics (2005, background): “Volume element d̃An on !Sn( ), is defined (see [14]) by d̃An = 2 n(n−1)/4 Π1≤i≤j≤n d[An]ij , (24)”
Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system (2013, unknown): “Finally, Soize [27] [28] developed a non-parametric approach which does not require identification of the uncertain local parameters.”
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2005, methodology): “Finally, the methods presented herein can be extended in a straightforward manner to situations where the Hermitian range space of the transformations is replaced with more general spaces such as the space of matrices or a Banach space [20, 21].”
Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2006, methodology): “From Refs.”
Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies (2008, background): “(2), under the constraints of Eqs (3)-(6) yields a closed form expression for the joint probability density function of the elements of the random matrix A (Soize, 2000, 2001).”
Non-linear dynamics of a drill-string with uncertain model of the bit–rock interaction (2009, methodology): “The nonparametric probabilistic approach [15, 16, 17] is used to model the uncertainties in the bit-rock interaction, which is represented by a nonlinear operator.”