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Microstructure model reduction and uncertainty quantification in multiscale deformation processes
7 references·8 citing·35 second hop
Microstructure model reduction and uncertainty quantification in multiscale deformation processes (2010)Microstructure model reduction and uncert…The effect of multiple sources of uncertainty on the convex hull of material properties of polycrystals (2009)The effect of multiple source…An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…Stochastic model reduction for chaos representations (2007)Stochastic model reduction fo…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes (2006)A non-intrusive stochastic Ga…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials (2023)Stochastic multiscale modelin…An uncertainty quantification framework for multiscale parametrically homogenized constitutive models (PHCMs) of polycrystalline Ti alloys (2021)An uncertainty quantification…Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations (2020)Uncertainty Quantified Parame…Uncertainty Quantification Accounting for Model Discrepancy Within a Random Effects Bayesian Framework (2020)Uncertainty Quantification Ac…Uncertainty Quantification for Parameter Estimation and Response Prediction (2019)Uncertainty Quantification fo…Quantification of uncertain macroscopic material properties resulting from variations of microstructure morphology based on statistically similar volume elements: application to dual-phase steel microstructures (2019)Quantification of uncertain m…Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics (2017)Uncertainty analysis in multi…A multiscale approach for model reduction of random microstructures (2012)A multiscale approach for mod…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)A least-squares approximation of partial differential equations with high-dimensional random inputs (2009)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances (2011)Stochastic Differential Equations: An Introduction with Applications. 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The Primer (2007)Modeling of viscoelastic structures with random material properties using time‐separated stochastic mechanics (2019)Efficient sampling technique for optimization under uncertainty (1997)Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability (2004)An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)Uncertainty Quantification Framework for Predicting Material Response with Large Number of Parameters: Application to Creep Prediction in Ferritic-Martensitic Steels Using Combined Crystal Plasticity and Grain Boundary Models (2022)Evidence-based uncertainty quantification for bending properties of bimetal composites (2023)Constructing Probability Boxes and Dempster-Shafer Structures (2003)On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data (2006)REIN: Reliability Estimation via Importance sampling with Normalizing flows (2023)Stochastic modeling and statistical calibration with model error and scarce data (2023)Learnable quantile polynomial chaos expansion: An uncertainty quantification method for interval reliability analysis (2024)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory (2010)Evaluating the response statistics of an uncertain bridge–vehicle system (2011)Sampling-free linear Bayesian update of polynomial chaos representations (2012)Stochastic Design Optimization of Microstructures with Utilization of a Linear Solver (2017)Uncertainty Quantification of Microstructural Properties due to Experimental Variations (2017)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2007Stochastic model reduction for chaos representations191 cited
  • 2006A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes86 cited
  • 2009The effect of multiple sources of uncertainty on the convex hull of material properties of polycrystals36 cited

Cited by

  • 2023Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials32 cited
  • 2021An uncertainty quantification framework for multiscale parametrically homogenized constitutive models (PHCMs) of polycrystalline Ti alloys31 cited
  • 2017Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics24 cited
  • 2012A multiscale approach for model reduction of random microstructures21 cited
  • 2019Uncertainty Quantification for Parameter Estimation and Response Prediction18 cited
  • 2019Quantification of uncertain macroscopic material properties resulting from variations of microstructure morphology based on statistically similar volume elements: application to dual-phase steel microstructures

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17 cited
  • 2020Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations15 cited
  • 2020Uncertainty Quantification Accounting for Model Discrepancy Within a Random Effects Bayesian Framework12 cited