Mathematical Properties of Polynomial Dimensional Decomposition

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/16m1109382 ◽

2018 ◽

Vol 6 (2) ◽

pp. 816-844 ◽

Author(s):

Sharif Rahman

Keyword(s):

Mathematical Properties ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Robust Design Optimization by Polynomial Dimensional Decomposition

12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference ◽

10.2514/6.2012-5564 ◽

2012 ◽

Author(s):

Xuchun Ren ◽

Sharif Rahman

Keyword(s):

Design Optimization ◽

Robust Design ◽

Robust Design Optimization ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method

Nonlinear Dynamics ◽

10.1007/s11071-018-4303-1 ◽

2018 ◽

Vol 93 (4) ◽

pp. 2003-2018 ◽

Author(s):

Kuan Lu

Keyword(s):

Dynamic System ◽

Decomposition Method ◽

Statistical Moment ◽

Degree Of Freedom ◽

Moment Analysis ◽

Statistical Moment Analysis ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Stochastic Computing by a New Polynomial Dimensional Decomposition Method

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference ◽

10.2514/6.2009-2252 ◽

2009 ◽

Author(s):

Sharif Rahman

Keyword(s):

Decomposition Method ◽

Stochastic Computing ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

Journal of Computational Physics ◽

10.1016/j.jcp.2016.03.026 ◽

2016 ◽

Vol 314 ◽

pp. 557-589 ◽

Author(s):

Kunkun Tang ◽

Pietro M. Congedo ◽

Rémi Abgrall

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Surrogate Modeling ◽

Fluid Simulation ◽

Global Sensitivity ◽

Sparse Polynomial ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Statistical Moments of Polynomial Dimensional Decomposition

Journal of Engineering Mechanics ◽

10.1061/(asce)em.1943-7889.0000117 ◽

2010 ◽

Vol 136 (7) ◽

pp. 923-927 ◽

Author(s):

Sharif Rahman

Keyword(s):

Statistical Moments ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Adaptive sparse polynomial dimensional decomposition for derivative-based sensitivity

Journal of Computational Physics ◽

10.1016/j.jcp.2019.04.042 ◽

2019 ◽

Vol 391 ◽

pp. 303-321 ◽

Author(s):

Kunkun Tang ◽

Jonathan M. Wang ◽

Jonathan B. Freund

Keyword(s):

Sparse Polynomial ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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A polynomial dimensional decomposition framework based on topology derivatives for stochastic topology sensitivity analysis of high-dimensional complex systems and a type of benchmark problems

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2020.103104 ◽

2020 ◽

Vol 62 ◽

pp. 103104

Author(s):

Xuchun Ren

Keyword(s):

Sensitivity Analysis ◽

Complex Systems ◽

High Dimensional ◽

Benchmark Problems ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2018.09.026 ◽

2019 ◽

Vol 344 ◽

pp. 910-937 ◽

Author(s):

Sharif Rahman

Keyword(s):

Uncertainty Quantification ◽

Random Variables ◽

Dependent Random Variables ◽

Generalized Polynomial ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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An adaptive sparse polynomial dimensional decomposition based on Bayesian compressive sensing and cross-entropy

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-021-03120-w ◽

2022 ◽

Vol 65 (1) ◽

Author(s):

Wanxin He ◽

Gang Li ◽

Zhaokun Nie

Keyword(s):

Compressive Sensing ◽

Cross Entropy ◽

Sparse Polynomial ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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An Extended Polynomial Dimensional Decomposition Method for Arbitrary Probability Distributions

13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference ◽

10.2514/6.2010-9126 ◽

2010 ◽

Author(s):

Sharif Rahman

Keyword(s):

Decomposition Method ◽

Probability Distributions ◽

Dimensional Decomposition ◽

Polynomial Dimensional Decomposition

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