Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties

Chensen Ding; Rohit R. Deokar; Xiangyang Cui; Guangyao Li; Yong Cai; Kumar K. Tamma

doi:10.1007/s00466-018-1607-4

Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties

Chensen Ding, Rohit R. Deokar, Xiangyang Cui, Guangyao Li, Yong Cai, Kumar K. Tamma

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit.

Original language	English (US)
Pages (from-to)	521-533
Number of pages	13
Journal	Computational Mechanics
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s00466-018-1607-4
State	Published - Mar 15 2019

Bibliographical note

Funding Information:
Acknowledgements This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079).

Funding Information:
This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079).

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

Geometric and force uncertainties
Isogeometric stochastic analysis
Multi-dimension uncertainties
Proper orthogonal decomposition coupled Monte Carlo method (POD–MC)
Separate and combined material

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10.1007/s00466-018-1607-4

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title = "Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties",

abstract = "This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit.",

keywords = "Geometric and force uncertainties, Isogeometric stochastic analysis, Multi-dimension uncertainties, Proper orthogonal decomposition coupled Monte Carlo method (POD–MC), Separate and combined material",

author = "Chensen Ding and Deokar, {Rohit R.} and Xiangyang Cui and Guangyao Li and Yong Cai and Tamma, {Kumar K.}",

note = "Funding Information: Acknowledgements This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079). Funding Information: This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079). Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

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T1 - Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties

AU - Ding, Chensen

AU - Deokar, Rohit R.

AU - Cui, Xiangyang

AU - Li, Guangyao

AU - Cai, Yong

AU - Tamma, Kumar K.

N1 - Funding Information: Acknowledgements This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079). Funding Information: This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079). Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/3/15

Y1 - 2019/3/15

N2 - This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit.

AB - This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit.

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KW - Isogeometric stochastic analysis

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KW - Proper orthogonal decomposition coupled Monte Carlo method (POD–MC)

KW - Separate and combined material

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Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties

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