TY - JOUR

T1 - An efficient reduced-order method for stochastic eigenvalue analysis

AU - Zheng, Zhibao

AU - Beer, Michael

AU - Nackenhorst, Udo

N1 - Funding Information: The authors are grateful to the Alexander von Humboldt Foundation and the International Research Training Group 2657 (IRTG 2657) funded by the German Research Foundation (DFG) (Grant reference number 433082294). Open Access funding enabled and organized by Projekt DEAL. Funding Information: Alexander von Humboldt-Stiftung, Deutsche Stiftung Friedensforschung, Grant/Award Numbers: IRTG2657; 433082294The authors are grateful to the Alexander von Humboldt Foundation and the International Research Training Group 2657 (IRTG 2657) funded by the German Research Foundation (DFG) (Grant reference number 433082294). Open Access funding enabled and organized by Projekt DEAL.

PY - 2022/11/9

Y1 - 2022/11/9

N2 - This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.

AB - This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.

KW - curse of dimensionality

KW - high-dimensional problems

KW - reduced-order equations

KW - stochastic finite element method

KW - structural stochastic eigenvalues

UR - http://www.scopus.com/inward/record.url?scp=85135909396&partnerID=8YFLogxK

U2 - 10.1002/nme.7092

DO - 10.1002/nme.7092

M3 - Article

AN - SCOPUS:85135909396

VL - 123

SP - 5884

EP - 5906

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 23

ER -