A subinterval bivariate dimension-reduction method for nonlinear problems with uncertainty parameters

Li, Feng; Zhao, Heng; Wei, Tonghui; Li, Hongfeng

doi:10.1007/s11012-022-01570-0

Cited by 1 publication

(2 citation statements)

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“…Uncertainties of things are divided into three types: stochastic uncertainty, 4‐6 fuzzy uncertainty 7,8 and interval uncertainty 9‐12 . They belong to the research areas of probability theory and mathematical statistics, fuzzy mathematics and interval mathematics, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Uncertainties of things are divided into three types: stochastic uncertainty, [4][5][6] fuzzy uncertainty 7,8 and interval uncertainty. [9][10][11][12] They belong to the research areas of probability theory and mathematical statistics, fuzzy mathematics and interval mathematics, respectively. Probabilistic/ stochastic models deal with uncertain engineering problems under the premise that empirical data are sufficient to determine the probability density function of uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

Zhao

Feng

et al. 2023

Numerical Meth Engineering

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To eliminate the errors caused by the conventional interval perturbation finite element method due to classic interval arithmetic and neglect of higher-order terms, we propose a novel univariate dimension-reduction based interval finite element method to predict the static response bounds of structures with uncertain but bounded parameters. First, a univariate dimension-reduction algorithm is derived using the generalized Taylor expansion. The global stiffness matrix is expressed as the sum of the median and the univariate disturbance radius. Compared with Taylor expansion approximation, the univariate dimension-reduction approximation has higher accuracy and does not increase the amount of calculation. Then the inverse of the interval global stiffness matrix is approximated as an improved Neumann series. Higher-order terms are included by summing up the geometric terms in the Neumann series. Finally, the improved interval algorithm is used to solve the upper and lower bounds of the structural displacement response and the element stress response. The dependence between the interval parameters is accounted in comparison with the classic interval algorithm. The accuracy and effectiveness of the new method are validated by numerical cases on 2D truss, 3D frame and truck frame with multiple interval parameters.

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Section: Introductionmentioning

confidence: 99%