Improving interval analysis in finite element calculations by means of affine arithmetic

By D. Degrauwe, Geert Lombaert, Guido De Roeck. 2010

165 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0f55504ed763a6144bb6b51fcb8158f194855f2a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Di Wu
2. Nong Zhang
3. Jinglai Wu
4. Chongmin Song
5. Wei Gao
6. Zhen Luo
7. Francis Tin-Loi
8. Yunqing Zhang

In Control and Systems Engineering

1. Zhen Luo
2. Nong Zhang
3. Jinglai Wu
4. Di Wu
5. Wei Gao
6. Yunqing Zhang
7. Chongmin Song
8. Francis Tin-Loi

In Statistics and Probability

1. Diego A. Alvarez
2. J. Hurtado
3. Nong Zhang
4. Jinglai Wu
5. Zhen Luo
6. Di Wu
7. Chongmin Song
8. Wei Gao

Citations in the corpus

• An efficient methodology for robustness evaluation by advanced interval analysis using updated second-order Taylor series expansion (2011, unknown): “Similar works of the interval analysis for the static response or eigenvalue have been developed by many researchers [6-15].”
• Fuzzy uncertainty propagation in composites using Gram–Schmidt polynomial chaos expansion (2016, methodology): “Consequently techniques employed in interval analysis such as classical interval arithmetic [15], affine analysis [16] or vertex theorems [17] can be used.”
• A new interval uncertain optimization method for structures using Chebyshev surrogate models (2015, background): “In particular, the intervalmodel has attracted much attention recently in the optimization of structures [11–14].”
• A review of uncertainty analysis in building energy assessment (2018, methodology): “generalization of interval arithmetic by considering the correlation between variables [155].”
• An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs (2014, methodology): “These and other considerations have fostered the research on alternative methods for incorporating uncertainty in the structural analysis, such as fuzzy sets and related theories [12–16], antioptimization or convex-set modeling [5,10,17], interval analysis [10,18–27], random sets [28–30], ellipsoid ”
• Fuzzy structural analysis based on fundamental reliability concepts (2012, background): “Moreover, the existence of other kinds of uncertainty, different from pure randomness, has fostered the consideration of different approaches to the problem such as fuzzy sets [14–16], antioptimization or convex-set modeling [8,17,12], interval analysis [12,18–22], random sets [23–25], ellipsoid mod”
• Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method (2011, methodology): “Combined with interval operations, antioptimization method [25], perturbation method [26,27], convex method [28,29], Monte-Carlo simulation method [30], interval finite element method [31,32] and affine arithmetic [33] have been adopted to analyze structures with interval parameters.”