A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics

By Sharif Rahman, H. Xu. 2004

582 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d4e308517c5c3e807ae1b77dc441b5e946d762d3

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. Ikjin Lee
2. Sanghoon Lee
3. Byeng Dong Youn
4. Kyung K. Choi
5. David J. Gorsich
6. Wei Chen
7. Zhimin Xi
8. Marcos A. Valdebenito

In Management Science and Operations Research

1. Sanghoon Lee
2. Byeng Dong Youn
3. Zhimin Xi
4. Wei Chen
5. Shikui Chen
6. David J. Gorsich
7. Kyung K. Choi
8. Chao Hu

In Statistics and Probability

1. Ikjin Lee
2. Byeng Dong Youn
3. David J. Gorsich
4. Kyung K. Choi
5. Sanghoon Lee
6. Wei Chen
7. Marcos A. Valdebenito
8. Zhimin Xi

Citations in the corpus

• Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems with Correlated Random Variables (2011, methodology): “However, to obtain a more accurate optimum design, more quadrature points are required, such as the DRM7, etc.”
• A survey on approaches for reliability-based optimization (2010, methodology): “Aside the application of classical approximate reliability methods, the so-called Dimension Reduction Method (DRM) (Rahman and Xu, 2004; Xu and Rahman, 2004) has also been applied within the context of RBO using a double-loop approach.”
• Robustness-based design optimization under data uncertainty (2011, methodology): “A more recent approach to estimating the mean and variance of the performance function is the dimension reduction method (DRM) (Rahman and Xu 2004; Xu and Rahman 2004; Lee et al. 2008).”
• Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis (2008, methodology): “In fact, the error produced by the additive decomposition is less than that of a second-order Taylor expansion method for probability analysis (Rahman and Xu 2004).”
• Robust design with arbitrary distributions using Gauss-type quadrature formula (2009, methodology): “For multidimensional integrations, the tensor product quadrature (TPQ) formula (Evans 1967) and the univariate dimension reduction (UDR) method (Rahman and Xu 2004) are adopted, both of which are constructed based on the one dimensional Gauss-type quadrature formulas.”
• Level set based robust shape and topology optimization under random field uncertainties (2010, methodology): “With the univariate dimension reduction (UDR) method ( Rahman and Xu 2004 ), the multivariate function g(z) is approximated by a sum of univariate functions which depend on only one variable with the other variables fixed”
• Sensitivity analyses of FORM‐based and DRM‐based performance measure approach (PMA) for reliability‐based design optimization (RBDO) (2010, methodology): “DRM was originally proposed to approximate a multi-dimensional function using the sum of lower-dimensional functions for statistical moment estimation [12–16].”
• A comparative study of uncertainty propagation methods for black-box-type problems (2008, methodology): “The UDR method ( Rahman and Xu 2004 ; X u and Rahman 2004; Youn et al. 2006) approximates a multivariate function with multiple univariate functions, which can be used for efficient calculation of multivariate statistical moment integration.”