A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics

By H. Xu, Sharif Rahman. 2004

454 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/516e59027e6fdd8755e1f018a4362ca99c39d9cc

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In Computational Theory and Mathematics

In Management Science and Operations Research

In Statistics and Probability

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.”
Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method (2009, methodology): “In the general DR method (Xu and Rahman 2004), the theoretical error of the univariate DR method can be reduced by considering multivariate integrations.”
Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations (2013, methodology): “The DRM [26, 27] is a technique for approximating a multidimensional integral by the summation of a series of D-dimensional integrals (D N , usually D D 1 or 2).”
Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions (2009, methodology): “Using the multivariate function theorem of Xu and Rahman 2004 , it can be shown that a special R-variate approximation of y x , defined by ŷR x ª k=0 R − 1 k N − R + k − 1 k k1,. .”
Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis (2008, methodology): “The DR method suggests the use of a moment-based quadrature rule (Rahman and Xu 2004; Xu and Rahman 2004) to perform the one-dimensional numerical integration in (6).”