A univariate approximation at most probable point for higher-order reliability analysis

By Sharif Rahman, D. Wei. 2006

140 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/27053fed8cde2c803df3fe826def82eb66fee87e

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In Civil and Structural Engineering

In Mechanics of Materials

In Statistics and Probability

Citations in the corpus

Weighted stochastic response surface method considering sample weights (2011, methodology): “Therefore, for this case instead of treating all ten variables as random in Rahman and Wei (2006) , we set the first four variables as random variables following a normal distribution (Xi ∼ N (2, 5, 0.5), i = 1, 2, 3, 4), while the rest of the six variables are fixed at 2.5 in 2 . In this example, ”
A survey on approaches for reliability-based optimization (2010, methodology): “…analysis at reduced numerical costs using, e.g. uni-dimensional numerical integration (Rahman and Wei, 2008), an appropriate response surface (Rahman and Wei, 2006), etc. A.2 Simulation Methods Simulation methods estimate the value of the probability integral by generating samples of the…”
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.”
Structural reliability analysis by univariate decomposition and numerical integration (2007, methodology): “003030 29b MPP-based univariate method with simulation [12] 0.”
Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems (2008, methodology): “DRM [13–18] is a recently developed method to approximate the multi-dimensional integration of a performance function using a function with reduced dimension.”
System reliability-based design optimization using the MPP-based dimension reduction method (2010, unknown): “Then, using the transformation from the standard normal U-space to the rotated standard normal V-space (Rahman and Wei 2006; Wei 2006; Lee et al. 2007a, b, 2008) and the constraint shift given as”
Design sensitivity and reliability-based structural optimization by univariate decomposition (2008, methodology): “respectively, where @yk;j vk;j; d @vk;j can be calculated directly or by taking the partial derivative of the Lagrange interpolation of yk;N vk;N ; d (Rahman and Wei 2006).”
Statistical volume element method for predicting microstructure–constitutive property relations (2008, methodology): “Within the context of these material modeling methodologies and theories, the uncertainties in macroscale properties due to the randomness in microstructure parameters and constituent properties can be quantified via various techniques such as the Monte Carlo method [19], importance sampling [10], L”
A comparative study of uncertainty propagation methods for black-box-type problems (2008, methodology): “For this reason, the MPP-based UDR was developed recently and successfully applied to reliability analysis ( Rahman and Wei 2006; Lee et al. 2007).”