Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations

By Beiqing Huang, Xiaoping Du. Design Automation Conference, 2005

174 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/355c5e48285c08bdbd15f239fc25927a9c4bdcd6

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. Kyung K. Choi
3. David J. Gorsich
4. Liu Du
5. Byeng Dong Youn
6. Chao Hu
7. Zhimin Xi
8. Hongzhong Huang

In Management Science and Operations Research

1. Byeng Dong Youn
2. Chao Hu
3. Kyung K. Choi
4. David J. Gorsich
5. Liu Du
6. Zhimin Xi
7. Ikjin Lee
8. Hongzhong Huang

In Statistics and Probability

1. Ikjin Lee
2. Kyung K. Choi
3. David J. Gorsich
4. Liu Du
5. Byeng Dong Youn
6. Chao Hu
7. Kai Zhang
8. Gang Li

Citations in the corpus

• 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 combined reliability analysis approach with dimension reduction method and maximum entropy method (2011, methodology): “Singularities can arise during the numerical procedure in Saddlepoint approximations (Huang and Du 2006).”
• Unified uncertainty analysis by the mean value first order saddlepoint approximation (2012, methodology): “4.3 Burst margin of disk The burst margin Mb of a disk is defined as (Huang and Du 2006) Z = Mb = g ( f, S, δ, N , R, R0) = √√√ √ f S 3 · 385.82δ ( N 2π60 )2 ( R3 − R30 ) (R − R0) where f is the material utilization factor, S is the ultimate tensile strength, δ is the density, N is the rotor speed,…”
• Reliability sensitivity analysis for structural systems in interval probability form (2011, methodology): “The performance function is given by (Huang and Du 2006) Z = f (P, L , a, S, d, b f , tw, t f ) = σmax − S where σmax = Pa (L − a) d 2L I and I = b f d 3 − (b f − tw ) ( d − 2t f )3 12 The distribution details of random variables are given in Table 5.”
• Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations (2013, unknown): “The performance function is given by [34]”
• Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems (2008, methodology): “The PDF approximation method [7–9] evaluates PDF of the performance function by”
• System reliability-based design optimization using the MPP-based dimension reduction method (2010, unknown): “1997; Denny 2001; Walker 1986) and the probability density function (PDF) approximation method (Rosenblueth 1981; Du and Huang 2006; Youn et al. 2008), for the actual calculation of the system probability of failure.”
• A comparative study of probability estimation methods for reliability analysis (2011, methodology): “In recent years, these methods have been employed to approximate the PDF, probabilities, and reliabilities of system responses from the known statistical information (Farnum 1997; Chen and Kamburowska 2001; Soize 2001; Huang and Du 2006; Straeten and Beck 2008; Youn and Xi 2009).”
• Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis (2008, methodology): “An I-beam example (Huang and Du 2006) is used to demonstrate that the EDR method is capable of handling all kinds of input uncertainties such as symmetric, asymmetric, bounded, and unbounded distributions.”