Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Component tolerance design for minimum quality loss and manufacturing cost
Computers in Industry
Data mining: concepts and techniques
Data mining: concepts and techniques
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Adaption of fast Fourier transformations to estimate structural failure probability
Finite Elements in Analysis and Design
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Dimension reduction method for reliability-based robust design optimization
Computers and Structures
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Journal of Computational Physics
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Sampling-based approach for design optimization in the presence of interval variables
Structural and Multidisciplinary Optimization
Hi-index | 0.00 |
This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse PCE) method for performing engineering reliability analysis and design. The proposed method combines three ideas: (i) an adaptive-sparse scheme to build sparse PCE with the minimum number of bivariate basis functions, (ii) a new projection method using dimension reduction techniques to effectively compute the expansion coefficients of system responses, and (iii) an integration of copula to handle nonlinear correlation of input random variables. The proposed method thus has three positive features for reliability analysis and design: (a) there is no need for response sensitivity analysis, (b) it is highly efficient and accurate for reliability analysis and its sensitivity analysis, and (c) it is capable of handling a nonlinear correlation. In addition to the features, an error decomposition scheme for the proposed method is presented to help analyze error sources in probability analysis. Several engineering problems are used to demonstrate the three positive features of the adaptive-sparse PCE method.