Abstract
Conventional stochastic response surface methods (SRSM) based on polynomial chaos expansion (PCE) for uncertainty propagation treat every sample point equally during the regression process and may produce inaccurate estimations of PCE coefficients. To address this issue, a new weighted stochastic response surface method (WSRSM) that considers the sample probabilistic weights in regression is studied in this work. Techniques for determining sample probabilistic weights for three sampling approaches Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR), and Latin Hypercube Design (LHD) are developed. The advantage of the proposed method is demonstrated through mathematical and engineering examples. It is shown that for various sampling techniques WSRSM consistently achieves higher accuracy of uncertainty propagation without introducing extra computational cost compared to the conventional SRSM. Insights into the relative accuracy and efficiency of various sampling techniques in implementation are provided as well.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 837-849 |
| Number of pages | 13 |
| Journal | Structural and Multidisciplinary Optimization |
| Volume | 43 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2011 |
Funding
The grant supports from National Science Foundation of China (NO. 10972034), US National Science Foundation (NO. CMMI-0928320) and China Poster-doctoral Science Foundation (20100470213) are greatly acknowledged. The views expressed are those of the authors and do not necessarily reflect the views of the sponsors.
Keywords
- Gauss quadrature
- Latin hypercube design
- Monomial Cubature rule
- Sample probabilistic weights
- Stochastic response surface method
ASJC Scopus subject areas
- Software
- Control and Systems Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Control and Optimization