NDLI: A Weighted Three-Point-Based Strategy for Variance Estimation

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Buranathiti, Thaweepat Cao, Jian Chen, Wei
Copyright Year	2004
Abstract	In manufacturing processes, it is widely accepted that uncertainty plays an important role and should be taken into account during analysis and design processes. However, uncertainty quantification of its effects on an end-product is a very challenging task, especially when an expensive computational effort is already needed in deterministic models such as sheet metal forming simulations. In this paper, we focus our work on the variance estimation of the system response. A weighted three-point-based strategy is proposed to efficiently and effectively estimate the variance of the system response. Three first-order derivatives for each variable are used to estimate the nonlinear behavior and variance of the system. The details of the derivation of the approach are presented in the paper. The optimal locations of the three points along each axis in the standard normal space and weights for input variables following normal distributions are proposed as (−1.8257,0.0,+1.8257) and (0.075,0.850,0.075), respectively. For input variables following uniform distributions U(−1,1), the optimal locations and weights are proposed as (−0.84517,0.0,+0.84517) and (0.04667,0.90666,0.04667), respectively. The proposed approach is applicable to nonlinear and multivariable systems as well as problems having no explicit function such as those design simulations based on finite element methods. The significant accuracy improvement over the traditional first-order approximation is demonstrated with a number of test problems. The proposed method requires significantly less computational effort compared with the Monte Carlo simulations. Discussions and conclusions of this work are given at the end of the paper.
Sponsorship	Design Engineering Division and Computers and Information in Engineering Division
Starting Page	637
Ending Page	645
Page Count	9
File Format	PDF
ISBN	0791846946
DOI	10.1115/DETC2004-57363
e-ISBN	0791837424
Volume Number	Volume 1: 30th Design Automation Conference
Conference Proceedings	ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Language	English
Publisher Date	2004-09-28
Publisher Place	Salt Lake City, Utah, USA
Access Restriction	Subscribed
Subject Keyword	First order approximation Uncertainty propagation Weighted three-point-based strategy Design under uncertainty Variance estimation Design Uncertainty Approximation Simulation Gaussian distribution Uncertainty quantification Engineering simulation Manufacturing Engineering design processes Finite element methods Sheet metal work
Content Type	Text
Resource Type	Article

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