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A Weighted Three-Point-Based Strategy for Variance Estimation

Thaweepat Buranathiti · Jian Cao · Wei Chen

8 citations0/0 files storedASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)

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Probabilistic and Robust Engineering Design Advanced Multi-Objective Optimization Algorithms Gaussian Processes and Bayesian Inference

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.

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References

1991Stochastic Finite Elements: A Spectral Approach 2003Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems 1986Random field finite elements 2002Error and uncertainty in modeling and simulation 1999A general procedure for first/second-order reliabilitymethod (FORM/SORM)1998Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis 1999Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design 2001Robust optimization considering tolerances of design variables

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2011Reliability-based design optimization using surrogate model with assessment of confidence level

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