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Polynomial chaos expansion based robust design optimization

Fenfen Xiong · Bin Xue · Yan Zhang · Shuxing Yang

29 citations0/0 files storedInternational Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering

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

Abstract

In this paper, we present the polynomial chaos expansion (PCE) approach as a rigorous method for uncertainty propagation and further extend its use to robust design optimization. Thus a PCE based robust design optimization approach is developed. The mathematical background of PCE is introduced, where techniques of full factorial numerical integration (FFNI) and sparse grid numerical integration (SGNI) are proposed to estimate the PCE coefficients for low and high dimensional cases, respectively. Through a rocket design example, it is shown that the robustly optimized designs of the rocket are significantly less sensitive to the input variations compared to the deterministic oneS, which demonstrates the effectiveness of the proposed PCE based robust design procedure in the designs involving varying random dimensions. Specifically, the “curse of dimensionality” is significantly alleviated for high-dimension problems by SGNI, which indicates the high efficiency of our approach.

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References

1991Stochastic Finite Elements: A Spectral Approach 1996A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors 1998Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems 1999Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design 1997An efficient method for parametric uncertainty analysis of numerical geophysical models 2008A comparative study of uncertainty propagation methods for black-box-type problems 1999Uncertainty Analysis of Transport-Transformation Models 2001Robust optimization considering tolerances of design variables

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2023Optimizing upside variability and antifragility in renewable energy system design 2015Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels 2024A gradient-assisted learning strategy of Kriging model for robust design optimization 2023A discrete adjoint framework coupled with adaptive PCE for robust aerodynamic optimization of turbomachinery under flow uncertainty

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