Journal article
HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION
International journal for uncertainty quantification, Vol.13(4), pp.23-59
2023
DOI: 10.1615/Int.J.UncertaintyQuantification.2023043457
Abstract
Newly restructured generalized polynomial chaos expansion (GPCE) methods for high-dimensional design optimization in the presence of input random variables with arbitrary, dependent probability distributions are reported. The methods feature a dimensionally decomposed GPCE (DD-GPCE) for statistical moment and reliability analyses associated with a high-dimensional stochastic response; a novel synthesis between the DD-GPCE and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and a standard gradient-based optimization algorithm, constructing the single-step DD-GPCE and multi-point single-step DD-GPCE (MPSS-DD-GPCE) methods. In these new design methods, the multivariate orthonormal basis functions are assembled consistent with the chosen degree of interaction between input variables and the polynomial order, thus facilitating to deflate the curse of dimensionality to the extent possible. In addition, when coupled with score functions, the DD-GPCE leads to analytical formulae for calculating the design sensitivities. More importantly, the statistical moments, failure probability, and their design sensitivities are determined concurrently from a single stochastic analysis or simulation. Numerical results affirm that the proposed methods yield accurate and computationally efficient optimal solutions of mathematical problems and design solutions for simple mechanical systems. Finally, the success in conducting stochastic shape optimization of a bogie side frame with forty-one random variables demonstrates the power of the MPSS-DD-GPCE method in solving industrial-scale engineering design problems.
Details
- Title: Subtitle
- HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION
- Creators
- Dongjin LeeSharif Rahman
- Resource Type
- Journal article
- Publication Details
- International journal for uncertainty quantification, Vol.13(4), pp.23-59
- DOI
- 10.1615/Int.J.UncertaintyQuantification.2023043457
- ISSN
- 2152-5080
- eISSN
- 2152-5099
- Language
- English
- Date published
- 2023
- Academic Unit
- Mechanical Engineering; Iowa Technology Institute
- Record Identifier
- 9984363421302771
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