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Significance Statement
To relieve the computational load and manage the complexity in the design and analysis processes, a complex system is often decomposed into several submodels in a hierarchical manner according to functional attributes, physical structure, and scale magnitudes of submodels. On the other hand, metamodeling techniques have been extensively implemented to replace the original high fidelity computer simulation models, e.g., finite element models (FEM) and molecular dynamics simulations, to further alleviate the computation burden in the simulation-based design and analysis. However, the metamodeling uncertainty characterizing the discrepancy between the computer simulation model and the metamodel will propagate across multiple submodels and eventually produce significant influences on the performance analysis and design optimization of multi-level systems.
To quantify the metamodeling uncertainty and improve the global fidelity in the context of multi-level systems design and analysis, a metamodeling uncertainty quantification (MUQ) approach to quantify the uncertainty of metamodels, specifically the kriging model, propagated from bottom-level submodels to the top-level response of interest, is developed in this work. The Gaussian quadrature rule is adopted to alleviate the computational demand in evaluating the mean and variance of the top-level response. A tailored sequential sampling strategy, together with the proposed metamodeling uncertainty quantification, is proposed to seek the new sample site across all of the metamodels to maximally reduce the uncertainty of the top-level response.
As demonstrated in our case studies, the proposal sequential sampling method is prone to assign extra samples to the metamodel that has the most significant contribution to the top-level of interest. Thereby, with the same number of extra samples to be added, the proposed sequential sampling method is superior to the other sampling strategies in terms of improving the global fidelity of metamodels for multi-level systems. Additionally, using the tailored Gaussian quadrature, the computational time for quantifying the metamodeling uncertainty across multiple submodels can be significantly reduced, but it also maintained a high accuracy
Journal Reference
Structural and Multidisciplinary Optimization, June 2016, Volume 53, Issue 6, pp 1295-1313.
Yu Liu1, Yi Shi1, Qiang Zhou2, Renqiang Xiu1
[expand title=”Show Affiliations”]- Institute of Reliability Engineering, School of Mechatronics Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Avenue, West Hi-Tech Zone, Chengdu, Sichuan, 611731, People’s Republic of China
- Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong. [/expand]
Abstract
In engineering design, complex systems that involve a multitude of decision variables and parameters are often decomposed into several submodels (also called subsystems and/or components) with a hierarchical (multi-level) manner to manage complexity. Metamodeling techniques are widely used to replace the original time-consuming computer simulation models to further reduce computational burden in multi-level system performance analysis and design optimization. However, due to the limited samples from simulation models, metamodels may contain metamodeling uncertainties at un-sampled sites. Such metamodeling uncertainties arising from metamodels across the entire hierarchy will propagate from the lower to upper levels and eventually impact the top-level response of interest. With the aim of improving the global fidelity of metamodels for multi-level system performance analysis and design optimization, a new sequential sampling strategy is proposed in this paper. The proposed method contains two basic elements: (1) quantifying metamodeling uncertainty propagated from the lower-level metamodels to the top-level response of interest and (2) seeking a new sample site at which the global fidelity of the multi-level system model can be maximally improved. As exemplified by the two numerical examples and a multi-scale bracket structure example, with the same amount of samples from computer simulation models, the new sequential sampling strategy is superior to existing sequential sampling strategies in terms of improving the global fidelity of the metamodels of multi-level systems.
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