A robust optimization approach based on multi-fidelity metamodel

Zhou, Qi; Wang, Yan; Choi, Seung-Kyum; Jiang, Ping; Shao, Xinyu; Hu, Jiexiang; Shu, Leshi

doi:10.1007/s00158-017-1783-4

Cited by 55 publications

(14 citation statements)

References 62 publications

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“…Xu and Zeger (2001) use an EoS and introduce two independent processes to highlight their advantages instead of individual surrogates. On the other hand, Zhou et al (2018) study the drawbacks of compound and ensemble surrogates and their inadequacy based on quasi-concavity. Samad et al (2006) analyze the use of an EoS and performance approximation simultaneously.…”

Section: Frame Of Referencementioning

confidence: 99%

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

Alizadeh

Jia

Nellippallil

et al. 2019

AIEDAM

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In engineering design, surrogate models are often used instead of costly computer simulations. Typically, a single surrogate model is selected based on the previous experience. We observe, based on an analysis of the published literature, that fitting an ensemble of surrogates (EoS) based on cross-validation errors is more accurate but requires more computational time. In this paper, we propose a method to build an EoS that is both accurate and less computationally expensive. In the proposed method, the EoS is a weighted average surrogate of response surface models, kriging, and radial basis functions based on overall cross-validation error. We demonstrate that created EoS is accurate than individual surrogates even when fewer data points are used, so computationally efficient with relatively insensitive predictions. We demonstrate the use of an EoS using hot rod rolling as an example. Finally, we include a rule-based template which can be used for other problems with similar requirements, for example, the computational time, required accuracy, and the size of the data.

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Section: Frame Of Referencementioning

confidence: 99%

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

Alizadeh

Jia

Nellippallil

et al. 2019

AIEDAM

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“…hierarchal kriging [8]) instead of direct simulations for MCS or directly build surrogates [9,10] of mean and variance. Alternatively, people resort to develop formulations of mean and the variance directly by polynomial chaos expansion [11,12] and kriging [13][14][15] as well.…”

Section: Introductionmentioning

confidence: 99%

“…Concerning the problem as how to deal with optimization design variables and uncertainty parameters, they are often merged as uncertainty variables in most references [11][12][13][14][15][16][17][18], and doubled loop optimization strategies are frequently adopted, i.e., the variables are searched in a large space to obtain better nominal performance in an outer loop. Then, by varying corresponding variables of optimized solution in its neighborhood of small range, UQ was conducted in an inner loop.…”

Section: Introductionmentioning

confidence: 99%

“…Then, by varying corresponding variables of optimized solution in its neighborhood of small range, UQ was conducted in an inner loop. Most of the UQ methods [8,9,11,[13][14][15] shown in the previous paragraph are designed for the uncertainty variables, which doesn't distinguish between optimization variables and uncertainty parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The first issue is the RO objectives and corresponding optimization strategies. The mean and variance are most frequently used for probabilistic optimization framework; both the strategies of multiobjective optimization [9,10,[16][17][18] and weighted forms of mean and variance in single-objective optimization [11][12][13][14][15] were reported in the references. By comparing to some single-objective RO, Ryan et al [18] stated that the multiobjective strategy was able to cover the solutions of singleobjective RO while capturing tradeoffs within the design space.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Optimization for Vortex Generators in U-Bend Channel of High-Temperature Blades

Guo¹,

Tao²,

Song³

2019

Proceedings of Global Power &Amp; Propulsion Society

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The uncertainties such as manufacturing errors and environmental variations are inevitably encountered in engineering design, therefore in order to find robust solutions which keep high performance over a wide range, a meanvariance multi-objective robust optimization (RO) framework was proposed. Specifically, a kriging-based uncertainty quantification (UQ) formulation was proposed, which formulates uncertainty parameters and optimization design variables in product form, thereby the optimization search and UQ are conducted simultaneously in RO. Before RO, the sequential sampling strategies were employed to build high-accurate surrogate, which was shown effective by our five-variable engineering problem. Through aero-thermal design of vortex generators (VG) in U-bend channel of hightemperature blades, some issues such as constraints selection and knowledge mining in RO space were addressed. The RO of VG was carried out with one Gaussian-distributed and one uniformly-distributed uncertainty parameter, and three optimization design variables. One deterministic optimization (DO) process at the nominal condition and several RO process with different constraints were conducted. It was shown that the proposed RO was able to find robust solutions that have high-performance and are not sensitive to uncertainty fluctuations; which were validated by CFD. Meanwhile, the solution of DO was found helpful to exclude variance-dominated solutions which have much worse performance. But some constraints based on solution of DO would make the RO solution set to be null, therefore the RO can be an iterative process, in this regard, it is attractive to build high-accurate surrogates before RO. From another perspective, the several RO with different constraints are useful to group the solutions and get a insight into black-box design space like VG, which is valuable to select the final solution from many Pareto solutions.

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