The multi-objective robust optimization of the loading path in the T-shape tube hydroforming based on dual response surface model

Huang, Tianlun; Song, Xiaojie; Liu, Xinyang

doi:10.1007/s00170-015-7494-3

Cited by 21 publications

(12 citation statements)

References 49 publications

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“…The use of RSM to analysis THF process can be referred to [30,31]. The authors experienced the application of dual RBF for multi-objective robust optimization and the use of adaptive RBF to optimize the loading path for T-shape THF process [32,33]. An [34,35] used KRG to accelerate calculation speed in multi-objective optimization in THF process.…”

Section: Introductionmentioning

confidence: 99%

The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

Huang

Song

Liu

2016

Int J Adv Manuf Technol

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The objective of this study is to introduce adaptive support vector regression, whose accuracy and efficiency are illustrated through a numerical example, to determine the Pareto optimal solution set for T-shape tube hydroforming process. A validated finite element model developed by the explicit finite element code LS-DYNA is used to conduct virtual T-shape tube hydroforming experiments. Multiobjective optimization problem considering contact area between the tube and counter punch, maximum thinning ratio, and protrusion height is formulated. Then, the Latin hypercube design is employed to construct the initial support vector regression model, and some extra sampling points are added to reconstruct the support vector regression model to obtain the Pareto optimal solution set during each iteration. Finally, the ideal point is used to obtain a compromise solution from the Pareto optimal solution set for the engineers.

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Section: Introductionmentioning

confidence: 99%

The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

Huang

Song

Liu

2016

Int J Adv Manuf Technol

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“…Copper-release response surface model (13) where C Cu µ is the mean response of copper release in mg/L, C Cu σ is the standard deviation response of copper release; T is the temperature in • C; Alk is the concentration of alkalinity in mg/L as calcium carbonate (CaCO 3 ); SO 4 and SiO 2 are the concentrations of sulfates and silica in mg/L, respectively; A H+ is the molar concentration of the activity of hydrogen ions in 10 9 mol/L (in order to keep the same order of magnitude as the pH value). R 2 is the correlation coefficient.…”

Section: Dual Response Surface Modelmentioning

confidence: 99%

“…As a consequence, it searches for an optimal set of input variables to optimize the response by using a set of designed experiments. In the past few years, several robust DRSO techniques have been developed [12,13]. Yanikoglu et al (2016) introduced Taguchi's Robust Parameter Design approach into DRSO to develop a method that uses only experimental data, and it can yield a solution that is robust against ambiguity in the probability of inputs [12].…”

Section: Introductionmentioning

confidence: 99%

Developing a Statistical Model to Improve Drinking Water Quality for Water Distribution System by Minimizing Heavy Metal Releases

Peng

Mayorga

2018

Water

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This paper proposes a novel statistical approach for blending source waters in a public water distribution system to improve water quality (WQ) by minimizing the release of heavy metals (HMR). Normally, introducing a new source changes the original balanced environment and causes adverse effects on the WQ in a water distribution system. One harmful consequence of blending source water is the release of heavy metals, including lead, copper and iron. Most HMR studies focus on the forecasting of unfavorable effects using precise and complicated nonlinear equations. This paper uses a statistical multiple objectives optimization, namely Multiple Source Waters Blending Optimization (MSWBO), to find optimal blending ratios of source waters for minimizing three HMRs in a water supply system. In this paper, three response surface equations are applied to describe the reaction kinetics of HMR, and three dual response surface equations are used to track the standard deviations of the three response surface equations. A weighted sum method is performed for the multi-objective optimization problem to minimize three HMRs simultaneously. Finally, the experimental data of a pilot distribution system is used in the proposed statistical approach to demonstrate the model's applicability, computational efficiency, and robustness.Keywords: water quality (WQ); blending; release of heavy metals (HMR); dual response surface optimization (DRSO); multiple source waters blending optimization (MSWBO)

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“…Therefore, some efforts were drawn to use surrogates (e.g. 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%

“…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%

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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The multi-objective robust optimization of the loading path in the T-shape tube hydroforming based on dual response surface model

Cited by 21 publications

References 49 publications

The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

Developing a Statistical Model to Improve Drinking Water Quality for Water Distribution System by Minimizing Heavy Metal Releases

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

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