Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

Toal, David J. J.

doi:10.1007/s00158-014-1209-5

Cited by 104 publications

(34 citation statements)

References 23 publications

(28 reference statements)

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“…The r 2 correlation coefficient values for the outputs IC3 to IC7 satisfy the r 2 > 0.9 recommendation in Toal (2015). The low r 2 values for IC1 and IC2 are attributed to the low sensitivities of the two responses toward changes in x 1 and x 2 , where the range of observed values are an order of magnitude smaller than the remaining outputs.…”

Section: Two-variable Optimization Of An Engine Intercasingsupporting

confidence: 52%

Multi-fidelity Kriging-assisted structural optimization of whole engine models employing medial meshes

Yong

Wang

Toal

et al. 2019

Struct Multidisc Optim

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Finite element models of whole gas turbine engines, also known as whole engine models (WEMs), which consist of threedimensional solid elements are not commonly used in design optimization studies due to the high computational cost of solving them for many designs. WEMs consisting of two-dimensional shell elements can be a suitable replacement for high-fidelity solid WEMs as they approximate the responses well while being significantly quicker to solve. However, in a surrogate-assisted optimization study, the accumulation of errors in the shell WEM evaluations can result in the construction of a surrogate model that can be somewhat misleading compared to the solid WEM response surface. Such a surrogate model could return promising designs that, when validated using solid WEMs, turn out to be suboptimal or infeasible. A novel approach which combines medial meshing and multi-fidelity surrogate modelling techniques is proposed to increase the feasibility of conducting whole engine optimization studies. We demonstrate the workflow for generating medial meshes on an engine intercasing geometry. The accuracy of medial mesh simulations with respect to solid mesh simulations is evaluated and discussed in the context of their suitability as a source of low-fidelity structural information for multi-fidelity surrogate models. The impact of this combination of techniques is subsequently illustrated using two case studies. The first case study is the optimization of an intermediate compressor casing for minimum mass with constraints on the casing stiffness. The results show that the multi-fidelity approach is able to find optimum designs that are equivalent to the expensive singlefidelity approach of using only solid mesh evaluations but at a significantly lower computational cost. The second case study is the optimization of a whole engine geometry. This case study serves to demonstrate the effectiveness of the multi-fidelity approach for solving realistic design problems.

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Section: Two-variable Optimization Of An Engine Intercasingsupporting

confidence: 52%

Multi-fidelity Kriging-assisted structural optimization of whole engine models employing medial meshes

Yong

Wang

Toal

et al. 2019

Struct Multidisc Optim

Self Cite

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“…As long as the low fidelity data is well correlated with the high fidelity data [22] the low fidelity data can be used to better define the trend in the response in regions of the design space where there is little or no high fidelity data. Figure 11, recreated from Forrester et al [21], is an excellent example of the advantages of a multi-fidelity approach.…”

Section: Krigingmentioning

confidence: 99%

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

Zhang

Toal

Keane

et al. 2015

Journal of Engineering for Gas Turbines and Power

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The prometheus combustor design system aims to reduce the complexity of evaluating combustor designs by automatically defining preprocessing, simulation, and postprocessing tasks based on the automatic identification of combustor features within the computer-aided design (CAD) environment. This system enables best practice to be codified and topological changes to a combustor's design to be more easily considered within an automated design process. The following paper presents the prometheus combustor design system and its application to the multiobjective isothermal optimization of a combustor prediffuser and the multifidelity isothermal optimization of a fuel injector feed arm in combination with a surrogate modeling strategy accelerated via a high-performance graphical processing unit (GPU).

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“…The LF model is artificially constructed so it represents the HF model but with a discrepancy, which is measured by the r 2 lh correlation value and mean absolute relative error (MARE) between the LF and HF function MARE lh . These two statistical measures can be used to perform a preliminary analysis of whether the LF function is similar to the HF one or not [78]. The equation for r 2 lh correlation and MARE lh are…”

Section: Resultsmentioning

confidence: 99%

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Palar

Zuhal

Shimoyama

et al. 2018

Reliability Engineering & System Safety

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The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations are required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the lowfidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.

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Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

Cited by 104 publications

References 23 publications

Multi-fidelity Kriging-assisted structural optimization of whole engine models employing medial meshes

Multi-fidelity Kriging-assisted structural optimization of whole engine models employing medial meshes

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

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