Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics

Serafino, Aldo; Obert, Benoit; Cinnella, Paola

doi:10.3390/a13100248

Cited by 4 publications

(3 citation statements)

References 69 publications

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“…Such a response surface provides an estimation of E[J] and STD[J] and it is constructed leveraging the evaluations of the low-fidelity UQ model, which is cheap but inaccurate, with only few runs of the high-fidelity UQ model, that is more accurate but extremely expensive: this multi-fidelity approach allows to perform UQ estimations accurate as the high-fidelity model at the cost of the lowfidelity one. A detailed description of the present RDO strategy can be found in Serafino et al (2020a). Specifically, here the first order method of moments (Hazelton, 2011) is used as low-fidelity UQ model and the Bayesian Kriging (Wikle and Berliner, 2007) as the high-fidelity one.…”

Section: Figure 4: Workflow Of the Robust Design Optimization Methodo...mentioning

confidence: 99%

Multi-fidelity robust design optimization of an ORC turbine for high temperature waste heat recovery

Serafino¹,

Obert²,

Cinnella

2023

Energy

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Section: Figure 4: Workflow Of the Robust Design Optimization Methodo...mentioning

confidence: 99%

Multi-fidelity robust design optimization of an ORC turbine for high temperature waste heat recovery

Serafino¹,

Obert²,

Cinnella

2023

Energy

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“…22 Some variants apply adaptive refinement only on LFMs, others only on the HFMs, and others on both of them. Tao et al 28 proposed an adaptive scheme which adds a set of points to the HFM DoE; Serafino et al 29 proposed a hybrid strategy with an adaptive refinement which is applied on the HFM based on the EI criterion. An interesting study by Guo et al 30 has shown the impact of the refinement process on the efficiency of the MFMBO.…”

Section: Introductionmentioning

confidence: 99%

Robust optimization of the aerodynamic design of a helicopter rotor blade based on multi-fidelity meta-models

Eddine

Khalfallah

Cerdoun

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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Robust optimization (RO) of designs becomes indispensable to deal with inherent manufacturing uncertainties. Yet, RO is still too expensive to solve complex problems such as the design of helicopter rotor blades. A promising way to reduce this cost is to use the multi-fidelity meta-model-based optimization (MFMBO), which combines low fidelity models (LFM), high fidelity models (HFM), meta-models, design of experiment (DoE), and optimization techniques. The field of MFMBO is not been completely explored despite the high number of proposed strategies. This paper contributes to the MFMBO cost-effectiveness improvement by proposing a new strategy. The main feature of the latter is the mutual adaptive refinement of the HFM and LFM DoE sets. A new idea is proposed to generate initial nested DoEs, which is implemented using an ordinary and an optimal Latin Hyper Cube method. These DoEs are refined adaptively and mutually using an improved MaxMin-distance criterion. The expensive HFM is used only to define a correction C of the LFM. C is used to adjust LFM evaluations during MBO. Meta-models are constructed using the Radial Basis Functions technique. The strategy is tested with two RO techniques, namely, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D). The implemented strategy is validated on three different mathematical benchmarks, compared with four different MFMBO strategies and applied on a helicopter rotor blade. This validation shows that the proposed MFMBO is competitive and can produce solutions as accurate as the HFM-based MBO while reducing significantly the overall computation time (up to 40%).

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“…the uncertain variables usually computed using a combination of adjoint methods and direct differentiation of the governing PDEs. [2][3][4][5] Though the cost of the MoM (with a second-order Taylor expansion) scales only linearly with the number of uncertain variables M, the need to compute high-order derivatives of the QoI w.r.t. the uncertain variables has prevented its widespread use in the industry.…”

Section: Introductionmentioning

confidence: 99%

Development and assessment of an intrusive polynomial chaos expansion‐based continuous adjoint method for shape optimization under uncertainties

Papageorgiou

Papoutsis‐Kiachagias

Giannakoglou

2021

Numerical Methods in Fluids

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This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier-Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint-enabled, gradient-based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.

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Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics

Cited by 4 publications

References 69 publications

Multi-fidelity robust design optimization of an ORC turbine for high temperature waste heat recovery

Multi-fidelity robust design optimization of an ORC turbine for high temperature waste heat recovery

Robust optimization of the aerodynamic design of a helicopter rotor blade based on multi-fidelity meta-models

Development and assessment of an intrusive polynomial chaos expansion‐based continuous adjoint method for shape optimization under uncertainties

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