Adaptive N-Fidelity Metamodels for Noisy CFD Data

Wackers, Jeroen; Visonneau, Michel; Ficini, Simone; Pellegrini, Riccardo; Serani, Andrea; Diez, Matteo

doi:10.2514/6.2020-3161

Cited by 10 publications

(12 citation statements)

References 27 publications

(37 reference statements)

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“…In detail, we have considered the a posteriori adaptive MISC method already presented in [16], with slight modifications on the profit computation, and we have highlighted in passing that MISC is not an interpolatory method, contrary to its single-fidelity counterpart (i.e., sparse grids); this detail was never previously discussed (up to the authors' knowledge) in the MISC literature. SRBF has been used as an interpolatory surrogate model for the analytical test problem and as a regressive surrogate model [22] for the RoPax problem.…”

Section: Discussionmentioning

confidence: 99%

“…Another widely studied class of multi-level methods employs kernel-based surrogates such as hierarchical kriging [20], co-kriging [21], Gaussian processes [22], and radialbasis functions [23]. Additive, multiplicative, or hybrid correction methods, also known as "bridge functions" or "scaling functions" [24], are used to build multi-fidelity surrogates.…”

Section: Introductionmentioning

confidence: 99%

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Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

Piazzola

Tamellini

Pellegrini

et al. 2022

Engineering with Computers

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This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of a roll-on/roll-off passenger ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, and kurtosis), and the probability density function for such quantity of interest (QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index Stochastic Collocation (MISC) and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF). The QoI is evaluated via computational fluid dynamics simulations, which are performed with the in-house unsteady Reynolds-Averaged Navier–Stokes (RANS) multi-grid solver $$\chi$$ χ navis. The different fidelities employed by both methods are obtained by stopping the RANS solver at different grid levels of the multi-grid cycle. The performance of both methods are presented and discussed: in a nutshell, the findings suggest that, at least for the current implementation of both methods, MISC could be preferred whenever a limited computational budget is available, whereas for a larger computational budget SRBF seems to be preferable, thanks to its robustness to the numerical noise in the evaluations of the QoI.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

Piazzola

Tamellini

Pellegrini

et al. 2022

Engineering with Computers

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“…Considering a QoI that can be evaluated with N fidelity levels (where the first level is the highest-fidelity and the N -th level is the lowest-fidelity) the MF extension of the GP is built as follows [9]. Given a training set…”

Section: Multi-fidelity Approachmentioning

confidence: 99%

Uncertainty Quantification of an Autonomous Surface Vehicle by Multi-fidelity Surrogate Models

Ficini¹,

Pellegrini²,

Odetti³

et al. 2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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A multi-fidelity Gaussian process (MF-GP) is presented for the forward uncertainty quantification (UQ) of the performance of an autonomous surface vehicle (ASV) subject to uncertain operating conditions. The ASV is a shallow water autonomous multipurpose platform (SWAMP), designed for the acquisition of the environmental parameters in the extremely shallow waters of wetlands. The quantity of interest (QoI) is the hydrodynamic resistance of the SWAMP subject to variable payload and longitudinal position of its center of mass. The QoI is assessed by a linear potential-flow solver coupled with the rigid body equations of motion. Multiple fidelity levels are defined based on the computational grid size and the level of coupling between hydrodynamic loads and motions. The MF-GP is based on a low-fidelity surrogate, corrected with an additive function, representing the error between higher and lower fidelity solutions. The MF-GP provides the prediction with the associated uncertainty. The latter is used to adaptively train the MF-GP, adding points where the prediction uncertainty is maximum. Finally, the UQ of the QoI is performed by Monte Carlo sampling on the MF-GP surrogate. The first four statistical moments, the 95th percentile, and the probability density function of the QoI are assessed. MF-GP is compared to its single-fidelity (high-fidelity based) counterpart, showing overall better results.

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“…The presence of numerical noise can be a critical issue for the adaptive sampling/learning process. The output-noise, if not taken into account, can deteriorate the model quality/efficiency (e.g the optimization algorithm may prematurely converge to local minima [15] or the adaptive sampling method may react to noise by adding many training points in noisy region, rather than selecting new points in unseen region [16]). There are different strategies to deal with noise in a SBDO process, e.g Meliani et al [17] filter-out the noise by co-Kriging regression, and Wackers et al [16] use a MF-SRBF with least square regression and a MF-GPR to filter-out and assess the noise in the training set of each fidelity level.…”

Section: Introductionmentioning

confidence: 99%

“…The MF-GPR used in this work has been applied, in authors' previous work, for a CFD-based optimization of a NACA 4-digit airfoil [16] and the uncertainty quantification of an autonomous surface vehicle [18]. In both the applications the MF-GPR with 3 fidelity levels has shown better performance than the MF-GPR with 1 and 2 fidelity levels.…”

Section: Introductionmentioning

confidence: 99%

Assessing the Performance of an Adaptive Multi-Fidelity Gaussian Process with Noisy Training Data: A Statistical Analysis

Ficini,

Iemma,

Pellegrini

et al. 2021

Preprint

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Despite the increased computational resources, the simulation-based design optimization (SBDO) procedure can be very expensive from a computational viewpoint, especially if highfidelity solvers are required. Multi-fidelity metamodels have been successfully applied to reduce the computational cost of the SBDO process. In this context, the paper presents the performance assessment of an adaptive multi-fidelity metamodel based on a Gaussian process regression (MF-GPR) for noisy data. The MF-GPR is developed to: (i) manage an arbitrary number of fidelity levels, (ii) deal with objective function evaluations affected by noise, and (iii) improve its fitting accuracy by adaptive sampling. Multi-fidelity is achieved by bridging a low-fidelity metamodel with metamodels of the error between successive fidelity levels. The MF-GPR handles the numerical noise through regression. The adaptive sampling method is based on the maximum prediction uncertainty and includes rules to automatically select the fidelity to sample. The MF-GPR performance are assessed on a set of five analytical benchmark problems affected by noisy objective function evaluations. Since the noise introduces randomness in the evaluation of the objective function, a statistical analysis approach is adopted to assess the performance and the robustness of the MF-GPR. The paper discusses the efficiency and effectiveness of the MF-GPR in globally approximating the objective function and identifying the global minimum. One, two, and three fidelity levels are used. The results of the statistical analysis show that the use of three fidelity levels achieves a more accurate global representation of the noise-free objective function compared to the use of one or two fidelities.

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Adaptive N-Fidelity Metamodels for Noisy CFD Data

Cited by 10 publications

References 27 publications

Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

Uncertainty Quantification of an Autonomous Surface Vehicle by Multi-fidelity Surrogate Models

Assessing the Performance of an Adaptive Multi-Fidelity Gaussian Process with Noisy Training Data: A Statistical Analysis

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