Continuation Multilevel Monte Carlo Evolutionary Algorithm for Robust Aerodynamic Shape Design

Pisaroni, Michele; Nobile, Fabio; Leyland, Pénélope

doi:10.2514/1.c035054

Cited by 13 publications

(8 citation statements)

References 31 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For small errors in the sample estimate of and (exact values indicated by ×) are acceptable but optimal variance reduction cannot be achieved 1 . Pisaroni 27 suggests a least-square fitting procedure to obtain the model constants but uses the cost model of Giles 18 . For the multilevel variance estimate we used the approach of Geraci 28 where the number of pilot samples chosen across levels equals the samples chosen across model fidelities.…”

Section: Insights On Model Correlation and Optimal Samplingmentioning

confidence: 99%

“…Where

{\tilde{G}}_{m}^{MC}

is an estimate of the approximation‐model mean

𝔼 [G_{m}^{MC}]

. Pisaroni 32 uses a weighted formulation of bias and statistical error in a multilevel control variate formulation called the continuation MLMC. In this work we consider the analysis error ε to be negligibly small (similar to the work of Ng 16 and Geraci 1 ).…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Mohanamuraly

Müller

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

In this work we propose, analyse, and demonstrate a new adjoint-based multilevel multifidelity Monte Carlo framework called FastUQ. The framework unifies the multifidelity analysis of Ng 1 , multilevel multifidelity analysis of Geraci 2 and an adjoint error correction surrogate model due to Ghate 3. The optimal mean squared error estimator shows that introducing multilevel in a multifidelity framework guarantees reduction in computational cost. Moreover, unlike the surrogate model of Ghate 3 , the method does not suffer from the curse of dimensionality. FastUQ is demonstrated here to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis considering the adjoint sensitivities of multiple quantities of interest (QoI). The proposed method achieves a reduction of 70% in computational cost in predicting the mean quantities like total-pressure loss and mass flow rate compared to state-of-art MLMC method. The robustness of the method is shown in application to the highly non-linear case of a heavily loaded turbine cascade operating at off-design conditions.

show abstract

Section: Insights On Model Correlation and Optimal Samplingmentioning

confidence: 99%

“…Where

{\tilde{G}}_{m}^{MC}

is an estimate of the approximation‐model mean

𝔼 [G_{m}^{MC}]

Section: Problem Formulationmentioning

confidence: 99%

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

Mohanamuraly

Müller

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Moving away from the multi-level/multi-index paradigm, multi-fidelity methods that are based on different physical models rather than multiple discretizations have been proposed, e.g., in [25][26][27][28][29].…”

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

View full text Add to dashboard Cite

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.

show abstract

“…Another possibility when dealing with uncertainty quantification is the use of variable fidelity methods in combination with Multi Level Monte Carlo approaches [24,25]. However, several levels of fidelity for a given black box problem are not always available, and the number of samples required to accurately compute statistics for large scale industrial problems is still very large.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach for quantile optimization problems with high-dimensional uncertainty sources

Sabater

Maître

Congedo

et al. 2021

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

Continuation Multilevel Monte Carlo Evolutionary Algorithm for Robust Aerodynamic Shape Design

Cited by 13 publications

References 31 publications

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

An adjoint‐assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

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

A Bayesian approach for quantile optimization problems with high-dimensional uncertainty sources

Contact Info

Product

Resources

About