Framework for Convergence and Validation of Stochastic Uncertainty Quantification and Relationship to Deterministic Verification and Validation

Mousaviraad, Maysam; He, Wei; Diez, Matteo; Stern, Frederick

doi:10.1615/int.j.uncertaintyquantification.2012003594

Cited by 24 publications

(7 citation statements)

References 21 publications

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“…A different criterion based on the residual error between the true function and the prediction of the meta-model has been employed for the present study. Following [3], where the meta-model results are validated using the approach formulated in [9], the convergence of the meta-model has been set at 5% residual of the uncertainty quantification error (E U Q )…”

Section: Dynamic Adaptive Meta-modellingmentioning

confidence: 99%

Radial Basis Functions for Stochastic Metamodels Tailored to Aeroacoustic Applications

Iemma

Burghignoli

Rossetti

2019

25th AIAA/CEAS Aeroacoustics Conference

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The paper presents a preliminary investigation on the applicability of stochastic Radial Basis Functions (RBF) in the development of dynamically adaptive meta-models for aeroacoustic applications. The analysis focuses on the influence of the RBF kernel and the chosen stochastic parameters on the modelling of target functions of interest in the aeroacoustics of aircraft. The rationale underlying the research is related to the key role that aeroacoustics plays in the establishment of the commercial aviation scenario foreseen for the next three decades. Indeed, the sustainable development for the airborne transportation system is strongly constrained by community noise, which, nowadays, limits the increase of the capacity of the existing airports and prevents the building of new ones. In such a situation, the design of the next generation of aircraft must take into account the impact of noise on the population since the early conceptual phase of the design. This causes a substantial increase of the required computational resources, especially for unconventional, breakthrough concepts for which simple semi-empirical models are not available and the only viable strategy is computational aeroacoustics. The availability of reliable meta-models can give a significant contribution in two ways: i) in a process of multiobjective, multidisciplinary design optimization a dynamic adaptive stochastic meta-model can reduce significantly the calls to the computationally expansive tools and enhance the effectiveness of the design space exploration; ii) the versatility and applicability range of end-user tools for the estimate community noise impact can be greatly improved by fast yet accurate models of the noise signature of novel concepts. Two target functions are analysed here: the total acoustic field induced by a point source co-moving with a scattering profile, and the shielding factor along a line of observation points below the scatterer. The performance of RBF meta-models based on tailored kernels is compared to the most commonly used kernels in terms of accuracy and convergence rate. The effectiveness of the dynamic meta-model update based on uncertainty quantification is assessed for different choices of the stochastic parameter.

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Section: Dynamic Adaptive Meta-modellingmentioning

confidence: 99%

Radial Basis Functions for Stochastic Metamodels Tailored to Aeroacoustic Applications

Iemma

Burghignoli

Rossetti

2019

25th AIAA/CEAS Aeroacoustics Conference

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“…It may be noted that, here, {·} 2 stands for the elementwise square, and μ(f) and σ 2 (f) are vectors of dimension 1 + N + M. The evaluation of the integrals in (6) and (7) is often referred as Uncertainty Quantification, UQ (Najm 2009;Iaccarino 2008;Mousaviraad et al 2011). With respect to the uncertainties outlined above, different approaches may be followed for the recasting of the optimization problem.…”

Section: (C) Uncertain Evaluation Of the Functions Of Interestmentioning

confidence: 99%

“…Although surrogate models for design optimization and UQ are often very fruitful and dramatically abate the computational effort, their use is beyond the scope of the present work and, therefore, no further addressed. The interested reader is addressed to, e.g., Alexandrov and Lewis (2001), Peri and Campana (2005), Allaire and Willcox (2010) and Mousaviraad et al (2011).…”

Section: Multidisciplinary Robust Design Optimizationmentioning

confidence: 99%

“…In other words, the analysis codes may be seen as a black box, without the need of modifying their source codes; the UQ is done by embedding the deterministic analysis tool in an integration scheme. Issues related to deterministic and stochastic convergence and validation of non-intrusive UQ methods are addressed in Mousaviraad et al (2011).…”

Section: Uncertainty Quantification (Uq)mentioning

confidence: 99%

See 1 more Smart Citation

Hydroelastic optimization of a keel fin of a sailing boat: a multidisciplinary robust formulation for ship design

Diez

Peri

Fasano

et al. 2012

Struct Multidisc Optim

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The paper presents a formulation for multidisciplinary design optimization of vessels, subject to uncertain operating conditions. The formulation couples the multidisciplinary design analysis with the Bayesian approach to decision problems affected by uncertainty. In the present context, the design specifications are no longer given in terms of a single operating design point, but in terms of probability density function of the operating scenario. The optimal configuration is that which maximizes the performance expectation over the uncertain parameters variation. In this sense, the optimal solution is "robust" within the stochastic scenario assumed. Theoretical and numerical issues are addressed and numerical results in the hydroelastic optimization of a keel fin of a sailing yacht are presented.

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“…More recently, the research moved to stochastic UQ for environmental and operating conditions. Stochastic UQ studies using high-fidelity simulations for ship hydrodynamic problems have been presented in [4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

A Multi-Fidelity Adaptive Sampling Method for Metamodel-Based Uncertainty Quantification of Computer Simulations

Pellegrini¹,

Leotardi²,

Iemma³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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A multi-fidelity global metamodel is presented for uncertainty quantification of computationally expensive simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high-and low-fidelity simulations. The metamodel is based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are added where the prediction uncertainty is largest, according to an adaptive sampling procedure. The prediction uncertainty of both the low-fidelity and the error metamodel are considered for the adaptive training of the low-and high-fidelity metamodels, respectively. The method is applied to a steady fluid-structure interaction (FSI) problem of a 3D NACA 0009 stainless steel hydrofoil. Two functions are considered simultaneously, namely lift and drag coefficients, versus angle of attack and Reynolds number. Two problems are presented: in the first problem the high-fidelity evaluations are obtained through steady FSI computer simulations, whereas in the second problem they are given by available experimental data from literature. Low-fidelity evaluations are provided in both cases by steady hydrodynamic simulations. The overall uncertainty of the multi-fidelity metamodel is used as a convergence criterion.

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Framework for Convergence and Validation of Stochastic Uncertainty Quantification and Relationship to Deterministic Verification and Validation

Cited by 24 publications

References 21 publications

Radial Basis Functions for Stochastic Metamodels Tailored to Aeroacoustic Applications

Radial Basis Functions for Stochastic Metamodels Tailored to Aeroacoustic Applications

Hydroelastic optimization of a keel fin of a sailing boat: a multidisciplinary robust formulation for ship design

A Multi-Fidelity Adaptive Sampling Method for Metamodel-Based Uncertainty Quantification of Computer Simulations

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