Generalized Polynomial Chaos for Non-intrusive Uncertainty Quantification in Computational Fluid Dynamics

Couaillier, Vincent; Savin, Éric

doi:10.1007/978-3-319-77767-2_8

Cited by 6 publications

(4 citation statements)

References 65 publications

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“…Because the two input distributions are uniform, following the Wiener-Askey scheme [10] for optimal convergence, we use Legendre polynomials for the basis functions. Since the uncertainty dimension is d = 2 < 4, we use the full quadrature to solve Equation (12). In addition, with d = 2, there is no need to limit the number of polynomial coefficients, so we choose a q-norm of 1.…”

Section: Linear Stringmentioning

confidence: 99%

“…Furthermore, for problems with low dimensionality (small number of uncertain inputs) gPC is much faster in converging to the solution than traditional methods, such as the Monte Carlo (MC) method. Generalized Polynomial Chaos is a well established procedure in uncertainty quantification and sensitivity analysis of computational fluid dynamics (CFD) simulations, see e.g., [11,12] and the references therein. It has been applied to study, for example, the dynamics of vehicles [13] and train wagons [14].…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty Quantification in Mooring Cable Dynamics Using Polynomial Chaos Expansions

Paredes

Eskilsson

Engsig-Karup

2020

JMSE

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Mooring systems exhibit high failure rates. This is especially problematic for offshore renewable energy systems, like wave and floating wind, where the mooring system can be an active component and the redundancy in the design must be kept low. Here we investigate how uncertainty in input parameters propagates through the mooring system and affects the design and dynamic response of mooring and floaters. The method used is a nonintrusive surrogate based uncertainty quantification (UQ) approach based on generalized Polynomial Chaos (gPC). We investigate the importance of the added mass, tangential drag, and normal drag coefficient of a catenary mooring cable on the peak tension in the cable. It is found that the normal drag coefficient has the greatest influence. However, the uncertainty in the coefficients plays a minor role for snap loads. Using the same methodology we analyze how deviations in anchor placement impact the dynamics of a floating axi-symmetric point-absorber. It is shown that heave and pitch are largely unaffected but surge and cable tension can be significantly altered. Our results are important towards streamlining the analysis and design of floating structures. Improving the analysis to take into account uncertainties is especially relevant for offshore renewable energy systems where the mooring system is a considerable portion of the investment.

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Section: Linear Stringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Mooring Cable Dynamics Using Polynomial Chaos Expansions

Paredes

Eskilsson

Engsig-Karup

2020

JMSE

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“…In particular, non-intrusive UQ methods [26] [27] are appealing because they decouple the deterministic solution of the governing equations (considered in a black-box fashion) from the statistical analysis on the input-QoI relationship. In engineering applications, this strategy is particularly convenient given the vast legacy of complex computational codes, which cannot be customized intrusively for UQ analysis.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems

Wang,

Broccardo,

Song

2020

Preprint

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Since the early 1900s, numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as solved when a complete or partial probabilistic description on the quantity of interest (QoI) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond mere probabilistic descriptions. In fact, to gain a full understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoI, especially when the QoI solution is obtained in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: 1) an illustrative example with hypothetical stochastic processes input and output; 2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and 3) a simplified shearbuilding model subjected to a stochastic ground motion excitation.

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“…This technique provides a straightforward way to derive Sobol' indices from model representation coefficients (Crestaux et al, 2009). Thanks to these advantages, GPC surrogates have been recently applied for GSA in environmental modelling (Sochala and Le Maître, 2013;Couaillier and Savin, 2019;Kaintura et al, 2018;Zoccarato et al, 2020;Friedman et al, 2021).…”

mentioning

confidence: 99%

Sensitivity Analysis of Factors Controlling Earth Fissures Due To Excessive Groundwater Pumping

Friedman

Teatini

et al. 2022

Preprint

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Aseisimic earth fissures are complex consequences of groundwater withdrawal and natural hydrogeologic conditions. This paper aims to improve the understanding of the mechanism of earth fissuring and investigate the relative importance of various factors to fissure activity, including bedrock geometry, piezometric depletion, compressibility and thickness of the exploited aquifer. For these purposes, a test case characterized by an impermeable and incompressible rock ridge in a subsiding basin is developed, where stress/displacement analyses and fissure state are predicted using an interface finite element model. Three different methods for global sensitivity analysis are used to quantify the extent of the fissure opening to the aforementioned factors. The conventional sampling based Sobol' sensitivity analysis is compared to two surrogate based methods, the general polynomial chaos expansion based Sobol' analysis and a feature importance evaluation of a gradient boosting decision tree model. Numerical results indicate that earth fissure is forming in response to tensile stress accumulation above the ridge associated to pore pressure depletion, inducing the fissure opening at land surface with further downward propagation. Sensitivity analysis highlights that the geometry of bedrock ridge is the most influential feature. Specifically, the fissure grows more when the ridge is steeper and closer to the land surface. Pore pressure depletion is a secondary feature and required to reach a certain threshold to activate the fissure. As for this specific application, the gradient boosting tree is the most suitable method for its better performance in capturing fissure characteristics.

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Generalized Polynomial Chaos for Non-intrusive Uncertainty Quantification in Computational Fluid Dynamics

Cited by 6 publications

References 65 publications

Uncertainty Quantification in Mooring Cable Dynamics Using Polynomial Chaos Expansions

Uncertainty Quantification in Mooring Cable Dynamics Using Polynomial Chaos Expansions

Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems

Sensitivity Analysis of Factors Controlling Earth Fissures Due To Excessive Groundwater Pumping

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