Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet

Constantine, Paul G.; Emory, Michael; Larsson, Johan; Iaccarino, Gianluca

doi:10.1016/j.jcp.2015.09.001

Cited by 135 publications

(91 citation statements)

References 58 publications

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“…Nevertheless a wide range of functions of interest in engineering applications present an active subspace of dimension one or two, resulting in a great reduction of the parameter space. Among others we cite shape optimization [23], and uncertainty quantification in the numerical simulation of the HyShot II screamjet [10]. We would also like to mention some naval engineering applications of the active subspaces: coupled with boundary element method and free form deformation [41], for propeller blade design [24], and a shared subspace application for constraint optimisation [38].…”

Section: Active Subspaces For Modal Coefficient Reconstructionmentioning

confidence: 99%

A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

Demo

Tezzele

Rozza

2019

Comptes Rendus. Mécanique

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Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions -computed for properly chosen parameters, using a full-order model -in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI) -a data-driven reduced order method -with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one. * nicola.demo@sissa.it †

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Section: Active Subspaces For Modal Coefficient Reconstructionmentioning

confidence: 99%

A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

Demo

Tezzele

Rozza

2019

Comptes Rendus. Mécanique

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“…If the points in the scatter plot reveal a univariate or near univariate relationship, then the ridge approximation Equation 6 with W 1 = w is a good approximation to f (x). If the points in the scatter plot do not reveal a functional relationship, then the model Equation 6 with W 1 = w may not be appropriate.…”

Section: Validating Important Directions With Summary Plotsmentioning

confidence: 99%

Time‐dependent global sensitivity analysis with active subspaces for a lithium ion battery model

Constantine

Doostan

2017

Statistical Analysis

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Renewable energy researchers use computer simulation to aid the design of lithium ion storage devices. The underlying models contain several physical input parameters that affect model predictions. Effective design and analysis must understand the sensitivity of model predictions to changes in model parameters, but global sensitivity analyses become increasingly challenging as the number of input parameters increases. Active subspaces are part of an emerging set of tools for discovering and exploiting low‐dimensional structures in the map from high‐dimensional inputs to model outputs. We extend linear and quadratic model‐based heuristics for active subspace discovery to time‐dependent processes and apply the resulting technique to a lithium ion battery model. The results reveal low‐dimensional structure and sensitivity metrics that a designer may exploit to study the relationship between parameters and predictions.

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“…trailing edge half-thickness x 7 wedge angle x 8 wedge half-angle x 9 upper surface inflection x 10 lower surface inflection x 11 leading edge radius…”

Section: Iid Parsec Airfoilsmentioning

confidence: 99%

Active Subspaces of Airfoil Shape Parameterizations

Grey

Constantine

2017

58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties.In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.

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Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet

Cited by 135 publications

References 58 publications

A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

Time‐dependent global sensitivity analysis with active subspaces for a lithium ion battery model

Active Subspaces of Airfoil Shape Parameterizations

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