Turbomachinery Active Subspace Performance Maps

Seshadri, Pranay; Shahpar, Shahrokh; Constantine, Paul G.; Parks, Geoffrey T.; Adams, Mike

doi:10.1115/1.4038839

Cited by 43 publications

(35 citation statements)

References 12 publications

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“…The second term, which depends only upon the covariance function, is known as the complexity penalty, while the third term is simply a normalizing constant. The problem of computing the maximum in (35) can be readily solved via a gradient-based optimizer; formulas for the gradients of log p with respect to the hyperparameters are given in section 5.9 of [33].…”

Section: Connections Between Ridge Subspaces and Active Subspacesmentioning

confidence: 99%

“…In their work investigating the use of active subspaces for learning turbomachinery aerodynamic pedigree rules of design, the authors of [35] parameterize an aero-engine fan blade with 25 design variables-five degrees of freedom defined at five spanwise locations. Once the geometry is generated, the mesh generation and flow solver codes described in [35] are used to solve the Reynolds average Navier Stokes equations (RANS) for the particular blade design; a post-processing routine is then utilized for estimating the efficiency-our quantity of interest. In the aforementioned paper, the authors run a design of experiment (DOE) with 548 different designs for estimating the active subspaces via a global quadratic model, which required estimating 351 polynomial coefficients.…”

Section: 2mentioning

confidence: 99%

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Dimension Reduction via Gaussian Ridge Functions

Seshadri¹,

Yuchi²,

Parks³

2019

SIAM/ASA J. Uncertainty Quantification

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Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting between techniques rooted in statistical regression and those rooted in approximation theory. This sets the stage for our new algorithm that approximates what we call a Gaussian ridge function-the posterior mean of a Gaussian process on a dimensionreducing subspace-suitable for both regression and approximation problems. To compute this subspace we develop an iterative algorithm that optimizes over the Stiefel manifold to compute the subspace, followed by an optimization of the hyperparameters of the Gaussian process. We demonstrate the utility of the algorithm on two analytical functions, where we obtain near exact ridge recovery, and a turbomachinery case study, where we compare the efficacy of our approach with three well-known sufficient dimension reduction methods: SIR, SAVE, CR. The comparisons motivate the use of the posterior variance as a heuristic for identifying the suitability of a dimensionreducing subspace.

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Section: Connections Between Ridge Subspaces and Active Subspacesmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Dimension Reduction via Gaussian Ridge Functions

Seshadri¹,

Yuchi²,

Parks³

2019

SIAM/ASA J. Uncertainty Quantification

Self Cite

View full text Add to dashboard Cite

show abstract

“…More recently (and of greater relevance to this work), Seshadri et al (25) detail methods for generating turbomachinery active subspace performance maps. These 2D contour plots illustrate and quantify the variation of key flow performance metrics with different designs-even when the number of design variables is greater than two.…”

Section: Introductionmentioning

confidence: 99%

“…24 in Ref. (25)), where the contours reflect the changes in pressure ratio, flow capacity and efficiency with a change in the design of the blade. Their work raises several critical questions-both from a computational perspective and from a turbomachinery design standpoint-motivating our paper.…”

Section: Introductionmentioning

confidence: 99%

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Supporting multi-point fan design with dimension reduction

et al. 2020

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Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

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Kernel‐based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

Romor

Tezzele

Lario

et al. 2022

Numerical Meth Engineering

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Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel‐based nonlinear method. In particular, we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric computational fluid dynamics application solved with the discontinuous Galerkin method.

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Turbomachinery Active Subspace Performance Maps

Cited by 43 publications

References 12 publications

Dimension Reduction via Gaussian Ridge Functions

Dimension Reduction via Gaussian Ridge Functions

Supporting multi-point fan design with dimension reduction

Kernel‐based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

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