Active Subspace Development of Integrally Bladed Disk Dynamic Properties due to Manufacturing Variations

Abstract

The impact of geometry variations on integrally bladed disk eigenvalues is investigated. A large population of industrial Bladed Disks (Blisks) are scanned via a structured light optical scanner to provide as-measured geometries in the form of point-cloud data. The point cloud data is transformed using Principal Component Analysis that results in a Pareto of Principal Components (PCs). The PCs are used as inputs to predict the variation in a Blisk’s eigenvalues due to geometry variations from nominal when all blades have the same deviations. A large subset of the PCs are retained to represent the geometry variation, which proves challenging in probabilistic analyses because of the curse of dimensionality. To overcome this, the dimensionality of the problem is reduced by computing an active subspace that describes critical directions in the PC input space. Active variables in this subspace are then fit with a surrogate model of a Blisk’s eigenvalues. This surrogate can be sampled efficiently with the large subset of PCs retained in the active subspace formulation to yield a predicted distribution in eigenvalues. The ability of building an active subspace mapping PC coefficients to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.

PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK)

“…A. Beck, Brown, Kaszynski, & Carper, 2018), , (D. L. Gillaugh, Kaszynski, Brown, Johnston, & Slater, 2018), (D. L. Gillaugh, Kaszynski, Brown, Beck, & Slater, 2019) PVGeo (github.com/OpenGeoVis/PVGeo) is a Python package of VTK-based algorithms to analyze geoscientific data and models. PyVista is used to make the inputs and outputs of PVGeo's algorithms more accessible and to streamline the process of visualizing geoscientific data.…”

A dimension-reduction metamodeling approach to simulation-based uncertainty quantification problems with high dimensionalities

“…Studies on utilizing the AS method with combinations of various metamodels for highdimensional engineering problems can be found in. [29][30][31][32][33][34][35] Despite great efforts devoted to DR, most methods developed in the open literature were focused on combating high-dimensional inputs with scalar value outputs. As for a high-dimensional problem with a limited number of scalar value outputs, the AS method can be used to search an independent AS for each output quantity.…”

A Lanczos-Stieltjes method for one-dimensional ridge function approximation and integration

“…Several of these exploratory approaches for estimating ridge directions and generating shadow plots have revealed one-dimensional ridge structure in a range of computational science applications, including wind farm modeling [46], aerospace design [55,36,3,42], hypersonic vehicle modeling [15], turbine manufacturing [61,2], hydrologic models [45,29], and energy models [32,10,18]. Figure 1 shows shadow plots from several applications demonstrating the near one-dimensional ridge structure.…”