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

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 are transformed using principal component (PC) analysis that results in a Pareto of 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 is 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 coefficient to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.