Output Based Dimensionality Reduction of Geometric Variability in Compressor Blades

A method for reducing the dimensionality of systems with high stochastic dimension is presented. The singular value decomposition of randomly sampled Jacobian matrices is used to determine the directions in the input space that have the largest impact on the behavior of the system. By considering only these dominant directions, it is possible to dramatically reduce the number of dimensions required to parameterize the system. This approach is used to reduce the number of dimensions required to predict the performance of turbomachinery components subject to geometric variability introduced during the manufacturing process. We apply this framework to analyze a compressor blade with random geometric variability and construct a surrogate model of performance that accurately predicts the compressor performance.