Gaussian Stochastic Process Modeling of Blend Repaired Airfoil Modal Response Using Reduced Basis Mode Shape Approach

Abstract

A machine learning (ML) approach is developed to predict effects of blend repairs on airfoil frequency, modal assurance criterion (MAC), and modal displacement. The method is demonstrated on a transonic compressor rotor airfoil. A parametric blend geometry is developed that encompassing a large range of blend geometries. This repair geometry is used to modify the airfoil surface definition and a mesh morphing process transforms the nominal finite element model to the repaired configuration. A multi-level full factorial sampling of the blend repair design space provides training data to a Guassian stochastic process (GSP) regressor. Frequency and MAC results create a vector of training data for GSP calibration, but the airfoil mode shapes require further mathematical manipulation to avoid GSP models for each nodal displacement. This paper develops a method to reduce blended airfoil mode shape emulation cost by transforming the mode shape data into a reduced basis space using principal component analysis (PCA). The coefficients of this reduced basis train a GSP that predicts results for new blended airfoils. The emulated coefficients are used with the reduced basis vectors in a reconstruction of blended airfoil mode shape. Validation data is computed at a full-factorial design that maximizes the distance from training points. It is found that large variations in modal properties from large blend repairs can be accurately emulated with a reasonable number of training points. The reduced basis approach of mode shape variation is found to more accurately predict MAC variation when compared to direct MAC emulation.