Dimensionality-reduction-based surrogate models for real-time design space exploration of a jet engine compressor blade

Design space exploration (DSE) is a systematic analysis of designs based on parameters that are varied. DSE, however, often involves computationally expensive analyses that require large amounts of time and computer resources. To overcome this obstacle, tools and methods have been developed that allow the designer to quickly explore the design space. One such tool is surrogate modeling. A surrogate model's predictions are based off the relationship between the inputs and the outputs. If this relationship is sufficiently nonlinear, a nonlinear dimensionality reduction technique may unfold the data and create a linear relationship by discovering the data's true dimensionality. The resultant surrogate has the potential to be more accurate due to the simplified relationship between the inputs and outputs. This paper uses surrogate models based on dimensionality reduction to predict finite element analysis (FEA) nodal properties of a jet engine compressor blade. Four different dimensionality reduction methods are compared, namely PCA, KPCA, ISOMAP, and LLE. The results show that nonlinear dimensionality-reduction-based surrogate models can reduce surrogate error in sufficiently nonlinear data spaces. To measure the linearity of the manifold, a new term, called the manifold distance ratio (MDR), is introduced. Nonlinear dimensionality-reduction-based surrogate models can have less error than PCA-based surrogate models when the MDR >1.7. For our application, ISOMAP-based surrogate models decreased the mean error of the surrogate for predicting nodal stresses by 35.7% compared to PCA. The lowest error in predicting the nodal coordinates was the inverse-transform-based PCA. While all errors in nodal coordinates were small, less than 0.23%, the other linear and nonlinear algorithms had between 2.4 and 3.2 times more error.