A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection

A proper-orthogonal-decomposition (POD)-based procedure has been developed to identify the tests/experiments strictly needed for modelling a complex system. The case here studied concerns the aerodynamic efficiency response of a low-pressure-turbine cascade to the variation of the most influencing flow parameters. A large number of experimental tests have been carried out to sample the design space. POD has been applied to reduce data dimensionality, identifying the rank of the problem and defining a vector subspace where data are as compact as possible. Lasso and Gaussian process regressions, complemented by cross-validation and marginal-likelihood criteria, have been used to learn parsimonious efficiency trends in the POD subspace. It will be shown that a model educated with the most orthogonal combination of data projected in the POD space performs as well as the model educated with the entire dataset. Then, it will be shown that the strictly needed tests can be iteratively localized (a priori) in the design space by means of the data-driven procedure here proposed, thus allowing for an active application. This will provide significant time reduction in the execution of tests and can be generalized to other complex systems, either of an experimental or numerical nature, even pertaining to other disciplines.