Parameter spaces are the set of all possible combinations of values for all the different parameters contained in a particular model. Reducing the dimensions of these spaces is a powerful aid for model-based design studies. Identifying important parameters, or key 'subspaces' of interest can result in more efficient design representations and faster design cycle times. For instance, if one is designing an aeroplane wing's aerofoil, and if only 3 of the 200 design parameters are important, why use the remaining 197?
Explaining the science
This field is grounded in methods for identifying structure in high-dimensional design spaces and parameterisations. High dimensional data occurs when the number of features of a dataset (attributes, independent variables etc) is greater than the number of samples (data points, instances). This project leverages ideas from dimension reduction, active 'subspaces' - parts of a larger parameter spaces - and ridge approximations.
This project involves a answering a number of challenges and questions. The first is how to identify what the important parameters are in, particularly high-dimensional spaces or indeed the key 'subspaces'. Once identified how do you empower a better understanding of the governing physics of the problem - e.g. flow over an aerofoil. Finally, how do you leverage the fact that a large majority of parameters are not important from the perspective of manufacturing? Can they be used to specify more design and performance-centric tolerances?
The work being developed to answer the challenges and questions raised above will be of use to the design and manufacturing of aerospace components, as in the example above of an aerofoil design.