Comparison of the CSRT and the CST parameterization methods

Class Shape Refinement Transformation (CSRT) is a new shape parameterization method developed by adding the Refinement Function to the Class Shape Transformation (CST) to enbance the ability of local region shape definition. Based on the representation residuals and the condition numbers of linear systems in the parameterization process, a study is performed on the differences in the precision and the numerical uniqueness between the two parameterization methods mentioned above. Using the CSRT and CST methods respectively with the same parameter number, zero-lift wave drag optimizations and the corresponding result comparisons of the supersonic wing-body are carried out using the Far-field Composite Element (FCE) wave drag optimization method. The superior result is obtained by the two-level optimization based on CSRT, yielding a 34.7% reduction of wave drag. It is suggested that in comparison with the CST method, although the CSRT method requires more parameters to achieve the similar precision, its numerical uniqueness degrades much more slowly. Two-level shape optimizations based on the CSRT method, may have some more applicability yielding superior results than that of single-level optimizations based on the CST method.