A Comparative Analysis of Nature-Inspired Optimization Approaches to 2D Geometric Modelling for Turbomachinery Applications

A vast variety of population-based optimization techniques have been formulated in recent years for use in different engineering applications, most of which are inspired by natural processes taking place in our environment. However, the mathematical and statistical analysis of these algorithms is still lacking. This paper addresses a comparative performance analysis on some of the most important nature-inspired optimization algorithms with a different basis for the complex high-dimensional curve/surface fitting problems. As a case study, the point cloud of an in-hand gas turbine compressor blade measured by touch trigger probes is optimally fitted using B-spline curves. In order to determine the optimum number/location of a set of Bezier/NURBS control points for all segments of the airfoil profiles, five dissimilar population-based evolutionary and swarm optimization techniques are employed. To comprehensively peruse and to fairly compare the obtained results, parametric and nonparametric statistical evaluations as the mathematical study are presented before designing an experiment. Results illuminate a number of advantages/disadvantages of each optimization method for such complex geometries’ parameterization from several different points of view. In terms of application, the final appropriate parametric representation of geometries is an essential, significant component of aerodynamic profile optimization processes as well as reverse engineering purposes.