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

Memetic simulated annealing for data approximation with local-support curves

This paper introduces a new memetic optimization algorithm called MeSA (Memetic Simulated Annealing) to address the data fitting problem with local-support free-form curves. The proposed method hybridizes simulated annealing with the COBYLA local search optimization method. This approach is further combined with the centripetal parameterization and the Bayesian information criterion to compute all free variables of the curve reconstruction problem with B-splines. The performance of our approach is evaluated by its application to four different shapes with local deformations and different degrees of noise and density of data points. The MeSA method has also been compared to the non-memetic version of SA. Our results show that MeSA is able to reconstruct the underlying shape of data even in the presence of noise and low density point clouds. It also outperforms SA for all the examples in this paper.This work has been supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under grants TEC2013-47141-C4-R (RACHEL) and #TIN2012-30768 (Computer Science National Program) and Toho University (Funabashi, Japan)

Firefly algorithm for polynomial Bézier surface parameterization

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy

Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunologicalbased approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data