Shape functional optimization with restrictions boosted with machine learning techniques

Authors:
M. López;J. Martínez;J. M. Matías;J. Taboada;J. A. Vilán
Affiliations:
Department of Mechanical Engineering, University of Vigo, 36310 Vigo, Spain;Department of Environmental Engineering, University of Vigo, 36310 Vigo, Spain;Department of Statistics, University of Vigo, 36310 Vigo, Spain;Department of Environmental Engineering, University of Vigo, 36310 Vigo, Spain;Department of Mechanical Engineering, University of Vigo, 36310 Vigo, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

Shape optimization is a widely used technique in the design phase of a product. Current ongoing improvement policies require a product to fulfill a series of conditions from the perspective of mechanical resistance, fatigue, natural frequency, impact resistance, etc. All these conditions are translated into equality or inequality restrictions which must be satisfied during the optimization process that is necessary in order to determine the optimal shape. This article describes a new method for shape optimization that considers any regular shape as a possible shape, thereby improving on traditional methods limited to straight profiles or profiles established a priori. Our focus is based on using functional techniques and this approach is, based on representing the shape of the object by means of functions belonging to a finite-dimension functional space. In order to resolve this problem, the article proposes an optimization method that uses machine learning techniques for functional data in order to represent the perimeter of the set of feasible functions and to speed up the process of evaluating the restrictions in each iteration of the algorithm. The results demonstrate that the functional approach produces better results in the shape optimization process and that speeding up the algorithm using machine learning techniques ensures that this approach does not negatively affect design process response times.