Aplicação de modelos substitutos baseados em redes neurais artificiais na otimização de estruturas laminadas

Abstract

The field of structural optimization is becoming increasingly present in engineering offices in the search for more efficient designs. However, the computational cost to perform an optimization problem can be very high, especially when dealing with complex structures without analytical solution, where numerical methods such as the Finite Element Method (MEF) or Isogeometric Analysis (AIG) are necessary. Thus, new approaches have been developed, to reduce the cost of processing. Surrogate models are based on statistical and computational techniques to replace costly numerical analyses by efficient and accurate approximate solutions. One well-known and applied technique is the Artificial Neural Networks (RNA), since they can handle nonlinear problems. The objective of the present work is to study the application of Multilayer Perceptron (MLP) Networks and Radial Basis Functions (RBF) Networks to replace the numerical analysis methods, evaluating the influence of each technique on the optimization time and the ability to recognize and simulate the behavior of a software of analysis of laminated structures. The first problem was that of maximizing the critical load, whose analytical solution is known. With this problem, it was possible to identify how sampling techniques (i.e. Latin Hypercube, Hammersley and Optimized Latin Hypercube) and the sample size influenced the accuracy of the surrogate model. Then, the optimization of a laminated cylindrical shell with the objective of minimizing its displacements was also considered. In this case, the surrogate models were trained using results obtained by Isogeometric Analysis (IGA). It can be noticed, that the sampling techniques had little influence for low complexity problems, since all methods lead to good results. In addition, the MLP and RBF networks by interpolation presented better results for a highly complex problem. Based on the training, it was observed that the RBF by interpolation was more advantageous, since the training time was shorter. As for the number of sampling points, the relationship provided by Amouzgar and Strömberg (2016) was sufficient for the problems studied. Optimized Latin Hypercube presented the best results for the cases studied. Finally, use of surrogate models allowed a significant reduction in processing time.