Оценка точности и сходимости задачи топологической оптимизации с применением нейронных сетей при различных стратегиях формирования топологии

Evaluation of the accuracy and convergence of a topological optimization problem using neural networks under various topology generation strategies

Topological optimization methods are becoming an integral part of aircraft structural design. In addition to the development of classical topological optimization methods, neural networks have also found their place in this field. There are many applications of neural networks to topological optimization problems. This work employs a feedforward neural network, which is used to reparameterize design variables using neural network parameters – weights and biases. The problem addressed was the cantilever bending of a plate under a plane stress state and subjected to a vertical concentrated force at the center of its right edge. Two types of studies were conducted. The first type involves the direct use of a neural network, where the input values are the coordinates of the geometric centers of the finite elements; the second type involves transforming the input values from coordinate space into the space of Fourier expansion coefficients. For each type of study, problems were solved using various filtering and projection techniques and methods to avoid convergence to a local minimum during the solution process, as well as with different material interpolation functions. A total of 1,371 problems were solved during the study. The results of the study are the value of the objective function and the relative value of the resulting volume. The study revealed that not all classical techniques for improving and preventing convergence to a local minimum for the topological optimization problem lead to adequate results. The «rational material approximation» interpolation function yields the greatest number of acceptable results.