A fast algorithm of sensitivity filtering for BESO method based on vectorization

The checkerboard and grid-dependent phenomena often appear in the optimization results using the Bidirectional Evolutionary Structural Optimization (BESO) algorithm. The elemental sensitivity filtering is an effective method to solve such problems. However, as the size of the structure increases, the number of elements increases, and the calculation of the elemental weight factor will take a considerable amount of time. The reason is that when calculating the weight factor data of the element, it is necessary to perform multiple loop nesting, and calculate the center distance of the unit one by one. This serial algorithm makes the calculation efficiency low. By combining the idea of vectorized preprocessing of the data set in the deep learning training model, the vectorized preprocessing of the data required for the sensitivity filtering calculation was carried out. The vectorization-based elemental sensitivity filtering algorithm was deduced. The one by one scalar operation was improved as Parallelizable matrix operations. For the problem that the storage space may be too large in the vectorization algorithm, a sparse matrix was used to optimize the storage space, and a further improved Sparse algorithm was proposed. The improved BESO topology optimization process was realized through the secondary development of ABAQUS, and the calculation time was verified by using two-dimensional and three-dimensional cantilever beam examples respectively. The results show that the speedup ratio of the vectorized sensitivity filtering algorithm is up to 6 compared with the double loop algorithm, and the speedup ratio of the Sparse algorithm is up to 8. The improved algorithm greatly improves the calculation speed of the elemental weight factor and sensitivity filtering. When calculating the weight factor, the time consumption of the Sparse algorithm is slightly higher than that of the vectorization algorithm. In terms of optimizing the total time consumption, the Sparse algorithm is better than the vectorization algorithm. When there are too many units to expand the size of the structure, the vectorization algorithm may be limited by the hardware memory capacity and cannot be calculated, while the Sparse algorithm can be calculated normally. © 2023, Central South University Press. All rights reserved.