基于深度学习的多参数结构拓扑优化方法

Multi-Parameter Structural Topology Optimization Method Based On Deep Learning

摘要:

基于有限元的拓扑优化方法，需要多次有限元求解与迭代，由此消耗了大量的计算资源与时间。为提高拓扑优化效率，本文以悬臂梁结构拓扑优化设计为例，引入过滤半径、体积分数、载荷作用点及加载方向4个优化参数，提出了一种基于残差连接的生成式卷积神经网络（CNN）模型，分析了样本数量及损失函数类型对生成式CNN模型精度的影响规律。结果表明：所建立的生成式CNN模型具有较高的精度与泛化能力，模型预测值与有限元仿真结果平均结构相似度可达0.972 0，平均绝对误差为0.014 3。该模型预测耗时仅为有限元法的0.004 1倍，显著提升了结构拓扑优化效率。

Abstract:

The traditional topology optimization method based on finite element method requires multiple finite element calculation and iterations， which consumes a lot of computational resources and time. In order to improve the efficiency of topology optimization， the paper takes topology optimization of cantilever beam as an example and proposes a generative convolutional neural network （CNN） model based on residual connections， which considers four optimization parameters： filter radius， volume fraction， loading point and loading direction. And the influence of different loss functions and number of samples on the accuracy of generative CNN model is discussed at length. The results show that the proposed model has high accuracy and generalization ability， and the mean structural similarity index between the model prediction and finite element method can reach 0.9720， the mean absolute error is 0.0143. And the prediction time of the model is only 0.0041 of finite element method， which significantly improves the efficiency of topology optimization.