Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network

Abstract

Topology optimization techniques are essential for manufacturing industries, such as designing fiber-reinforced polymer composites (FRPCs) and structures with outstanding strength-to-weight ratios and light weights. In the SIMP approach, artificial intelligence algorithms are commonly utilized to enhance traditional FEM-based compliance minimization procedures. Based on an effective generalized regression neural network (GRNN), a new deep learning algorithm of compliance prediction for structural topology optimization is proposed. The algorithm learns the structural information using a fourth-order moment invariant analysis of the structural topology obtained from FEA at different iterations of classical topology optimization. A cantilever and a simply supported beam problem are used as ground-truth datasets, and the moment invariants are used as independent variables for input features. By comparing it with the well-known convolutional neural network (CNN) and deep neural network (DNN) models, the proposed GRNN model achieves a high prediction accuracy (R2 > 0.97) and drastically shortens the training and prediction cost. Furthermore, the GRNN algorithm exhibits excellent generalization ability on the prediction performance of the optimized topology with rotations and varied material volume fractions. This algorithm is promising for the replacement of the FEA calculation in the SIMP method, and can be applied to real-time optimization for advanced FRPC structure design.