Optimum design of nonlinear structures via deep neural network-based parameterization framework

• Published in: European journal of mechanics, A, Solids Vol. 98; p. 104869
• Main Authors: Mai, Hau T., Lee, Seunghye, Kim, Donghyun, Lee, Jaewook, Kang, Joowon, Lee, Jaehong
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01.03.2023
• Subjects: Bayesian optimization; Deep neural network; Geometric nonlinear; Hyperparameter optimization; Truss optimization; Hyperparameter optimization; Deep neural network; Bayesian optimization; Geometric nonlinear; Truss optimization
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2022.104869

In this paper, a robust deep neural network (DNN)-based parameterization framework is proposed to directly solve the optimum design for geometrically nonlinear trusses subject to displacement constraints. The core idea is to integrate DNN into Bayesian optimization (BO) to find the best optimum structural weight. Herein, the design variables of the structure are parameterized by weights and biases of the network with the spatial coordinates of all joints as the training data. A loss function of the network is built based on the predicted cross-sectional areas and deflection constraints obtained by supporting finite element analysis (FEA) and arc-length method. Accordingly, the optimum weight corresponding to the minimum loss function is indicated as soon as the complete training process. And then it is also serving as an objective of the BO for performing the hyperparameter optimization (HPO) to find the best optimum structural weight. Several illustrative numerical examples for geometrically nonlinear space trusses are examined to determine the efficiency and reliability of the proposed approach. The obtained results demonstrate that our framework can overcome the drawbacks of applications of machine learning in computational mechanics. •A deep neural network-based parameterization framework for structural optimization.•Automatic tuning of hyperparameters of the network by using Bayesian optimization.•The best optimum weight is found by training without any other algorithms.•The suggested model provides high-quality solutions and avoids the local optimum.