Enhanced model reduction method via combined supervised and unsupervised learning for real-time solution of nonlinear structural dynamics

To develop a predictive digital twin for future structural design or maintenance, a real-time solution for structural analysis is essential. However, a large-scale nonlinear structural analysis still requires recursive procedures that incur high computational costs. In this study, we propose a neural-network-based model order reduction method for a given parameter space. It is realized by combining an autoencoder with a deep neural network to efficiently address high-dimensional data. The key aspects of the proposed approach include the integration of projection-based model reduction for data mining and multistep model reduction. Moreover, the combination of two network architectures, which can learn a direct relationship between the parameter and the nonlinear displacement field, was considered. Transfer learning over the time span of interest was performed to broaden the time history prediction of nonlinear structural dynamics. The proposed approach was compared with the full-order model by considering numerical examples of nonlinear structural dynamics to demonstrate its efficiency and accuracy. As a result, the real-time prediction of nonlinear structural dynamics was achieved. Moreover, the proposed approach showed excellent computational efficiency in parameterized nonlinear structural analyses.