Creating Data-Driven Reduced-Order Models for Nonlinear Vibration via Physics-Informed Neural Networks

Modern engineering solutions often aim to improve the energy efficiency of their structures by including lightweight, flexible, and slender designs. In practice, it is not always possible to maximise these characteristics and hence the efficiency of the structures, as they exhibit complex, nonlinear structural dynamics. Unless this behaviour is accurately predicted or controlled, the system may encounter extremely destructive behaviour, which can lead to catastrophic mechanical failure. Non-intrusive reduced-order models (NIROMs)—which project the system dynamics onto a reduced set of modes and approximate the nonlinear components of the behaviour—have, therefore, been of great interest and have the potential to greatly increase the industrial uptake of high-efficiency, nonlinear structures. Existing methodologies for NIROM generation apply linear regression to static force and displacement cases, but this approach has previously been demonstrated to be overly dependent on the scale of these characteristics, a point that has prevented wider application. In this work, initial steps are taken to utilise physics-informed recurrent neural networks (RNNs) in place of the static step, allowing the dynamic behaviour to be more accurately captured in the NIROM. First, the use of random and periodic data series is applied in the training stage, with low-pass filtered white noise shown to provide the more reliable model. Following this, long short-term memory RNNs are developed both with and without a physics-informed loss function, with the former demonstrating faster convergence and more accurate predictions. This study represents the first steps taken in a wider project that aims to improve the accuracy and reliability of nonlinear NIROMs, so that they may be more readily applied in a real-world setting.