Incorporating Implicit Condensation into Data-Driven Reduced-Order Models for Nonlinear Structures

The global climate effort is increasingly dependent on lightweight, flexible designs to provide engineering solutions capable of meeting ambitious emissions targets. Examples of these designs include high-aspect-ratio wings, which are capable of achieving extended flight times using significantly less energy, but their complexity introduces geometric nonlinearity to the system, leading to a substantial increase in complexity. Although these nonlinear dynamics can be accurately modelled using finite element (FE) software, the required magnitude of such models is extremely computationally expensive, preventing their use in real-time applications or extensive modelling procedures. Non-intrusive reduced-order models (NIROMs) for nonlinear behaviour are of great interest to the mechanical engineering community, as they are capable of capturing the full system dynamics using a significantly reduced coordinate system (typically a subset of the vibration modes). However, the generation of reliable NIROMs remains an active challenge. This chapter combines the projection-based strategy adopted by the implicit condensation method with recent results from the field of machine learning to create a novel NIROM generation technique based on time series data. Specifically, a variational recurrent autoencoder is applied to the system dynamics on a reduced modal basis. To complement the ability of VRAEs to reproduce time series and create statistically consistent synthetic data, a second decoder is added to recreate the true parameterization of the nonlinear system of equations.