Summary
Multiple-degree-of-freedom (MDOF) linear dynamical systems can be exactly decomposed into single-degree-of-freedom (SDOF) oscillators via proper orthogonal decomposition (POD); however, techniques based on linear mappings do not generalise to nonlinear systems. Machine learning approaches have been proposed as a means to decompose/decouple nonlinear systems via nonlinear transformations. Normalising flows (NFs) map complex distributions onto a simplified, user-defined latent space. The current work proposes an augmented linear state-space model as the target space, and uses continuous NFs to solve a neural ordinary differential equation (ODE) that defines the nonlinear map from the data distribution to the latent, decomposed space. This approach is demonstrated using a simulated two-degree-of-freedom (2DOF), lumped-mass system with a cubic spring.
