Decoupling nonlinear normal modes using normalising flows

Multiple-degree-of-freedom (MDOF) linear dynamical systems can be exactly decomposed into single-degree-of-freedom (SDOF) oscillators via modal analysis; however, these techniques do not necessarily generalise to nonlinear systems. Approaches based on machine learning have been proposed as a means to decompose/decouple nonlinear systems via nonlinear transformations that are learnt under the assumption that latent modal variables are statistically independent. Normalising flows are one such method of transforming complex distributions into a simplified latent space. The current paper builds on previous efforts by applying normalising flows to a simulated three-degree-of-freedom (3DOF), lumped-mass system with a cubic spring.