  In many areas of engineering, nonlinear numerical analysis is playing an
increasingly important role in supporting the design and monitoring of
structures. Whilst increasing computer resources have made such formerly
prohibitive analyses possible, certain use cases such as uncertainty
quantification and real time high-precision simulation remain computationally
challenging. This motivates the development of reduced order modelling methods,
which can reduce the computational toll of simulations relying on mechanistic
principles. The majority of existing reduced order modelling techniques involve
projection onto linear bases. Such methods are well established for linear
systems but when considering nonlinear systems their application becomes more
difficult. Targeted schemes for nonlinear systems are available, which involve
the use of multiple linear reduction bases or the enrichment of traditional
bases. These methods are however generally limited to weakly nonlinear systems.
In this work, nonlinear normal modes (NNMs) are demonstrated as a possible
invertible reduction basis for nonlinear systems. The extraction of NNMs from
output only data using machine learning methods is demonstrated and a novel
NNM-based reduced order modelling scheme introduced. The method is demonstrated
on a simulated example of a nonlinear 20 degree-of-freedom (DOF) system.
