  Linear modal analysis is a useful and effective tool for the design and
analysis of structures. However, a comprehensive basis for nonlinear modal
analysis remains to be developed. In the current work, a machine learning
scheme is proposed with a view to performing nonlinear modal analysis. The
scheme is focussed on defining a one-to-one mapping from a latent `modal' space
to the natural coordinate space, whilst also imposing orthogonality of the mode
shapes. The mapping is achieved via the use of the recently-developed
cycle-consistent generative adversarial network (cycle-GAN) and an assembly of
neural networks targeted on maintaining the desired orthogonality. The method
is tested on simulated data from structures with cubic nonlinearities and
different numbers of degrees of freedom, and also on data from an experimental
three-degree-of-freedom set-up with a column-bumper nonlinearity. The results
reveal the method's efficiency in separating the `modes'. The method also
provides a nonlinear superposition function, which in most cases has very good
accuracy.
