On the application of generative adversarial networks for nonlinear modal analysis

TL;DR

This paper introduces a novel machine learning approach using cycle-GANs for nonlinear modal analysis, enabling the separation of modes and accurate nonlinear superposition in structures with nonlinearities.

Contribution

It develops a cycle-GAN-based scheme for nonlinear modal analysis that maintains mode orthogonality and provides accurate nonlinear superposition, advancing beyond linear methods.

Findings

Effective mode separation demonstrated on simulated data

Accurate nonlinear superposition achieved

Method validated on experimental nonlinear system

Abstract

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.