On the application of generative adversarial networks for nonlinear modal analysis
This work addresses a gap in structural analysis for engineers by enabling nonlinear modal analysis, but it is incremental as it applies existing machine learning techniques to a new domain-specific problem.
The paper tackled the problem of developing a comprehensive basis for nonlinear modal analysis in structural engineering by proposing a machine learning scheme using cycle-consistent generative adversarial networks (cycle-GAN) and neural networks to map from a latent modal space to natural coordinates while imposing orthogonality. The method was tested on simulated and experimental data, showing efficiency in separating modes and providing a nonlinear superposition function with very good accuracy in most cases.
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.