On the application of generative adversarial networks for nonlinear modal analysis. (1st March 2022)

• Record Type: Journal Article
• Authors: Tsialiamanis, G.; Champneys, M.D.; Dervilis, N.; Wagg, D.J.; Worden, K.
• Is Part Of: Mechanical systems and signal processing. Volume 166(2022)
• Publication Date: 2022-03-01
• Subjects: Generative adversarial networks (GANs) -- CycleGAN -- Nonlinear modal analysis -- Inductive biases; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2021.108473
• Languages: English
• ISSNs: 0888-3270

Abstract

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. Highlights: Cycle-GANs are used to define mappings between modal and physical coordinates. An assembly of neural networks is used to enforce orthogonality of the mode shapes. Statistical independence of modal coordinates is imposed by predefining the modal space. Orthogonality in the frequency domain is used to pick the most efficient decomposition. The effectiveness of the method is demonstrated on simulated and experimental systems.