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2023 | OriginalPaper | Buchkapitel

6. On the Use of Cycle-Consistent Generative Adversarial Networks for Nonlinear Modal Analysis

verfasst von: Georgios Tsialiamanis, Max D. Champneys, David J. Wagg, Nikolaos Dervilis, Keith Worden

Erschienen in: Topics in Modal Analysis & Parameter Identification, Volume 8

Verlag: Springer International Publishing

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Abstract

Linear modal analysis has been the major tool for analysis and design of structures. However, the method is restricted to structures with linear behaviour, and application of traditional methods in structures with nonlinearities yields results that do not typically have the desired characteristics of modal analysis. In the current work, a machine learning approach to performing nonlinear modal analysis is proposed. The idea is motivated by the Shaw–Pierre definition of nonlinear normal modes. The machine learning algorithm used is the cycle-consistent generative adversarial network (cycle-GAN). The algorithm provides a forward and inverse mapping between two spaces, which in the current application are the physical coordinate space and the modal space of the studied structures. Together with the cycle-GAN, an assembly of neural networks is used to tune the mappings so that they are angle-preserving (conformal) mappings; in this way, the orthogonality of the mode shapes is imposed during training. A criterion with a view to selecting the best model between the training epochs of the neural networks, based on the decomposition of the modes in the power spectral densities of the modal coordinates, is also introduced. The algorithm is tested on two simulated systems with cubic nonlinearities and different degrees of freedom. Moreover, it is tested on data recorded from an experimental structure, which has a harsh nonlinearity (impact nonlinearity). The results of the applications reveal that the algorithm is able to efficiently provide a decomposition of the modes in terms of the power spectral densities of the modal coordinates, provide an inverse mapping (from the modal space back to the natural coordinates), which is an essential part of modal analysis, and also provide modal coordinates that are statistically largely uncorrelated. The proposed approach seems to outperform previous approaches compared to both the decomposition provided and the definition of the inverse mapping.
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Metadaten
Titel
On the Use of Cycle-Consistent Generative Adversarial Networks for Nonlinear Modal Analysis
verfasst von
Georgios Tsialiamanis
Max D. Champneys
David J. Wagg
Nikolaos Dervilis
Keith Worden
Copyright-Jahr
2023
DOI
https://doi.org/10.1007/978-3-031-05445-7_6