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Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities

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Abstract

A method is introduced for the identification of the nonlinear governing equations of dynamical systems in the presence of discontinuous and nonsmooth nonlinear forces, such as the ones generated by frictional contacts, based on noisy measurements. The so-called Physics Encoded Sparse Identification of Nonlinear Dynamics (PhI-SINDy) builds upon the existing RK4-SINDy identification scheme, incorporating known physics and domain knowledge in three different ways (biases). In this way, it addresses the discontinuous behavior of frictional systems when stick–slip phenomena are observed, which can not be captured by existing state-of-the-art approaches. The potential of PhI-SINDy is highlighted through a plethora of case studies, starting from a simple yet representative Single Degree of Freedom (SDOF) oscillator with a Coulomb friction contact under harmonic load, using both synthetic and experimental noisy measurements. An alternative friction law, namely the Dieterich-Ruina one, is also considered as well as a more realistic excitation time series, which was generated based on the Jonswap spectrum. Lastly, a Multi Degree of Freedom system with single and multiple friction contacts is used as a testbed, showcasing the applicability of PhI-SINDy to more complicated systems and/or multiple sources of discontinuous nonlinearities.

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Data Availibility

The datasets generated during and/or analyzed during the current study, along with the Python scripts, are available in the GitHub repository https://github.com/xristosl0610/PhI-SINDy.

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Acknowledgements

The authors would like to thank Luca Marino and Saurabh Mahajan for the helpful discussions, and valuable insights, and for providing the experimental dataset.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN, Delft, The Netherlands

    Christos Lathourakis & Alice Cicirello

  2. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    Alice Cicirello

Authors
  1. Christos Lathourakis
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  2. Alice Cicirello
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Christos Lathourakis. The first draft of the manuscript was written by Christos Lathourakis and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript

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Correspondence to Christos Lathourakis.

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Lathourakis, C., Cicirello, A. Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09652-2

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