Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities | Nonlinear Dynamics | Springer Nature Link

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.

1 Introduction An ongoing problem in structural engineering is the characterization of friction damping in structural dynamics. Frictional joints appear in most applications and industries, including aerospace, automotive, and construction. However, the friction force identification is hindered by its discontinuous nature, which is responsible for the non-smooth response of engineering systems, and frequently leads to stick–slip phenomena. To this end, alternative constitutive laws have been suggested as a solution [1, 2], and experimental data has been used to validate proposed friction…

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• Alima Deen

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