Abstract Summary
Frictional joints are present in a plethora of applications and fields, such as the aerospace, automotive, and building industries. Therefore, an ever-important challenge in the analysis of engineering systems is the understanding of friction damping in structural dynamics. Due to its nonlinear and non-smooth nature, the available approaches, including proposing alternative constitutive laws and validating models based on experimental data, cannot deal with the identification of friction forces. One way around this is to take advantage of the rapid increase of data availability through measurements for complex engineering systems, and newly developed identification techniques of the underlying differential equations of physical problems based on noisy measurements. A promising framework called Sparse Identification of Nonlinear Dynamics (SINDy) was developed for this purpose, aiming to derive parsimonious solutions for nonlinear systems. This framework has been recently further developed by combining the principles of dictionary-based learning, which is a key concept in SINDy, with numerical analysis tools, and more specifically the 4th-order Runge-Kutta integration scheme. This approach, the so-called RK4-SINDy was proven to be more efficient when dealing with noisy and sparsely collected data, not exploring though the incorporation of physics in discovering nonlinear models. In the current work, the incorporation of physics in RK4-SINDy is investigated for identifying the governing equations of a Single-Degree-of-Freedom (SDOF) oscillator under harmonic excitation, including Coulomb friction damping. In the proposed methodology, part of the system’s equation of motion is assumed known during the identification of the vector field of the global response, incorporating in this way part of the known physics. This simple, yet representative case study, is examined using both artificially generated noisy data, as well as data obtained from an experimental setup. It is shown that this approach can lead to accurate results even for significant noise levels, while maintaining a parsimonious solution to avoid overfitting the noisy data.
