Abstract
In recent years, sophistication of mechanical systems complicates derivation of their governing equations. On the other hand, with the recent development of data-driven modeling methods, discovery of the governing equation of relatively simple dynamical system is becoming feasible from measurement data. However, when mechanical systems involve piecewise-linear nonlinearity such as junction points or cracks, it is difficult to identify their governing equations using these methods. Furthermore, piecewise-linear systems have an issue that it is difficult to identify the switching point in the phase space where the system changes its state. To overcome this issue, this study proposes a method to identify not only the governing equations but also the switching points for piecewise-linear systems. It is shown that the proposed method can be successfully applied to generate the governing equation of a single degree of freedom oscillator that involves repetitive contacts with a spring. This dynamic model is a piecewise-linear system and has two states: the system with a spring and without the spring. In addition, an experimental apparatus was built and the proposed method was applied to the measured data. By optimizing the threshold value and order of candidate functions, it was able to derive governing equations that reproduce the dynamics of the experimental equipment.
