Mathematical Model Identification of Self-Excited Systems Using Experimental Bifurcation Analysis Data

Self-excited vibrations can be found in many engineering applications such as flutter of aerofoils, stick-slip vibrations in drill strings, and wheel shimmy. These self-excited vibrations are generally unwanted since they can cause serious damage to the system. To avoid such phenomena, an accurate mathematical model of the system is crucial. Self-excited systems are typically modelled as dynamical systems with Hopf bifurcations. The identification of such non-linear dynamical system from data is much more challenging compared to linear systems. In this research, we propose two different mathematical model identification methods for self-excited systems that use experimental bifurcation analysis data. The first method considers an empirical mathematical model whose coefficients are identified to fit the measured bifurcation diagram. The second approach considers a fundamental Hopf normal form model and learns a data-driven coordinate transformation mapping the normal form state-space to physical coordinates. The approaches developed are applied to bifurcation data collected on a two degree-of-freedom flutter rig and the two methods show promising results. The advantages and disadvantages of the methods are discussed.