Machine learning-based state maps for complex dynamical systems: applications to friction-excited brake system vibrations

In this work, a purely data-driven approach to mapping out the state of a dynamical system over a set of chosen parameters is presented and demonstrated along a case study using real-world experimental data from a friction brake system. Complex engineering systems often exhibit a rich bifurcation behavior with respect to one or several parameters, which is difficult to grasp using experimental approaches or numerical simulations. At the same time, the growing need for energy-efficient machines that can operate under varying or extreme environmental conditions also calls for a better understanding of these systems to avoid critical transitions. The proposed method combines machine learning techniques with synthetic data augmentation to create a complete state map for a dynamical system. First, a machine learning model is trained on experimental data, picking up hidden mechanisms and complex parametric relations of the underlying dynamical system. The model is then exploited to assess the state of the system for a set of synthetically generated data to obtain a state map over the complete space spanned by the chosen parameters. In addition, an extension of the concept to a probability state map is introduced. The results indicate that the proposed method can uncover hidden variables which drive dynamical transitions between different states of a system that were previously inaccessible.