Session: MSNDC-04-01 Nonlinear Dynamics of Structures

Paper Number: 66831

Start Time: August 17, 11:10 AM

66831 - Boosting the Model Discovery of Hybrid Dynamical Systems in an Informed Sparse Regression Approach 

Harvesting models from data is a critical step in data science. More recently, it has become mainstream in many branches of engineering. Despite the acquisition is often scarce, fragmented and noisy, the measurements carry enough signatures on the dynamics such that they allow to reconstruct the underlying dynamical structure. Thus, efficient data-driven identification methods must be developed to transform raw monitoring into relevant information and behavioural models for the system. 

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identify discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In our approach, we first focus to identify the switches between the separate vector fields. Then, the dynamics among the manifolds are regressed by making use of the recent model discovery algorithm of Brunton et al. . The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro- clusters) and a rigid library of models. This allows to identify all the many possible switch points that are clustered to determine the actual discontinuity surfaces. The performances of the method are tested on two numerical examples, namely, a canonical spring–mass hopper and a free/impact electromagnetic energy harvester. These applications are characterized by the presence of a single and double discontinuity, respectively. The analyses demonstrate that in the supervised approach, i.e. where the number of discontinuities is preassigned, we are capable to determine accurately both discontinuities and set of governing equations. Nuisance in the data does not modify the computational performance in the identification of the switch conditions. It is found a great improvement in time of computation reaching the maximum achievable reliability that outperform existing data-driven identification approaches for hybrid systems. Due to its efficiency, the present approach could be implemented for rapid identification of discontinuity surfaces while collecting data in real time. The switch search algorithm is insensitive to the system complexity, enabling code to work efficiently regardless to the application and number of discontinuities.  

Presenting Author: Nico Novelli Polytechnic University of Marche

Authors:

Nico Novelli Polytechnic University of Marche
Stefano Lenci Polytechnic University of Marche
Pierpaolo Belardinelli Polytechnic University of Marche