Data-Driven Modeling of Linear and Nonlinear Dynamic Systems for Noise and Vibration Applications

Data-driven modeling can help improve understanding of the governing equations for systems that are challenging to model. In the current work, the Sparse Identification of Nonlinear Dynamical systems (SINDy) is used to predict the dynamic behavior of dynamic problems for NVH applications. To show the merit of the approach, the paper demonstrates how the equations of motions for linear and nonlinear multi-degree of freedom systems can be obtained. First, the SINDy method is utilized to capture the dynamic behavior of linear systems. Second, the accuracy of the SINDy algorithm is investigated with nonlinear dynamic systems. SINDy can output differential equations that correspond to the data. This method can be used to find equations for dynamical systems that have not yet been discovered or to study current systems to compare with our current understanding of the dynamical system. With this amount of flexibility, SINDy can be used for NVH applications to help analyze vibration-related datasets as the study shows that SINDy results are consistent with ODE solutions. This study demonstrates how SINDy can accurately replicate mature known dynamical system models to highlight its potential to extract equations for more complex systems whose dynamic equations are challenging or impossible to obtain.