Data-Driven Modelling of Mechanical Systems Using SINDy
This project investigates the use of machine learning for modeling and estimating parameters in a mechanical system. The goal is to develop a data-driven modeling framework that can be generalized for a variety of similar but distinct systems. The small differences necessitate individual modeling of the systems when using first principles. The method investigated is the Sparse Identification of Non-linear Dynamics (SINDy), which aims to provide a sparse system of differential equations that accurately describes the system based on measurements. A number of candidate functions are defined, and a regression algorithm finds coefficients for a minimal number of these functions. The Sequentially Thresholded Least Squares (STLS) algorithm is used, promoting sparsity more than ordinary least squares. Two approaches are proposed. The first approach involves a relatively large number of candidate functions, providing accurate models but including more terms than necessary, especially for noisy data. The second approach derives a symbolic model from the Euler-Lagrange equations, limiting candidate functions to terms in the symbolic model. This approach seeks to estimate coefficients in the Euler-Lagrange equations to estimate unknown system parameters, simplifying analysis.