Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Modeling a dynamical system from low-sampled data
Submission Author:
Davi Saadi de Almeida Lettieri , RJ , Brazil
Co-Authors:
Davi Saadi de Almeida Lettieri, Leonardo Santos de Brito Alves
Presenter: Davi Saadi de Almeida Lettieri
doi://10.26678/ABCM.COBEM2023.COB2023-1366
Abstract
The derivation of differential equation models for experimentally observed dynamics has always been a challenge in any field of science. In general, two approaches are employed to do so. One derives such models from first-principles using a heavy dose of mathematical manipulation. In this physics-driven approach, experimental data is employed to validate the model’s accuracy. Another is based on recent developments in measurement capabilities, which can provide a wealth of information that allows optimization methods to reverse engineer these models. Arguably the most prominent method within this data-driven approach is the Sparse Identification of Nonlinear Dynamics, i.e. SINDy. It takes advantage of data wealth and model sparsity to employ linear regression techniques to cheaply estimate the nonlinear differential model. Since its release, many expansions have made SINDy even more robust and flexible. However, some obstacles still exist when trying to use this tool on experimental data. In particular, low-sampled data makes the calculation of the time derivatives required by SINDy too inaccurate for it to provide a valid model. In order to overcome this, a sample-rearranging technique was developed for low-sampled periodic data sets that span many periods. The idea is based on the fact that, even for a low sampling rate, the phase portrait topology contains all the relevant information for a periodic nonlinear regime. This technique accurately reconstructs the temporal dynamics of a single period by accordingly rearranging the available data in all other periods into it using the dynamics characteristic period. In the present paper, the method's efficacy is tested using an artificially low-sampled data set from the Lorenz equations for periodic parametric conditions. SINDy works, but only when used in conjunction with the sample-rearranging.
Keywords
reduced order model, Low-Sampled Data, SINDy, Sample-Rearranging
