Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements

TL;DR

This paper introduces an ensemble WSINDy method to identify PDE-based governing equations from full-field laser vibrometry data, enabling material property estimation and uncertainty quantification for beam-like structures.

Contribution

The work develops an ensemble WSINDy approach for PDE discovery from experimental data, providing uncertainty estimates and validating results with finite element simulations.

Findings

Successfully identified Euler-Bernoulli beam PDEs from experimental data

Estimated Young's moduli for aluminum and composite materials

Achieved reasonable accuracy in PDE simulation comparisons

Abstract

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.