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.

本研究针对传统方法中治理方程数据获取困难的问题，采用激光振动测量与稀疏非线性动态识别的弱形式（WSINDy）相结合，从全场实验数据中学习宏观治理方程。研究发现，通过集成WSINDy算法，能够有效识别出与材料特性相关的偏微分方程及其不确定性，为动态系统的非破坏性分析提供了新的思路。

基于激光全场测量的治理方程数据驱动发现的集成WSINDy