用激光测量+算法自动发现材料动态方程，还能估计弹性模量。
Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements
- 结合激光测振与弱形式稀疏识别法，从全场数据中找控制方程。
- 成功发现符合欧拉-伯努利梁模型的方程，并估算出两种材料的杨氏模量。
- 引入集成方法，可量化系数和模量的不确定性，适合实验力学研究者。
本研究利用激光测振技术与偏微分方程的弱形式稀疏识别方法（WSINDy for PDEs），从全场实验数据中学习宏观控制方程。实验中对两根梁状试样——一根铝材、一根IDOX/Estane复合材料——施加低频剪切波激励，测量其表面质点速度响应。将得到的时空数据输入WSINDy算法，从一组候选PDE中发现试样的有效动力学行为。所发现的PDE形式符合经典的欧拉-伯努利梁模型，据此估算了两种材料的杨氏模量。同时采用集成版WSINDy算法，获得方程系数与杨氏模量的不确定性信息。通过有限元仿真对比实验数据，结果具有合理精度。该方法结合全场实验数据与WSINDy，是发现未知控制方程、揭示动态机械系统特性的有力无损手段。
原文摘要 · Abstract (English)
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.
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