Rubaiyat Abu Hasnat Mohammad, Thai Duy H, Nichols Jonathan M, Hutchinson Meredith N, Wallen Samuel P, Naify Christina J, Geib Nathan, Haberman Michael R, Rohde Gustavo K
Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
U.S. Naval Research Laboratory, Washington, DC, 20375, USA.
Comput Methods Appl Mech Eng. 2024 Mar 15;422. doi: 10.1016/j.cma.2024.116822. Epub 2024 Feb 7.
This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit [1].
本文提出了一种全新的数据驱动方法，用于识别动态系统的偏微分方程（PDE）参数。具体而言，我们针对动态系统在特定空间位置的解采用了一种数学“传输”模型，该模型使我们能够准确估计模型参数，包括与结构损伤相关的参数。这是通过一种新开发的数学变换——符号累积分布变换（SCDT）来实现的，该变换被证明可将一般的非线性参数估计问题转化为简单的线性回归。这种方法还有一个实际优势，即无需了解激励源（或者初始条件）。通过使用训练数据，我们设计了一种粗糙回归程序，以从在单个位置测量的PDE解中恢复不同的PDE参数。数值实验表明，与一些最近开发的机器学习方法相比，所提出的回归程序能够以更高的精度检测和估计PDE参数。此外，在一个公开可用数据集上进行的损伤识别实验有力地证明了所提方法在结构健康监测（SHM）应用中的有效性。所提出的系统识别技术的Python实现被集成到软件包PyTransKit [1] 中作为一部分。
