Physics-Constrained Data-Driven Variational Method for Discrepancy Modeling.
Physics-Constrained Data-Driven Variational Method for Discrepancy Modeling.
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DOI：
10.1016/j.cma.2023.116295
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发表时间：
2023-09
影响因子：
7.2
通讯作者：
Arif Masud;Sharbel Nashar;Shoaib A. Goraya
中科院分区：
文献类型：
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作者：
Arif Masud;Sharbel Nashar;Shoaib A. Goraya
提出了一种数据驱动的差异建模方法，该方法将测量数据变化地嵌入到建模和分析框架中。所提出的方法利用变分导出的损失函数，该损失函数由第一原理理论和基于传感器的测量之间的残差组成，以增强基于物理的模型。该方法首先在线性弹性的背景下开发（Masud和Goraya，J.Appl.Mech.89（11）2022），其中导出差异模型和损失项之间的关系，以表明数据嵌入项表现得像基于残差的最小二乘回归函数。作为核函数的稳定张量的解释正式成立，其作用在同化的问题的建模方法中的优先知识被突出。本文采用线性弹性动力学作为模型问题，其中数据驱动变分（DDV）方法将高保真数据纳入正演计算。这导致不仅用边界和初始条件来驱动问题，而且用仅在总域的一小部分处可用的传感器数据来驱动问题。损失函数对系统的时变响应的影响进行了研究，在各种负载条件和模型差异。能量和Morlet小波分析表明，嵌入数据的问题恢复的能量和基本频带的目标系统。通过在无阻尼模型中加入已知数据，恢复了阻尼振动悬臂梁的应变能和动能时程。这突出了在参数和模型差异的组合效应下该方法的差异建模属性。
A data-driven discrepancy modeling method is presented that variationally embeds measured data in the modeling and analysis framework. The proposed method exploits the variationally derived loss function that is comprised of the residual between the first-principles theory and sensor-based measurements to augment the physics-based model. The method was first developed in the context of linear elasticity (Masud and Goraya,J. Appl. Mech.89 (11) 2022) wherein the relation between the discrepancy model and the loss terms was derived to show that the data embedding terms behave like residual-based least-squares regression functions. An interpretation of the stabilization tensor as a kernel function was formally established and its role in assimilatinga-prioriknowledge of the problem in the modeling method was highlighted. The present paper employs linear elastodynamics as a model problem where Data-Driven Variational (DDV) method incorporates high-fidelity data into forward calculations. This results in driving the problem with not only the boundary and initial conditions, but also with the sensor data that is available at only a small subset of the total domain. The effect of the loss function on the time-dependent response of the system is investigated under a variety of loading conditions and model discrepancies. The energy and Morlet wavelet analyses reveal that the problem with embedded data recovers the energy and the fundamental frequency band of the target system. Time histories of strain energy and kinetic energy of a cantilever beam undergoing damped oscillations are recovered by including known data in an undamped model. This highlights the discrepancy modeling attributes of the method under combined effects of parameter and model discrepancy.