神经模态常微分方程:将基于物理的建模与神经常微分方程集成在高维监测结构的建模中

IF 2.4 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE DataCentric Engineering Pub Date : 2022-07-16 DOI:10.1017/dce.2022.35
Zhilu Lai, Wei Liu, Xudong Jian, Kiran Bacsa, Limin Sun, E. Chatzi
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引用次数: 3

摘要

基于数据导出的模型的维度通常受到观测数量的限制,或者在被监测系统的背景下,感知节点。对于结构系统来说尤其如此,因为结构系统本质上是典型的高维结构。在物理信息机器学习的范围内,本文提出了一个框架-称为神经模态常微分方程(neural modal ode) -将基于物理的建模与深度学习相结合,用于对监测和高维工程系统的动态建模。在这个初步的探索中,我们将自己限制在线性或轻度非线性系统中。我们提出了一种将变分自编码器的动态版本与物理信息神经ode (Pi-Neural ode)耦合的架构。编码器作为自动编码器的一部分,学习从观测数据的前几项到潜在变量的初始值的映射,这通过Pi-Neural ode驱动嵌入式动态的学习,在潜在空间上施加模态模型结构。所提出的模型的解码器采用从应用于基于物理的模型的线性化部分的特征分析中导出的特征模式:一个隐含地携带自由度(dof)之间的空间关系的过程。该框架在一个数值示例和一个缩放斜拉桥的实验数据集上进行了验证,其中学习混合模型显示出优于纯粹基于物理的建模方法。我们进一步展示了所提出方案在虚拟传感环境中的功能,即从空间稀疏数据中恢复未测量dof中的广义响应量。
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Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structures
Abstract The dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems, which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this article proposes a framework—termed neural modal ordinary differential equations (Neural Modal ODEs)—to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via Pi-Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigenanalysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to out perform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, that is, the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.
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来源期刊
DataCentric Engineering
DataCentric Engineering Engineering-General Engineering
CiteScore
5.60
自引率
0.00%
发文量
26
审稿时长
12 weeks
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