The Industrial Internet of Things (IIoT) is reshaping manufacturing, industrial processes, and infrastructure management. By fostering new levels of automation, efficiency, and predictive maintenance, IIoT is transforming traditional industries into intelligent, seamlessly interconnected ecosystems. However, achieving highly reliable IIoT can be hindered by factors, such as the cost of installing large numbers of sensors, limitations in retrofitting existing systems with sensors, or harsh environmental conditions that may make sensor installation impractical. Soft (virtual) sensing leverages mathematical models to estimate variables from physical sensor data, offering a solution to these challenges. Data-driven and physics-based modeling are the two main methodologies widely used for soft sensing. The choice between these strategies depends on the complexity of the underlying system, with the data-driven approach often being preferred when the physics-based inference models are intricate and present challenges for state estimation. However, conventional deep learning models are typically hindered by their inability to explicitly represent the complex interactions among various sensors. To address this limitation, we adopt graph neural networks (GNNs), renowned for their ability to effectively capture the complex relationships between sensor measurements. In this research, we propose physics-enhanced GNNs, which integrate principles of physics into graph-based methodologies. This is achieved by augmenting additional nodes in the input graph derived from the underlying characteristics of the physical processes. Our evaluation of the proposed methodology on the case study of district heating networks reveals significant improvements over purely data-driven GNNs, even in the presence of noise and parameter inaccuracies. Our code and data are available under https://github.com/EPFL-IMOS/PEGNN_SS .

中文翻译：

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用于工业物联网软传感的物理增强图神经网络


工业物联网 （IIoT） 正在重塑制造、工业流程和基础设施管理。通过促进更高水平的自动化、效率和预测性维护，IIoT 正在将传统行业转变为智能、无缝互连的生态系统。然而，实现高度可靠的 IIoT 可能会受到多种因素的阻碍，例如安装大量传感器的成本、使用传感器改造现有系统的限制或可能使传感器安装不切实际的恶劣环境条件。软（虚拟）传感利用数学模型来估计物理传感器数据中的变量，从而为这些挑战提供解决方案。数据驱动和基于物理的建模是广泛用于软传感的两种主要方法。这些策略之间的选择取决于底层系统的复杂性，当基于物理的推理模型错综复杂并且对状态估计构成挑战时，数据驱动的方法通常是首选。然而，传统的深度学习模型通常受到阻碍，因为它们无法明确表示各种传感器之间的复杂交互。为了解决这一限制，我们采用了图神经网络 （GNN），该网络以其有效捕获传感器测量之间的复杂关系的能力而闻名。在这项研究中，我们提出了物理增强的 GNN，它将物理原理集成到基于图的方法中。这是通过在 Importing Graph 中增加从物理过程的底层特征派生的附加节点来实现的。 我们在区域供热网络案例研究中对所提出的方法进行了评估，发现即使在存在噪声和参数不准确的情况下，也比纯数据驱动的 GNN 有了显着改进。我们的代码和数据可在 https://github.com/EPFL-IMOS/PEGNN_SS 下获得。