Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamics

TL;DR

This work tackles virtual sensing in complex industrial systems by addressing heterogeneity in sensor modalities, temporal dynamics, and exogenous operating conditions. It introduces HTGNN, a heterogeneous temporal graph neural network that encodes low- and high-frequency signals with context-aware dynamics, learns intra- and inter-modality interactions, and infers targets via a BiLSTM over graph embeddings. The approach is validated on bearing-load and bridge live-load tasks using two new datasets, showing significant performance gains and robust behavior under varying conditions. The framework demonstrates practical potential for real-time monitoring, predictive maintenance, and scalable IIoT deployments, with data and code openly available for reproducibility.

Abstract

Real-time condition monitoring is crucial for the reliable and efficient operation of complex systems. However, relying solely on physical sensors can be limited due to their cost, placement constraints, or inability to directly measure certain critical parameters. Virtual sensing addresses these limitations by leveraging readily available sensor data and system knowledge to estimate inaccessible parameters or infer system states. The increasing complexity of industrial systems necessitates deployments of sensors with diverse modalities to provide a comprehensive understanding of system states. These sensors capture data at varying frequencies to monitor both rapid and slowly varying system dynamics, as well as local and global state evolutions of the systems. This leads to heterogeneous temporal dynamics, which, particularly under varying operational end environmental conditions, pose a significant challenge for accurate virtual sensing. To address this, we propose a Heterogeneous Temporal Graph Neural Network (HTGNN) framework. HTGNN explicitly models signals from diverse sensors and integrates operating conditions into the model architecture. We evaluate HTGNN using two newly released datasets: a bearing dataset with diverse load conditions for bearing load prediction and a year-long simulated dataset for predicting bridge live loads. Our results demonstrate that HTGNN significantly outperforms established baseline methods in both tasks, particularly under highly varying operating conditions. These results highlight HTGNN's potential as a robust and accurate virtual sensing approach for complex systems, paving the way for improved monitoring, predictive maintenance, and enhanced system performance. Our code and data are available under https://github.com/EPFL-IMOS/htgnn.

Figures (14)

• Figure 1: Architecture of the proposed Heterogeneous Temporal Graph Neural Network (HTGNN) for virtual sensing. HTGNN effectively infers target variable $\mathbf{y}^{t}$ by capturing complex relationships between heterogeneous sensor nodes with diverse modalities, including low-frequency signals ($\mathbf{X_L}^{t_l:t}$, blue circles), high-frequency signals ($\mathbf{X_H}^{t_l:t}$, orange squares) and exogenous variables ($\mathbf{W}^{t_l:t}$, dark blue triangle). The model incorporates three key stages: (1) Operating condition aware dynamics modeling: A Multilayer Perceptron (MLP) extracts operating conditions, informing both a Gated Recurrent Unit (GRU) for low-frequency dynamics and a gated Convolutional Neural Network (CNN) for high-frequency dynamics extraction, capturing operating condition-aware temporal patterns within each signal type. (2) Heterogeneous interaction learning: Specialized Graph Neural Networks (GNNs) learn complex inter- and intra-modality interactions between heterogeneous sensor nodes. (3) Target variable inference: A Bidirectional Long Short-Term Memory (BiLSTM) network followed by an MLP analyzes the combined information from the graph embedding to predict the target variable.
• Figure 2: Architecture of a Gated Recurrent Unit (GRU)-based low-frequency signal encoder with exogenous variable encoding as the initial state.
• Figure 3: Architecture of a multi-scale Gated Convolutional Layers (GCLs)-based encoder for high-frequency signals, considering exogenous variable encoding as the gating signal.
• Figure 4: The SKF Sven Wingquist Test Centre (SWTC) TRB bearing test-rig (a) with sensor installation locations (b) for vibration, temperature, and load measurements.
• Figure 5: Heterogeneous graphs for bearing sensor network relationship modeling. (a) Temperature-Temperature (b) Vibration-Vibration (c) Temperature-Vibration (d) Vibration-Temperature (e) Connectivity across two test rig bearings (the connectivity between T nodes omitted for simplicity).