  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.
