Sensor Fault Detection via Virtual Smart Heat Metering with Spatial-Temporal Graph Neural Networks

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Published Jul 3, 2026
Keivan Faghih Niresi Olga Fink

Abstract

Sensor faults and miscalibrated sensors represent an important challenge in district heating networks, where measurement errors, drift, calibration inaccuracies, or communication issues can compromise the reliability of thermal and hydraulic monitoring. Detecting such issues in a timely manner is essential for maintaining operational efficiency and ensuring the trustworthiness of system data. A promising approach for addressing these challenges is to compare physical measurements with estimates generated by virtual sensors. Virtual sensing enables the reconstruction of unmeasured or unreliable variables using data-driven models and existing measurements, thereby providing an estimate of the expected measurement value under the current operating and environmental conditions, which can serve as reference against which anomalous or inconsistent sensor behavior can be identified. In this work, we develop a virtual-sensor–based framework for sensor fault and miscalibration detection using a heterogeneous spatial–temporal graph neural network (HSTGNN). The proposed model learns both the spatial relationships among sensors and the temporal dynamics of their measurements to construct accurate virtual smart heat meter outputs. To evaluate the approach, we use a controlled laboratory dataset collected at the Aalborg Smart Water Infrastructure Laboratory, which provides synchronized high-resolution measurements of flow, temperature, and pressure representative of district heating operating conditions. Experimental results demonstrate that the proposed HSTGNN improves fault detection performance compared to several baseline methods.

How to Cite

Faghih Niresi, K., & Fink, O. (2026). Sensor Fault Detection via Virtual Smart Heat Metering with Spatial-Temporal Graph Neural Networks. PHM Society European Conference, 9(1), 1–10. https://doi.org/10.36001/phme.2026.v9i1.4944
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Keywords

graph neural networks, virtual sensing, sensor fault detection, district heating

References
Atwood, J., & Towsley, D. (2016). Diffusion-convolutional neural networks. Advances in Neural Information Processing Systems, 29.

Bank, T., Madsen, F. W., Mortensen, L. K., Søndergaard, H. A. N., & Shaker, H. R. (2023). Virtual sensor-based fault detection and diagnosis framework for district heating systems: A top-down approach for quick fault localisation. In Energy Informatics Academy Conference (pp. 292–307).

Belgacem, H., & Chihi, I. (2025). Toward reliable and intelligent sensor systems: A comprehensive study of fault diagnosis and mitigation. IEEE Sensors Reviews.

Bengio, Y., Léonard, N., & Courville, A. (2013). Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint arXiv:1308.3432.

Cini, A., Zambon, D., & Alippi, C. (2023). Sparse graph learning from spatiotemporal time series. Journal of Machine Learning Research, 24(242), 1–36.

Darvishi, H., Ciuonzo, D., Eide, E. R., & Rossi, P. S. (2020). Sensor-fault detection, isolation and accommodation for digital twins via modular data-driven architecture. IEEE Sensors Journal, 21(4), 4827–4838.

Fink, O., Nejjar, I., Sharma, V., Faghih Niresi, K., Sun, H., Dong, H., ... Kesmen, Y. (2026). From physics to observational bias in prognostics and health management (PHM). Reliability Engineering & System Safety, 274, 112376.

Fink, O., Sharma, V., Nejjar, I., Von Krannichfeldt, L., Garmaev, S., Zhang, Z., ... Steiner, K. (2026). From physics to machine learning and back: Part I — Learning with inductive biases in prognostics and health management (PHM). Reliability Engineering & System Safety, 271, 112213.

Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.

Hsu, C.-C., Frusque, G., & Fink, O. (2023). A comparison of residual-based methods on fault detection. In Annual Conference of the PHM Society (Vol. 15).

Huang, P., Copertaro, B., Zhang, X., Shen, J., Löfgren, I., Rönnelid, M., ... Svanfeldt, M. (2020). A review of data centers as prosumers in district energy systems: Renewable energy integration and waste heat reuse for district heating. Applied Energy, 258, 114109.

Jin, M., Koh, H. Y., Wen, Q., Zambon, D., Alippi, C., Webb, G. I., ... Pan, S. (2024). A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12), 10466–10485.

Kamstrup. (2026). MULTICAL® 303. Retrieved from https://www.kamstrup.com/en-en/product-centre/multical-303. Accessed: 2026-03-23.

Kipf, T. N., & Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907.

Kool, W., Van Hoof, H., & Welling, M. (2020). Ancestral Gumbel-Top-k sampling for sampling without replacement. Journal of Machine Learning Research, 21(47), 1–36.

Li, Y., Yu, R., Shahabi, C., & Liu, Y. (2017). Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. arXiv preprint arXiv:1707.01926.

Niresi, K. F., Bissig, H., Baumann, H., & Fink, O. (2024). Physics-enhanced graph neural networks for soft sensing in Industrial Internet of Things. IEEE Internet of Things Journal, 11(21), 34978–34990.

Niresi, K. F., Jensen, C. M., Kallesøe, C. S., Wisniewski, R., & Fink, O. (2026). Virtual smart metering in district heating networks via heterogeneous spatial-temporal graph neural networks. arXiv preprint arXiv:2604.10166.

Niresi, K. F., Kuhn, L., Frusque, G., & Fink, O. (2024). Informed graph learning by domain knowledge injection and smooth graph signal representation. In 2024 32nd European Signal Processing Conference (EUSIPCO) (pp. 2467–2471).

Niresi, K. F., Nejjar, I., & Fink, O. (2025). Efficient unsupervised domain adaptation regression for spatial-temporal sensor fusion. IEEE Internet of Things Journal.

Sun, Q., & Ge, Z. (2021). A survey on deep learning for data-driven soft sensors. IEEE Transactions on Industrial Informatics, 17(9), 5853–5866.

Theiler, R., & Fink, O. (2025). Heterogeneous graph neural networks for short-term state forecasting in power systems across domains and time scales: A hydroelectric power plant case study. arXiv preprint arXiv:2507.06694.

Val Ledesma, J., Wisniewski, R., & Kallesøe, C. S. (2021). Smart water infrastructures laboratory: Reconfigurable test-beds for research in water infrastructures management. Water, 13(13), 1875.

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems, 30.

Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2020). A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems, 32(1), 4–24.

Yoon, S., Choi, Y., Koo, J., Hong, Y., Kim, R., & Kim, J. (2020). Virtual sensors for estimating district heating energy consumption under sensor absences in a residential building. Energies, 13(22), 6013.

Zhao, M., Taal, C., Baggerohr, S., & Fink, O. (2025). Graph neural networks for virtual sensing in complex systems: Addressing heterogeneous temporal dynamics. Mechanical Systems and Signal Processing, 230, 112544.
Section
Technical Papers