Multi-Level Strategy for Placement of Measuring Devices in Engineering Systems with Distributed Loads Based on Hierarchical and Cluster Analysis

Building a digital model of a “smart city” in the context of rapid development of technical infrastructure requires effective methods for monitoring and managing engineering systems. One of the key tasks is to optimize the placement of measuring devices in systems such as water and energy supply, including gas, electricity and heat. In conditions of limited financial resources and the need to ensure high monitoring accuracy, it is important to take into account not only the geographical distribution of consumers, but also the intensity of their load. This is especially important for managing distributed technical systems, where it is necessary to minimize equipment costs, while ensuring full network coverage and timely detection of anomalies. The purpose of this study is to develop a methodology for the optimal placement of measuring devices in engineering systems that takes into account both the spatial location of consumers and their load. The paper uses a multi-level analysis strategy using Ward’s method for hierarchical clustering and the k-means algorithm. Based on the proposed me-thodology, four territorial clusters were identified using the example of the Gomel water supply system, on the basis of which 20 pressure sensors were distributed proportionally to the contribution of consumption. The article shows how multiparameter clustering can be used to determine optimal centers for placing measuring devices that are focused on more powerful consumers, while taking into account the geographic distribution of objects as a whole. The developed approach allows for the efficient distribution of measuring devices taking into account the actual load of objects in the system and their geographic location, which ensures the best coverage of the territory under conditions of a limited amount of equipment. The approach presented in the article can be adapted for various technical systems, ensuring universality and flexibility of application.

1. Gautam D. K., Kotecha P., Subbiah S. (2022) Efficient k-Means Clustering and Greedy Selection-Based Reduction of Nodal Search Space for Optimization of Sensor Placement in the Water Distribution Networks. Water Research, 220, 118666. https://doi.org/10.1016/j.watres.2022.118666.

2. Rajabi M., Tabesh M. (2024) Pressure Sensor Placement for Leakage Detection and Calibration of Water Distribution Networks Based on Multiview Clustering and Global Sensitivity Analysis. Journal of Water Resources Planning and Management, 150 (5). https://doi.org/10.1061/jwrmd5.wreng-6262.

3. Savin I. Yu., Blokhin Yu. I. (2022). On Optimizing the Deployment of an Internet of Things Sensor Network for Soil and Crop Monitoring on Arable Plots. Dokuchaev Soil Bulletin, 110, 22–50. https://doi.org/10.19047/0136-1694-2022-110-22-50 (in Rus-sian).

4. Kapanski A. A., Klyuev R. V., Boltrushevich A. E., Sorokova S. N., Efremenkov E. A., Demin A. Y., Martyushev N. V. (2025) Geospatial Clustering in Smart City Resource Management: An Initial Step in the Optimisa-tion of Complex Technical Supply Sys-tems. Smart Cities, 8 (1), 14. https://doi.org/10.3390/smartcities8010014.

5. Kazakovtsev L. A., Gudyma M. N. (2013) Statement of the Problem of Optimal Placement of a Network of Air and Water Pollution Monitoring Sensors. Perspektivy Razvitiya Informatsionnykh Tekhnologiy [Prospects for the Development of Information technolo-gy], (13), 19–24 (in Russian).

6. Immanuel S. D., Chakraborty U. Kr. (2019) Genetic Algorithm: An Approach on Optimization. 2019 International Conference on Communication and Electronics Systems (ICCES), 701–708. https://doi.org/10.1109/icces45898.2019.9002372.

7. Suman B., Kumar P. (2006) A Survey of Simulated Annealing as a Tool for Single and Multiobjective Op-timization. Journal of the Operational Research Society, 57 (10), 1143–1160. https://doi.org/10.1057/palgrave.jors.2602068.

8. Macêdo J. E. S. de, Azevedo J. R. G. de, Bezerra S. de T. M. (2021). Hybrid Particle Swarm Optimization and Tabu Search for the Design of Large-Scale Water Distribution Networks. Revista Brasileira de Recursos Hidricos, 26, https://doi.org/10.1590/2318-0331.262120210006.

9. Casillas M. V., Puig V., Garza-Castañón L., Rosich A. (2013) Optimal Sensor Placement for Leak Location in Water Distribution Networks Using Genetic Algorithms. Sensors, 13 (11), 14984–15005. https://doi.org/10.3390/s131114984.

10. Peng S., Cheng J., Wu X., Fang X., Wu Q. (2022) Pressure Sensor Placement in Water Supply Network Based on Graph Neural Network Clustering Method. Water, 14 (2), 150. https://doi.org/10.3390/w14020150.

11. Sousa J., Ribeiro L., Muranho J., Marques A. S. (2015). Locating Leaks in Water Distribution Networks with Simulated Annealing and Graph Theory. Procedia En-gineering, 119, 63–71. https://doi.org/10.1016/j.proeng.2015.08.854.

12. Rajabi M., Tabesh M. (2024) Pressure Sensor Placement for Leakage Detection and Calibration of Water Distribution Networks Based on Multiview Clustering and Global Sensitivity Analysis. Journal of Water Resources Planning and Management, 150 (5). https://doi.org/10.1061/jwrmd5.wreng-6262.

13. Sarrate R., Blesa J., Nejjari F. (2014) Clustering Techniques Applied to Sensor Placement for Leak Detection and location in Water Distribution Networks. 22nd Me-diterranean Conference on Control and Automation, 109–114. https://doi.org/10.1109/med.2014.6961356.

14. Eszergár-Kiss D., Caesar B. (2017) Definition of User Groups applying Ward’s Method. Transportation Research Procedia, 22, 25–34. https://doi.org/10.1016/j.trpro.2017.03.004.

15. Nainggolan R., Perangin-angin R., Simarmata E., Tarigan A. F. (2019) Improved the Performance of the K-Means Cluster Using the Sum of Squared Error (SSE) Optimized by using the Elbow Method. Journal of Physics: Confe-rence Series, 1361 (1), 012015. https://doi.org/10.1088/1742-6596/1361/1/012015.

16. Shahapure K. R., Nicholas C. (2020) Cluster Quality Analysis Using Silhouette Score. 2020 IEEE 7th Inter-national Conference on Data Science and Advanced Analytics (DSAA), 747–748. https://doi.org/10.1109/dsaa49011.2020.00096.