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A comparison between joint and dual UKF implementations for state estimation and leak localization in water distribution networks

Luis Romero-Ben, Paul Irofti, Florin Stoican, Vicenç Puig

TL;DR

This work evaluates two data-driven UKF-based approaches for hydraulic state estimation and leak localization in water distribution networks: a joint UKF (J-UKF-AW-GSI) that estimates head and flow jointly, and a dual UKF (D-UKF-AW-GSI) that alternates between head and flow estimation with virtual measurements. Through theoretical covariance and complexity analysis, it shows that the dual formulation reduces computational burden while delivering comparable (often slightly better for head) accuracy compared to the joint approach. Case studies on the L-TOWN benchmark demonstrate that D-UKF-AW-GSI achieves similar RMSE but with ~77% faster convergence, highlighting its practicality for real-time leak localization and state estimation in water networks. The findings suggest adopting the dual framework in deployment, while future work will broaden benchmarks and exploit explicit state relations to further improve robustness and scalability.

Abstract

The sustainability of modern cities highly depends on efficient water distribution management, including effective pressure control and leak detection and localization. Accurate information about the network hydraulic state is therefore essential. This article presents a comparison between two data-driven state estimation methods based on the Unscented Kalman Filter (UKF), fusing pressure, demand and flow data for head and flow estimation. One approach uses a joint state vector with a single estimator, while the other uses a dual-estimator scheme. We analyse their main characteristics, discussing differences, advantages and limitations, and compare them theoretically in terms of accuracy and complexity. Finally, we show several estimation results for the L-TOWN benchmark, allowing to discuss their properties in a real implementation.

A comparison between joint and dual UKF implementations for state estimation and leak localization in water distribution networks

TL;DR

This work evaluates two data-driven UKF-based approaches for hydraulic state estimation and leak localization in water distribution networks: a joint UKF (J-UKF-AW-GSI) that estimates head and flow jointly, and a dual UKF (D-UKF-AW-GSI) that alternates between head and flow estimation with virtual measurements. Through theoretical covariance and complexity analysis, it shows that the dual formulation reduces computational burden while delivering comparable (often slightly better for head) accuracy compared to the joint approach. Case studies on the L-TOWN benchmark demonstrate that D-UKF-AW-GSI achieves similar RMSE but with ~77% faster convergence, highlighting its practicality for real-time leak localization and state estimation in water networks. The findings suggest adopting the dual framework in deployment, while future work will broaden benchmarks and exploit explicit state relations to further improve robustness and scalability.

Abstract

The sustainability of modern cities highly depends on efficient water distribution management, including effective pressure control and leak detection and localization. Accurate information about the network hydraulic state is therefore essential. This article presents a comparison between two data-driven state estimation methods based on the Unscented Kalman Filter (UKF), fusing pressure, demand and flow data for head and flow estimation. One approach uses a joint state vector with a single estimator, while the other uses a dual-estimator scheme. We analyse their main characteristics, discussing differences, advantages and limitations, and compare them theoretically in terms of accuracy and complexity. Finally, we show several estimation results for the L-TOWN benchmark, allowing to discuss their properties in a real implementation.

Paper Structure

This paper contains 16 sections, 1 theorem, 15 equations, 2 figures, 1 table, 4 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. Kalman Filter
  4. Extended Kalman Filter
  5. Unscented Kalman Filter
  6. Methodology
  7. UKF-AW-GSI
  8. State prediction
  9. Measurement propagation
  10. Correction
  11. D-UKF-AW-GSI
  12. J-UKF-AW-GSI
  13. Theoretical discussion
  14. Case study and discussion
  15. Conclusions
  16. ...and 1 more sections

Key Result

Proposition 1

The utilization of steps 1-4 of Algorithm alg:UKF-prelimiaries or steps 1-2 of Algorithm alg:EKF-prelimiaries (considering the linear KF in eq:fF) is equivalent if the process function is linear.

Figures (2)

  • Figure 1: Scheme of the L-TOWN network.
  • Figure 2: Estimation results for D-UKF-AW-GSI and J-UKF-AW-GSI in Area A, in terms of head and flow estimation error, and execution time, for different values of $k_{max}$.

Theorems & Definitions (3)

  • Proposition 1
  • proof
  • Remark 1