ADAPTIVE IDENTIFICATION ALGORITHM FOR THE HAZEN–WILLIAMS COEFFICIENT (EPANET INTEGRATION)

SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 10 OCTOBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 25 ADAPTIVE IDENTIFICATION ALGORITHM FOR THE HAZEN–WILLIAMS COEFFICIENT (EPANET INTEGRATION) S. Axmadaliyev1, M. Axmadaliyeva2, Z. Axmadaliyev3, I. G’aniyeva4, Doctoral Student of Tashkent Architecture and Civil Engineering University1 English Language Teacher at School No. 341, Yashnobod District2 Electrical Engineer at the Modern Design Institute3 Operator of the Laboratory of Physical and Physicochemical Research Methods, Institute of Polymer Chemistry and Physics, Academy of Sciences of the Republic of Uzbekistan4 https://doi.org/10.5281/zenodo.17315743 Abstract. In water supply networks, accurately determining friction losses is of critical importance when modeling hydraulic processes. In practice, two primary formulas are widely used: Hazen–Williams (empirical and fast) and Darcy–Weisbach (physically based and universal). Due to its simplicity, Hazen–Williams is convenient for application in real networks; however, it does not take into account the flow regime and pipe roughness. Although Darcy– Weisbach is more accurate, it is more challenging to implement in real-time calculations. This study proposes an approach that combines these two methods and adapts the parameters in realtime based on pressure, velocity, and flow measurements, thereby improving the accuracy of hydraulic modeling in the water supply networks of Nurafshon. Keywords: node inflow-outflow balance, effective friction, operation (operational conditions), pressure, algorithm, new coefficient, hazen–williams coefficient, high-frequency noise, low-frequency noise. Introduction. During practical operation, significant discrepancies exist between calculated values and actual measured data, especially due to factors such as changes in the number of consumers, temporal fluctuations in pressure, and uncertainties in the hydraulic gradient. These factors ultimately reduce the accuracy of calculations, which in turn hinders the effective management of the water distribution system. To address this issue, a new approach has been developed. The main idea of the proposed algorithm is the introduction of an adaptive coefficient that is updated based on real-time measurements. As a result, the Hazen–Williams formula becomes adaptive, aligning the calculated flow and pressure values more closely with the measured data. The EPANET software is widely used for modeling water supply networks and enables the analysis of network elements based on parameters such as pressure, flow, and others. In this study, a new algorithm integrating the EPANET platform was developed for the adaptive identification of the Hazen–Williams coefficient. This approach adjusts the coefficient based on real-time measurements, aiming to significantly improve the accuracy of hydraulic modeling. Methodology. The new coefficient, in order to ensure the stable analysis of the system, is expressed in the following general form: 𝑘(𝑡)=𝑓(𝑃(𝑡),𝑉(𝑡),𝑄(𝑡)) [1,2] Here, 𝑃(𝑡)represents the pressure value over time, 𝑉(𝑡)is the flow velocity in the pipes, and 𝑄(𝑡)denotes the measured flow rate. The algorithm processes real-time measurements coming from the EPANET system and dynamically updates the Hazen–Williams coefficient 𝐶. The sequence of the algorithm begins with the input of the initial working parameters. C0 - initial SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 10 OCTOBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 26 Hazen–Williams coefficient, D - internal pipe diameter (m), L - pipe length (m), P - initial pressure, initial velocity or flow speed (m/s), dt - time (s), Sensor addresses — inputs from EPANET or other real-time measurement systems. In the second stage, sensor data or measured values are collected and filtered. Measurements are taken over time. The values 𝑃(𝑡), 𝑉(𝑡), and measured flow rate 𝑄(𝑡)are processed through filtering to reduce signal noise. In many cases, real measurement results exhibit random fluctuations or variable pressure and flow (for example, in flow or pressure values). To reduce process variability, the algorithm calculates the average of the last 𝑛measurements, acting as a filter by outputting the mean of multiple values to the system. 𝑋𝑓(𝑡)=1 𝑛∑𝑋(𝑡−𝑖∗𝑑𝑡) 𝑛−1 𝑖=0 [3,4] Here, 𝑋𝑓(𝑡)is the filtered signal (output value), 𝑋(𝑡)is the real measured signal (input value), 𝑛is the number of values used for averaging, 𝑑𝑡is the time interval, and 𝑖is the index (sequence of the most recent values). A low-pass filter allows slow-changing (smooth) signals to pass through while reducing or completely eliminating high-frequency (rapidly fluctuating, noisy) components. 𝑌(𝑡)=𝑎∗𝑋(𝑡)+(1−𝑎)∗𝑌(𝑡−1) Here, 𝑋(𝑡)is the input signal representing measured pressure and flow, 𝑌(𝑡)is the filtered signal, and 𝑎is the smoothing coefficient (where 0<𝑎<1). In water networks, the term "signal" in the algorithm typically refers to pressure, flow, or water consumption. These signals vary over time and exhibit two types of disturbances: high-frequency noise—rapid fluctuations occurring within seconds (such as sensor errors, electrical noise, or pump pulsations), and low-frequency noise—slowly varying parameters over longer periods. Sources of low-frequency noise include daily fluctuations in consumer demand. For example, pressure sharply decreases in the morning (07:00–09:00) and evening (18:00–21:00), while remaining relatively stable during the daytime. Although these fluctuations occur at a very low frequency (daily cycle), they represent significant sources of variation for the system.[6] Changes in the water tower or reservoir level also contribute to low-frequency fluctuations. The gradual rise and fall of the water level in the reservoir cause low-frequency oscillations in the pressure signal within the network. When pumps start and stop over extended periods or are automatically switched off and on multiple times per day, the system pressure experiences slow fluctuations. Additionally, the gradual change in the hydraulic gradient—for example, when consumption decreases in a certain area—leads to a slow increase in pressure. To allow lowfrequency signals to pass and attenuate high-frequency signals, the following expression is used for the filter. 𝐻(𝑓)=1 √1+(𝑓 𝑓𝑐)2 Here, 𝐻(𝑓)is the amplitude coefficient of the transfer function (the ratio of the output signal amplitude to the input signal amplitude), 𝑓is the signal frequency (Hz), and 𝑓𝑐=1 2𝜋𝑅𝐶 is the cutoff frequency. Results. In the algorithm, the model is selected based on the characteristics of the water supply system and the level of technological infrastructure (Case 1, Case 2, Case 3). Depending on the available system data and the technologies applied, the algorithm chooses an appropriate computational pathway. SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 10 OCTOBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 27 Path 1 (Case 1) – Linear correction based on pressure and velocity. 𝑘=1+𝑎∗𝑃(𝑡)−𝑃𝑝 𝑃𝑝+𝑏∗𝑉(𝑡)−𝑉𝑣 𝑉𝑣 This approach optimizes the relative changes in pressure and velocity and incorporates them into the coefficient. Path 2 (Case 2) – Multiplicative correction based on pressure and velocity, where empirical values are used. 𝑘=(𝑃(𝑡)𝑎 𝑃𝑣)∗(𝑉(𝑡)𝛽 𝑉𝑣) Here, 𝛼and 𝛽are experimentally determined exponents that define the influence of pressure and velocity on the coefficient 𝑘. First, the theoretical flow is calculated using the Hazen–Williams formula: 𝑄𝐻𝑊 =0,278∗С0∗𝐷2,63∗𝑆0,54 𝑘=𝑄𝑠𝑎𝑟𝑓 𝑄𝐻𝑊 and it is then adjusted to a physically reasonable limit. 𝑘−€(0,5,1,5) Updating the Hazen–Williams coefficient 𝐶(𝑡)=𝐶0∗𝑘 Calculating the slope (gradient) 𝑆(𝑡)=𝐻𝑏−𝐻𝑓 𝐿 Application of the Hazen–Williams Flow Formula 𝑄𝐻𝑊,(𝑡)=0,278∗𝐶(𝑡)∗𝐷2,63∗𝑆0,54 his formula is used with metric units, and the flow result is expressed in liters per second (L/s). 1-Figure: Comparison of real flow and models in the water facility network. SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 10 OCTOBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 28 2Figure: Comparison of real pressure and models in the water facility network. Conclusion. In the proposed algorithm, measured values of pressure, velocity, and flow consumption are processed and filtered (using Moving Average and Low-pass filters). Based on these values, the coefficient 𝑘(𝑡)is adaptively updated, and the Hazen–Williams formula is adjusted to real conditions. Three variants of the algorithm (Case 1 – linear correction, Case 2 – relative indicator, Case 3 – flow-based adjustment) were examined and their results compared. In practice, the highest accuracy was achieved by Case 3, as it directly adapts to the measured flow values. SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 10 OCTOBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 29 REFERENCES 1. Rossman, L.A. (2000). EPANET 2 Users Manual. U.S. Environmental Protection Agency, Cincinnati. (pp. 23–47: Hydraulic calculations and water quality modeling algorithms). 2. Walski, T.M., Chase, D.V., Savic, D.A. (2001). Water Distribution Modeling. Haestad Press. (pp. 89–124: Comparison of Hazen–Williams and Darcy–Weisbach formulas). 3. Hwang, H., Lansey, K. (2017). “Real-Time Water Distribution System Simulation and Control.” Journal of Water Resources Planning and Management, 143(5), pp. 6–12. (Realtime algorithms). 4. Brdys, M.A., Ulanicki, B. (1994). Operational Control of Water Systems: Structures, Algorithms and Applications. Prentice Hall. (pp. 45–62: Adaptive control algorithms). 5. Clark, R.M., Grayman, W.M. (1998). Modeling Water Quality in Distribution Systems. AWWA Research Foundation. (pp. 131–160: Chlorine and NaClO dispersion). 6. Rossman, L.A. (2000). EPANET 2 Users Manual. U.S. EPA. (pp. 69–84: Water quality module, advection–reaction equations).