استفاده از تئوری بیزین برای نشت‌یابی در سیستم انتقال آب

In recent decades, several methods have been developed for leak detection in water supply networks, one of which is the transient wave-based method. The transient wave-based leak detection method offers a growing and promising approach that comes with several challenges. The most important challenges of these methods are model uncertainty and noisy data. Model-based methods do not have high accuracy due to high uncertainties, and data-based methods also do not have high accuracy due to noisy data. This paper presents a method for detecting the leak location for a reservoir pipeline valve system using Bayesian theory. In detecting the pipeline leak location, the noise in the pressure signal collected from the sensors in the pipeline affects the accuracy of detection. In this research, a probability density function for the leak location is obtained by combining the prior probability density function obtained from the model and the data collected by the sensors. Then, the accuracy of the proposed method is investigated by solving a numerical example. In this regard, a pipe with a length of L=3,000m and a diameter of D=0.5m was considered. The Darcy-Weisbach friction factor was set to f=0.03. To initiate a transient wave, an instantaneous complete closure of the valve located at the downstream end of the pipe (x=L) was performed. This closure generated a transient wave with a speed of a=1,200 m/s, which propagated along the length of the pipe. The inlet of the pipe (x=0) was maintained at a constant pressure head of Hin=25 m. To measure the response of the pressure head, a sensor was strategically positioned at the end of the pipe (x*=L=3,000 m). The objective was to observe the pressure variations caused by the transient wave. The time required for the contact discontinuity, generated by the valve closure, to travel from the valve back to the inlet was calculated as τ=L/a=2.5 s. This represented the round-trip travel time of the wave within the pipe. To ensure that the simulations captured the full behavior of the transient wave, the total simulation time was set to T=2τ, thereby covering two complete cycles of the contact discontinuity passing through the sensor. In this numerical study, the effects of data noise, sensor location, and simulation time on the results were carefully investigated. The data collected from the sensors were subject to noise, which could affect the accuracy of leak detection. To investigate the impact of this noise, different scenarios with varying noise levels were simulated and analyzed. In addition, the location of the sensor also influenced the simulation results. Various sensor placements were tested to identify the optimal location for achieving higher accuracy in leak detection. These studies demonstrated that sensor placement could significantly improve the results and increase detection accuracy. Finally, simulation time was examined as a critical factor in the analyses. Different simulation durations were tested to observe their effects on the results and their impact on the accuracy of leak detection. The analyses revealed that selecting the appropriate simulation time could enhance the accuracy and speed of leak detection. The results of the numerical study demonstrated the ability of the method to identify leak locations in a water pipeline network. Overall, this study showed that data noise, sensor location, and simulation time are all factors that can affect the accuracy and quality of leak detection. By effectively managing these factors, the performance of leak detection systems can be improved. This innovative approach not only enhances the accuracy of leak detection but also provides a robust framework for addressing the inherent uncertainties and noise in the data.