Characteristics and Leak Localization of Transient Flow in Gas-Containing Water Pipelines
Abstract
:1. Introduction
2. Transient Flow Model for Gas-Containing Water Pipelines Leakage
2.1. Computational Model
2.2. Unsteady Friction Model
2.3. Discrete Gas Cavity Model
2.4. Calculation Method
2.4.1. Subsubsection
2.4.2. DGCM Model Solution Method
2.5. Boundary Conditions
2.5.1. Leakage Boundary Conditions
2.5.2. Upstream Reservoir Boundary Conditions
2.5.3. Downstream Valve Boundary Conditions
3. Result and Discussion
3.1. Subsection
3.2. Simulation Results and Analysis
3.2.1. The Impact of Valve Closing Time on End-of-Valve Pressure
3.2.2. The Impact of Initial Flow Rate on End-of-Valve Pressure
3.2.3. The Impact of Gas Content Rate on End-of-Valve Pressure
3.2.4. The Impact of Leak Location on End-of-Valve Pressure
3.2.5. The Impact of Leakage Amount on End-of-Valve Pressure
4. Prediction of Leakage Location
4.1. Data Preprocessing
4.2. Neural Network Model
- Population Initialization. Before solving the problem, parameters need to be encoded to form the initial solutions of the population. Real-number encoding is used to connect the weights and thresholds between the layers. Each individual is represented as a real number string, consisting of four parts: the weights connecting the input layer and hidden layer, the thresholds of the hidden layer, the weights connecting the hidden layer and output layer, and the thresholds of the output layer. The length of the encoding is calculated using the following formula:
- Fitness Function. The fitness function measures the quality of the individuals in the population by summing the absolute errors between the actual outputs and the desired outputs of the neural network. In this study, it refers to the difference between the true leakage location and the predicted value. A smaller error indicates a better fitness of the individual. The formula for the fitness function is as follows:
- Selection Operation. The purpose of the selection operation is to increase the probability of selecting individuals with smaller errors. Since the fitness function indicates that a smaller fitness value corresponds to a smaller error, the reciprocal of the fitness value is used. The formula is as follows:
- Crossover Operation. The crossover operation involves performing position-based crossover between different chromosomes to achieve gene exchange, thereby forming new individuals. Since the individuals are encoded using real numbers, real-number crossover methods are used. The crossover operation between the -th chromosome and the -th chromosome at the -th position is performed as follows:
- Mutation Operation. Select the -th individual’s -th gene for mutation. The operation method is as follows:
4.3. Leakage Location Prediction
5. Conclusions
- (1)
- Valve closing time has a significant impact on the end-of-valve pressure. When the valve closing time is increased from 1 s to 10 s, the pressure peak decreases from 42.67 m to 27.92 m, a reduction of 34.57%. Increasing the valve closing time also delays the arrival time of the pressure peak at the valve end.
- (2)
- Initial flow rate, leakage amount, and gas content rate have a certain impact on the end-of-valve pressure. After valve closure, the larger the initial flow rate, the lower the gas content rate, and the smaller the leakage amount, the greater the pressure peak at the valve end. When the initial flow rate increases from 0.005 m3/s to 0.04 m3/s, the pressure peak rises from 18.52 m to 45.92 m, an increase of 147.95%. When the gas content rate increases from 0.001 to 0.01, the pressure peak decreases from 54.27 m to 37.89 m, a reduction of 30.18%. As the leakage rate increases from 0.01Q₀ to 0.3Q₀, the pressure peak decreases from 41.81 m to 31.57 m, a decrease of 24.55%.
- (3)
- The GA-BP neural network can accurately predict the leakage location. The prediction model constructed using the GA-BP neural network had a mean absolute percentage error (MAPE) of 7.72% when predicting experimental data, indicating good prediction performance. The GA-BP neural network model can effectively solve complex prediction problems influenced by multiple factors, providing a new feasible approach for predicting pipeline leakage locations.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Number of Neurons | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|
Correlation Coefficient | 0.8832 | 0.8910 | 0.9690 | 0.9626 | 0.9786 | 0.9440 | 0.9787 | 0.97840 | 0.9832 | 0.9779 |
MAPE | 37.51% | 21.70% | 21.14% | 20.91% | 13.56% | 17.83% | 10.67% | 12.99% | 8.80% | 11.58% |
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Zhang, Q.; Zhang, Z.; Huang, B.; Yu, Z.; Luo, X.; Yang, Z. Characteristics and Leak Localization of Transient Flow in Gas-Containing Water Pipelines. Water 2024, 16, 2459. https://doi.org/10.3390/w16172459
Zhang Q, Zhang Z, Huang B, Yu Z, Luo X, Yang Z. Characteristics and Leak Localization of Transient Flow in Gas-Containing Water Pipelines. Water. 2024; 16(17):2459. https://doi.org/10.3390/w16172459
Chicago/Turabian StyleZhang, Qiaoling, Zhen Zhang, Biyun Huang, Ziyuan Yu, Xingqi Luo, and Zhendong Yang. 2024. "Characteristics and Leak Localization of Transient Flow in Gas-Containing Water Pipelines" Water 16, no. 17: 2459. https://doi.org/10.3390/w16172459