Genetic algorithm optimization of negative pressure wave method for robust real time leak detection in long distance pipelines

Abstract

Accurate leak detection in long-distance fluid transmission pipelines is essential for minimizing environmental and economic risks. Traditional negative pressure wave (NPW) techniques are often limited by sensitivity to wave speed estimation errors, sensor noise, and changing flow conditions. This study introduces a hybrid approach in which a genetic algorithm (GA) dynamically optimizes NPW parameters, including wave speed, fluid velocity, and leak position, based on real-time sensor data. Using results from ten field leak tests on a 175 km crude oil pipeline, the GA-enhanced NPW method reduced average localization error from 11% (NPW) and 18% (HGI) to 5%, corresponding to an 8.75 km deviation over the full pipeline length—well within operational thresholds for segment isolation in large-scale networks. Detection time decreased from 30 to 40 s to approximately 10 s, enabling operators to respond more rapidly to leak events. The system’s modular architecture supports seamless integration with Supervisory Control and Data Acquisition (SCADA) platforms, providing automated alerts and visual diagnostics for immediate decision-making. By combining multi-parameter optimization with field-validated robustness, the proposed GA-NPW framework offers a practical and scalable solution for real-time leak detection in critical pipeline infrastructure.

Introduction

Leakage in long-distance fluid transmission pipelines poses serious risks to safety, the environment, and economic stability. Even small undetected leaks can lead to large-scale environmental contamination, significant product losses, and prolonged service interruptions. The challenge of rapid and accurate leak localization is heightened under real-world conditions, where operational noise, fluctuating flow rates, and uncertainties in hydraulic parameters can obscure early leak signals¹.

Traditional leak detection methods such as the negative pressure wave (NPW) and hydraulic gradient intersection (HGI) techniques have been widely applied due to their simplicity and low cost. NPW detects leaks by capturing transient pressure waves generated at the leak site and estimating location from the time difference of arrival at upstream and downstream sensors. HGI estimates leak position by calculating and intersecting hydraulic gradients from both pipeline ends. While effective under controlled conditions, both methods face substantial challenges in real-world operations. Variations in boundary conditions, including fluctuating flow rates and pressures, can distort waveforms and gradient slopes, reducing accuracy. Sensor data are often affected by operational noise from pumps, valves, and environmental factors, leading to false positives or missed detections. Time synchronization errors between measurement stations can translate directly into large localization deviations. In addition, small leaks may remain undetected until they grow into larger failures, particularly in long-distance pipelines with sparse sensor placement. These limitations have motivated the development of hybrid approaches that combine conventional analytical techniques with computational optimization to enhance robustness, accuracy, and real-time applicability².

The novelty of this study lies in the integration of genetic algorithms (GA) with traditional detection techniques to form a hybrid methodology. In this work, “hybrid” refers specifically to the integration of a conventional NPW analytical framework with a genetic algorithm–based optimization module that continuously refines model parameters using real-time sensor data. Hybrid approaches integrate conventional leak detection techniques with computational optimization methods to combine the interpretability and physical grounding of analytical models with the adaptability of modern algorithms. In the context of NPW analysis, optimization methods such as genetic algorithms can dynamically calibrate parameters—wave speed, fluid velocity, and timing offsets—based on incoming sensor data, thereby reducing the effects of environmental variability and measurement noise. This coupling allows the NPW framework to maintain accuracy and responsiveness even in long-distance pipelines operating under variable conditions. Computational approaches like GAs have emerged as powerful tools for optimizing parameters and enhancing detection accuracy in complex scenarios. For instance, integrating GAs with deep learning models has shown promise in real-time pipeline leak detection, achieving high accuracy rates³.

Leak detection in fluid transmission pipelines is a critical engineering focus, aiming to mitigate environmental, economic, and safety hazards. Analytical and experimental methods are integral to identifying and localizing leaks effectively, providing complementary insights into fluid dynamics and pipeline integrity.

Analytical methods involve mathematical and computational modeling based on principles of fluid mechanics, wave propagation, and structural dynamics. Negative pressure wave (NPW) analysis remains a cornerstone of analytical approaches, detecting leaks through the propagation of pressure waves caused by leak events. Zhou et al.⁴ enhanced traditional NPW techniques by incorporating environmental noise and boundary condition variations. Their approach reduced localization errors by 30% in complex pipeline systems. Ferroudji et al.⁵ utilized multiphase flow modeling for leak detection, focusing on liquid-gas interactions in pipelines with multiple leaks. Their models, validated through computational fluid dynamics (CFD), demonstrated high accuracy in predicting leak locations.

Asada et al.⁶ developed transient wave-based analytical models for detecting leaks in irrigation pipelines. Using optimization techniques, their study highlighted the importance of wave speed calibration for improving detection accuracy.

Experimental methods provide real-world data to validate and refine analytical models, bridging the gap between theory and application. Ferroudji et al.⁵ conducted laboratory tests on multiphase flow pipelines, validating their CFD models under controlled conditions. Similarly, Zhu et al.⁷ investigated fluid-solid coupling vibration characteristics in pipelines, offering valuable data on how material properties affect leak detection sensitivity. Elizarov et al.⁸ used field pipelines to test magnetic flux leakage (MFL) detectors, integrating acoustic emission (AE) data for improved defect detection. Their experimental setup replicated real-world conditions, confirming the efficacy of hybrid analytical-experimental approaches. Keramat and Duan⁹ combined spectral and sample entropy analyses to enhance the detection of leaks using AE signals. Their experiments demonstrated that spectral entropy-based methods effectively differentiate between leak-induced and operational noises.

Combining analytical and experimental methods provides robust solutions for leak detection by leveraging the strengths of both approaches. Peng et al.¹⁰ employed CFD simulations alongside experimental tests to assess leak behavior in oil pipelines. This hybrid approach improved the reliability of analytical models by incorporating real-world data. Fahimipirehgalin et al.¹¹ applied machine learning (ML) models to refine experimental data, integrating statistical and wavelet analyses to distinguish between leak scenarios in multiphase pipelines. Lalitha¹² developed IoT-enabled sensors calibrated through analytical models, achieving real-time monitoring and enhanced detection reliability.

While significant progress has been made, challenges persist in small-leak detection under high-pressure and multiphase conditions. Analytical methods require refinement to handle environmental variability, while experimental methods face scalability issues for long-distance pipelines. Future research should prioritize hybrid approaches integrating AI-driven predictive models with robust experimental validations.

Recent advances in data-driven and IoT-enabled leak detection have produced several practical, high-accuracy approaches that complement physics-based methods. Attention-augmented LSTM networks have been shown to deliver near-perfect discrimination and interpretable sensor weighting in laboratory leakage experiments (AUC ≈ 0.99), improving trust in automated localization outputs¹³. Hybrid CNN–LSTM frameworks applied to acoustic emission scalograms, and in some cases combined with genetic algorithms for feature selection, have demonstrated robust, real-time identification of leak events on field-style datasets¹⁴. In parallel, IoT-based edge and remote monitoring architectures have been proposed and prototyped for onshore oil pipelines, illustrating feasible system designs for continuous remote surveillance in low-infrastructure regions¹⁵. These developments underscore two trends: (1) data-driven models can achieve strong detection performance when supplied with representative training data and careful preprocessing, and (2) IoT/edge architectures make continuous, near-real-time deployment increasingly practical. Our GA-NPW framework is complementary to these approaches in that it combines a physically interpretable NPW model with real-time parameter optimization, avoiding large retraining burdens and preserving model transparency while still enabling real-time operation^16,17.

This study combines GAs with conventional methods, utilizing experimental data and simulations to validate their performance in improving the localization of leaks under various operational conditions.

Traditional methods, such as NPW analysis and hydraulic HGI, have been widely used due to their simplicity and cost-effectiveness. However, these methods face challenges in dynamic operational environments, where pressure fluctuations and flow changes can reduce accuracy. Furthermore, HGI methods are often hindered by noise in sensor data and varying operational conditions, as noted by Zhou et al.¹⁸.

NPW and HGI methods rely heavily on capturing pressure inflections and gradient changes to identify and localize leaks. However, their performance is significantly affected by variations in boundary conditions, such as fluctuating flow rates, pressure changes, and operational noise. Gong et al.¹⁹ noted that hydraulic transient methods often fail to distinguish between actual leaks and pressure variations caused by valve operations or pump startups. This sensitivity to boundary conditions reduces the reliability of these methods, especially in dynamic systems.

Noise interference in sensor data poses another challenge for traditional methods. The inherent reliance on precise pressure measurements makes NPW techniques vulnerable to environmental and operational noise. Nguyen and Kim²⁰ demonstrated that acoustic-based leak detection methods often struggle to isolate true leak signals in noisy environments, resulting in false positives or missed detections.

Traditional methods are less effective in pipelines with nonuniform diameters or complex geometries. For instance, robotic inspection techniques, while useful for certain applications, cannot navigate nonuniform pipeline structures effectively, as noted by Kesavan et al.²¹. These limitations restrict the application of conventional methods to simple pipeline systems.

Real-time detection is critical for minimizing environmental and operational risks. However, traditional methods often require extensive post-processing or human interpretation, leading to delays in leak detection and response. Xu and Li²² highlighted that manual interpretation of data from traditional detection systems introduces significant latency, rendering these methods unsuitable for real-time applications.

Many traditional techniques rely on pre-defined models of pipeline behavior under normal and leak conditions. Abdelmoez et al.²³ observed that this dependency limits the adaptability of these methods in handling new or unforeseen scenarios, such as abrupt changes in flow dynamics or external disturbances.

Detecting small leaks is a persistent issue with traditional methods. Techniques like mass balance are often insensitive to minor discrepancies in flow rates, as their accuracy diminishes with decreasing leak size. Gong et al.¹⁹ noted that small leaks often go undetected until they escalate into larger failures, leading to significant environmental and operational consequences.

Given the limitations of traditional methods, hybrid approaches that integrate computational and analytical techniques are increasingly being explored. Nguyen and Kim²⁰ proposed a hybrid acoustic monitoring and event correlation method that mitigates the limitations of standalone techniques. Such approaches combine the strengths of conventional methods with the robustness of computational optimization tools like GAs.

Recent advancements in computational techniques have significantly enhanced the accuracy of leak detection systems. GAs, inspired by principles of natural selection, have emerged as robust optimization tools for solving complex, nonlinear problems in pipeline monitoring.

ML has proven invaluable in detecting leaks in complex pipeline systems. Techniques like neural networks, reinforcement learning, and fuzzy logic have enhanced leak detection by identifying anomalies in noisy environments.

For example, Shang et al.²⁴ used convolutional neural networks (CNNs) in combination with long short-term memory (LSTM) networks to improve the detection of transient pressure waves caused by leaks. Their method achieved superior detection rates, particularly in dynamic operational scenarios. Similarly, Fu et al.²⁵ employed reinforcement learning to train models for identifying optimal sensor placement, which significantly reduced false positives and improved system reliability.

GAs remain a cornerstone in computational optimization for pipeline leak detection. These evolutionary algorithms excel in solving multi-objective problems, such as optimizing leak localization under varying boundary conditions.

While Liu et al.²⁶ utilized GAs to enhance the accuracy of NPW analysis by dynamically adjusting propagation speed parameters. Their approach reduced average localization errors by over 30%. Further, Lalle et al.²⁷ combined GA with particle swarm optimization for multiphase flow applications, both approaches were primarily limited to offline or simulation-based optimization. In contrast, the GA-NPW framework developed in this study performs simultaneous optimization of wave speed, fluid velocity, and leak position in real time, and integrates wavelet-based noise suppression and automatic sensor time-alignment correction. The method has been validated on both real leak events and simulated pipelines of up to 300 km, demonstrating consistent accuracy even under high noise levels, flow variations, and synchronization errors. Its modular design enables direct integration into SCADA systems, achieving detection delays of around ten seconds, which represents a significant step toward practical, real-time leak detection in long-distance pipeline networks.

Hybrid frameworks combining GAs with other computational methods have shown tremendous potential for addressing the complexities of leak detection. Hu et al.²⁸ developed a GA-fuzzy logic hybrid system for detecting small leaks in long-distance pipelines. Their method adapted to changing flow dynamics, achieving high detection accuracy across varied pipeline conditions.

In another study, Ahn et al.²⁹ introduced a GA-optimized support vector machine (SVM) model for real-time anomaly detection. By combining SVMs’ classification power with GAs’ optimization capabilities, the model exhibited enhanced robustness against noisy data.

Simulation tools have become essential in validating computational models before field. GAs outperformed traditional methods in accurately localizing leaks in both single-phase and multi-phase pipelines. Real-time monitoring systems integrating computational methods have significantly enhanced pipeline safety. Shukla et al.³⁰ proposed a GA-based real-time detection system that dynamically adapts to operational changes, such as flow rate variations and sensor noise. This approach reduced detection time by 40% compared to traditional NPW systems.

Additionally, Bakhter et al.³¹ employed cloud-based platforms to integrate GA frameworks with IoT-enabled sensors, enabling real-time data processing and faster decision-making during leak events. Liu et al.³²developed a GA-based real-time monitoring framework that significantly reduced response times during leak events. The scalability of these systems has also been demonstrated by Chen et al.³³, who emphasized the ability of GA-based methods to handle large-scale pipeline networks efficiently.

Despite recent advances, existing GA-NPW implementations in the literature have been largely confined to simulation studies, have focused on optimizing a single parameter, or have lacked explicit integration into real-time monitoring frameworks. Few studies have demonstrated multi-parameter optimization of NPW in noisy, variable, long-distance pipeline environments validated against field data. This study addresses that gap by developing and validating a GA-NPW framework that optimizes wave speed, fluid velocity, and leak position in real time, incorporates wavelet-based noise suppression and sensor time-alignment correction, and operates within a SCADA-compatible modular architecture. While the current study focuses on genetic algorithms as an optimization tool, the concept of AI-driven predictive models is viewed as a complementary avenue for future development. In such a framework, predictive models based on machine learning could forecast leak probabilities and detect anomalous operating states, while the GA-NPW system would provide accurate localization once a potential leak is detected. This combination would allow both early warning and precise location estimation, strengthening the robustness of real-time leak detection systems. The objectives of this study are to evaluate the method’s accuracy against conventional NPW and HGI baselines under field and simulated conditions, assess its robustness to operational noise, flow variations, and synchronization errors, and demonstrate its scalability to pipelines of up to 300 km.

Method

Negative pressure waves (NPW)

When a leak occurs in a pipeline, the sudden drop in pressure causes a negative pressure wave to propagate in both upstream and downstream directions. These waves travel at a specific speed, determined by the pipeline’s and fluid’s physical properties, and carry crucial information about the leak’s location.

NPW detection relies on the physical principle that when a leak occurs, the sudden drop in pressure produces a transient wave that propagates in both directions along the pipeline. This wave travels at a characteristic speed determined by the compressibility of the fluid, the elasticity of the pipe wall, and the pipeline geometry. By measuring the difference in arrival times at two points, the leak position can be calculated. The wave speed, fluid velocity, and pipeline elasticity are critical because small deviations in these parameters can lead to large errors in localization. For clarity, in our mathematical formulations, each term is presented with its physical meaning to aid interpretation by non-specialist readers. The calibration based on references^11,20 process adjusts the wave speed to account for changes in temperature, pressure, and material properties, ensuring accurate leak location estimation under real operating conditions.

Mechanism of NPW detection

The wave’s propagation speed () and the fluid velocity () are critical parameters for leak localization. Figure 1 shows the NPW detection for a pipeline. The location of the leak () can be calculated based on the time delays () between the wave reaching the upstream () and downstream () ends. The relationship is expressed as³⁴:

1

Fig. 1.

Schematic of the leak localization mechanism using the NPW method, showing wave propagation from a leak site towards upstream and downstream sensors and illustrating the time difference used for position calculation.

where:

L = Total pipeline length (m).

= Negative pressure wave speed (m/s).

= Fluid velocity (m/s).

= Time difference between wave arrivals at upstream and downstream ends (s):

2

Hydraulic gradient intersection (HGI) baseline configuration

For comparative purposes, the HGI method was implemented following the procedures outlined by Zhou et al.⁴ and Gong et al.¹⁹. The method uses synchronized pressure data from upstream and downstream stations to compute hydraulic gradients as the slope of the pressure–distance relationship for each half of the pipeline. Leak location is determined from the intersection point of the upstream and downstream gradients. Prior to gradient calculation, the pressure signals were preprocessed using a moving-average filter with a one-second window to reduce high-frequency noise. No frequency-domain filtering or parameter optimization was applied, ensuring that the implementation reflects conventional HGI practice. The sampling rate for HGI measurements was 200 Hz, identical to that used for the NPW and GA-NPW methods, so that all techniques operated on the same input datasets under identical leak scenarios. This configuration provides a field-representative baseline for performance comparison.

Determination of wave speed

The accuracy of the NPW method heavily depends on the correct estimation of . The wave speed is influenced by the fluid properties, pipeline elasticity, and operating conditions. The wave speed is calculated as:

3

where:

= Bulk modulus of the fluid (Pa).

= Density of the fluid ().

= Modulus of elasticity of the pipe material (Pa).

= Thickness of the pipe (m).

= Internal diameter of the pipe (m).

Experimental calibration

Given the complexity of accurately measuring , the wave speed is often calibrated experimentally. By inducing controlled pressure waves and recording arrival times at upstream and downstream locations, aa is calculated using:

4

Here, represents the distance between the upstream and downstream sensors, and t is the measured time delay. In this study, wave speeds were calibrated using a 22-inch oil pipeline, where precise experimental setups ensured high accuracy.

The experimental calibration was performed on a 22-inch crude oil transmission pipeline with a total length of 175 km. The upstream and downstream measurement stations were each equipped with high-precision piezoresistive pressure transducers (Rosemount 3051, accuracy ± 0.05% of full scale), mounted directly to the main line through dedicated tapping points to minimize signal damping. The sensors sampled at 200 Hz and were connected to a SCADA-compatible data acquisition unit, providing GPS-synchronized time-stamping to within ± 1 ms. Controlled leaks were induced using a calibrated valve assembly located at predetermined distances from the upstream station. Leak sizes ranged from 1% to 5% of nominal flow rate, allowing assessment of method sensitivity across a representative range of severities. The pipeline was operated under typical service conditions encountered in crude oil transmission, ensuring the calibration reflected realistic operational scenarios. All tests were carried out with the line in service to incorporate operational noise sources such as pump and valve activity.

Challenges and enhancements

One limitation of the NPW method is its sensitivity to inaccuracies in timing and wave speed measurement. To address this, the integration of GA optimizes these parameters by minimizing errors between actual and predicted leak positions. This study further highlights that precise wave speed calibration, achieved through experimental and simulation data, significantly enhances NPW accuracy.

Leak localization using NPW

The NPW method is a robust tool for real-time leak localization. By analyzing pressure changes at pipeline ends, the exact position of the leak can be calculated. An alternative and simplified formula for leak localization is expressed as:

5

where:

= Average wave velocity (m/s).

L = Total pipeline length (m).

This formula assumes negligible fluid velocity compared to wave speed (), simplifying the computation.

Experimental application

The study used data of a project that tested the NPW method on a 175 km pipeline segment using both experimental and simulation setups. Real-world data were collected from ten leak tests, measuring the time delays and pressure changes across the pipeline. The findings revealed that:

• NPW provides an average error of 11%, outperforming traditional methods like the Hydraulic Gradient Intersection (HGI) method, which averaged 18%.

• GA optimization reduced NPW errors further, achieving a 5% error rate.

Key Insights are listed below:

1. Wave Speed Estimation: Variability in wave speed due to changes in fluid temperature and pressure was mitigated through dynamic calibration methods.

2. Time Synchronization: Accurate synchronization of sensor data minimized timing errors, which can introduce up to 1000 m of error for every second of mismatch.

3. Noise Reduction: Simulation tools and experimental setups were employed to filter operational noise and improve measurement reliability.

By incorporating GA into the NPW framework, the methodology achieved a balance between computational efficiency and practical accuracy, demonstrating scalability for real-time applications.

Validation

To validate the proposed leak detection approach, both experimental and simulated data were cross-compared using Pipeline Studio. The results from ten field leak tests were benchmarked against the simulated predictions. Key validation strategies included:

• Cross-Verification with Real Events: Each simulated leak was paired with a real test case, ensuring consistency in boundary conditions and input parameters.

• Statistical Analysis: The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics were calculated between the experimental leak points and those estimated via the GA-optimized NPW method.

• Model Calibration: The model’s dynamic parameters, such as pressure wave velocity and pipe elasticity, were calibrated iteratively based on observed field behavior.

This dual-track validation confirmed the robustness of the proposed approach in dynamic pipeline scenarios and supported its application in both static and transient conditions. Figure 2 shows the experimental setup and equipment. For validation, ten field leak tests were performed under varying boundary conditions. Each test involved intentional leak creation, with location, size, and duration recorded for comparison against method predictions. In addition to field tests, Pipeline Studio simulations were configured to replicate the same scenarios, ensuring direct comparability between measured and modelled results. Table 1 summarizes the key parameters for both calibration and validation phases.

Fig. 2.

The experimental setup and equipment used in this study.

Table 1.

Summary of experimental calibration and validation parameters.

Parameter	Value / Specification
Pipeline length	175 km
Pipeline diameter	22 inches
Pipeline material	API 5 L Grade B steel (typical for crude oil lines)
Operating conditions	Typical crude oil transmission service
Sensor type	Piezoresistive pressure transducer, Rosemount 3051
Sensor accuracy	± 0.05% F.S.
Sampling rate	200 Hz
Synchronization method	GPS-based, ± 1 ms accuracy
Leak induction method	Calibrated valve assembly
Leak size range	1% – 5% of nominal flow
Data acquisition system	SCADA-compatible logging unit
Noise sources present	Pump operation, valve events, ambient vibration

Optimization process

The optimization phase utilized a GA to minimize the location error between the detected and actual leak points. The parameters optimized included the wave speed (a) and fluid velocity (v), which directly influence the accuracy of the NPW method, as well as the leak position (x), with the fitness function minimizing the difference between predicted and observed leak locations according to the NPW equation. The configuration of the GA parameters was determined through a preliminary sensitivity analysis using simulated leak scenarios representative of the target pipeline conditions. Population sizes from 40 to 160, iteration counts from 100 to 300, and crossover rates from 0.1 to 0.8 were evaluated, with performance assessed in terms of mean localization error, convergence behavior, and computation time per detection cycle. The selected configuration—a population size of 80, 200 iterations, a crossover rate of 0.3, a mutation rate of 0.05, and tournament selection—achieved a balance between search-space exploration and computational efficiency. Convergence was reached in fewer than 150 iterations in all cases, and larger populations or higher iteration counts produced negligible accuracy gains while increasing computation time. This parameter set consistently maintained sub-5% localization errors in both field and simulated tests while keeping the processing time under 350 ms per detection cycle. With this configuration, the GA optimization process reduced the average localization error of the NPW method from 11% to 5% while preserving the real-time capability of the system.

Implementation architecture

The leak detection system was implemented using a modular framework comprising:

• Data Acquisition Module: Interfaces with upstream and downstream pressure sensors.

• Preprocessing Unit: Handles signal noise reduction using wavelet-based filters and time synchronization.

• Simulation Core: Executes Pipeline Studio simulations and performs scenario generation.

• Optimization Engine: Runs the GA algorithm to fine-tune parameters in real time.

• Visualization and Alerting: Provides real-time visual insights and leak alarms through an interactive dashboard.

This modular design allows for easy integration with existing SCADA systems and supports cloud deployment for remote pipeline monitoring. Figure 3 illustrates the modular GA-NPW architecture developed in this study. The system begins with the Data Acquisition Module, which collects synchronized pressure measurements from upstream and downstream sensors. The Preprocessing Unit applies wavelet-based filtering to suppress operational noise and corrects for any time misalignment between sensor signals. The processed data is then passed to the Simulation Core, which can replicate the pipeline’s hydraulic behavior using Pipeline Studio to support scenario testing and calibration. The Optimization Engine implements the GA to adjust key parameters—wave speed, fluid velocity, and leak position—in real time, minimizing the difference between measured and predicted leak locations. Finally, the Visualization and Alerting Module displays results through a SCADA-compatible interface, providing both graphical summaries and automated leak alarms. The modular design ensures that each component can be updated or scaled independently, facilitating integration into existing industrial monitoring systems. The overall conceptual framework and modular architecture of the proposed GA-NPW leak detection system are shown in Fig. 3.

Fig. 3.

Conceptual framework (a) and modular architecture (b) of the GA-NPW leak detection system. (a) Conceptual framework of the GA-NPW method integrating NPW analysis with real-time genetic algorithm optimization. (b) Modular GA-NPW leak detection system architecture showing data acquisition, preprocessing, simulation, optimization, and visualization components within a SCADA-compatible framework.

Results

Overview of experimental and simulation framework

In total, ten controlled leak scenarios were implemented in the 175 km, 22-inch crude oil pipeline while under normal service conditions. Leak locations were distributed from 15 km to 160 km from the upstream station, and leak magnitudes ranged from 1% to 5% of nominal flow rate. Testing was conducted over ambient temperatures between 5 °C and 28 °C, with pipeline flow rates varying between 0.9 m/s and 1.4 m/s. Operational disturbances such as pump start/stop cycles and valve actuations were intentionally introduced during some tests to simulate transient hydraulic changes. For the simulation phase, these same scenarios were replicated using Pipeline Studio, incorporating additional variations such as ± 10% wave speed changes, normalized Gaussian noise up to 1.0, and sensor synchronization offsets up to 2 s. This combined approach provided a comprehensive assessment of GA-NPW performance under a range of realistic operational and environmental conditions.

Comparative accuracy of leak localization techniques

The average localization error for each method is shown in Fig. 4. The GA-NPW method outperforms both NPW and HGI approaches, achieving a mean error of only 5%, while NPW and HGI recorded 11% and 18% respectively. The error variance is also notably smaller for GA-NPW, indicating improved consistency under various operating conditions. Figure 4 illustrates this performance gap, while Table 2 quantifies both mean and standard deviation for each method.

Fig. 4.

Average localization error (%) for NPW, HGI, and GA-NPW methods.

Table 2.

Mean and standard deviation of localization errors.

Method	Average error (%)	Standard deviation (%)
NPW	11	1.2
HGI	18	2.3
GA-NPW	5	0.8

The reported average localization error (%) of 5% for the 175 km pipeline corresponds to an absolute localization deviation of 8.75 km. In long-distance transmission pipelines, this level of precision is consistent with accepted industrial thresholds for real-time monitoring systems, which often regard relative errors under 10% as sufficient for initiating emergency response and isolation procedures. In practice, leak detection systems are designed to rapidly identify the affected segment, enabling operators to shut down or isolate the relevant section, after which more targeted inspection techniques, such as in-line inspection tools or ground surveys, are employed for pinpointing. The GA-NPW framework meets these requirements while offering enhanced robustness compared to NPW and HGI methods, maintaining low relative error even under high operational noise and boundary condition variability³⁵.

For consistency in comparative analysis, all methods were evaluated using a set of defined metrics: (1) Average localization error (%) – the mean absolute difference between predicted and actual leak positions normalized by total pipeline length; (2) Standard deviation of localization error (%) – a measure of variability in predictions across test cases; (3) Root Mean Square Error (RMSE) and (4) Mean Absolute Error (MAE) – both expressed in meters to quantify absolute positional deviation; (5) Detection delay (s) – the time from leak initiation to system alarm; and (6) Average computation time per detection cycle (ms) – the processing load required to deliver a result. These metrics capture both the precision and robustness of each method, as well as their responsiveness and computational feasibility. Table 3 shows a summary of evaluation metrics used in comparative analyses.

Table 3.

Summary of evaluation metrics used in comparative analyses.

Metric	Definition	Units	Purpose in analysis
Average localization error	Mean absolute difference between predicted and actual leak position, normalized by pipeline length	%	Measures overall accuracy across scenarios
Standard deviation of localization error	Variability of localization error across test cases	%	Assesses consistency of method performance
RMSE (Root mean square error)	Square root of the mean of squared differences between predicted and actual leak locations	m	Quantifies absolute deviation magnitude
MAE (Mean absolute error)	Mean of the absolute differences between predicted and actual leak locations	m	Provides average absolute positional error
Detection delay	Time between leak occurrence and system alarm generation	s	Evaluates responsiveness in real-time operation
Average computation time per detection cycle	Mean processing time to analyze data and produce a leak location estimate	ms	Measures computational feasibility for real-time use

In this paper, percentage-based results are reported as localization error (%), the normalized absolute difference between predicted and actual leak positions, while positional differences expressed in meters or kilometers are reported as localization deviation (m or km). This terminology is applied consistently throughout all results and figure captions.

Genetic algorithm optimization convergence

The optimization capability of the Genetic Algorithm was assessed by analyzing the fitness score over 200 iterations. Figure 5 shows a steady decline in error over the iterations, indicating efficient convergence. The fitness stabilized after approximately 150 iterations, suggesting that the algorithm had effectively minimized the localization error.

Fig. 5.

Genetic algorithm optimization convergence curve.

The convergence profile of the GA has direct implications for computational feasibility in real-time leak detection. In all tested cases, convergence occurred within 150 iterations—well before the 200-iteration maximum—while maintaining an average processing time of 320–350 ms per detection cycle on standard industrial-grade hardware. This runtime fits comfortably within the available computation window for 200 Hz data streams in a SCADA-integrated monitoring loop, allowing optimization, signal processing, and alert generation to occur without introducing latency beyond operational thresholds. As a result, the GA-NPW method achieves rapid parameter refinement without necessitating specialized high-performance computing resources, making it practical for continuous deployment in field monitoring systems.

Accuracy of leak location predictions

To further evaluate the precision of the leak localization, predicted leak positions for each method were compared against actual leak coordinates for ten test cases. Figure 6 clearly shows that GA-NPW predictions resulting in localization deviations of less than 9 km for all cases, while NPW and HGI deviate more substantially.

Fig. 6.

Localization deviation (km) between predicted and actual leak positions for all test cases.

Sensitivity to wave speed Estimation

Leak localization methods are highly sensitive to wave speed estimation. As shown in Fig. 7, a ± 10% deviation in wave speed leads to increased localization errors in all methods, but GA-NPW shows minimal sensitivity. While NPW and HGI errors rise to 16–21%, GA-NPW remains below 7%, even under extreme deviations.

Fig. 7.

Effect of wave speed deviation on localization error (%).

Impact of operational noise on accuracy

Sensor data in pipelines is frequently affected by operational noise from pumps, valves, and environmental interference. Figure 8 demonstrates that as normalized noise levels increase from 0 to 1.0, traditional methods (NPW and HGI) experience a sharp rise in error, while GA-NPW demonstrates resilience, limiting the impact of noise to only a 2% increase.

Fig. 8.

Impact of operational noise on localization error.

A summary of extreme cases (± 10% wave speed, high noise) is presented in Table 4.

Table 4.

Sensitivity analysis for noise and wave speed Deviation.

Condition	NPW error (%)	HGI error (%)	GA-NPW error (%)
+ 10% wave speed	16	21	6
-10% wave speed	16	21	6
High noise (1.0)	18	24	7

Adaptability to flow rate variability

Pipeline systems often operate under variable flow rates due to pump adjustments, system demands, or partial closures. The sensitivity of leak detection accuracy to flow rate changes was examined across a range from 60% to 120% of nominal flow. As shown in Fig. 9, both NPW and HGI methods exhibit increasing error with greater deviation from the nominal condition. NPW error rises from 9% to 15%, and HGI ranges from 15% to 24%. In contrast, the GA-NPW method maintains a consistently low error profile, rising only from 5% to 7% across the same range.

Fig. 9.

Effect of flow rate variation on localization error (%).

This confirms the GA-NPW framework’s superior adaptability to hydraulic variability, ensuring robust performance without requiring extensive recalibration.

Impact of sensor synchronization errors

Accurate time synchronization between upstream and downstream sensors is crucial for the NPW technique. Even minor mismatches can result in large errors, as the localization formula depends on precise time-of-arrival differences. Figure 10 shows the impact of increasing synchronization error (0 to 2 s) on localization accuracy.

Fig. 10.

Impact of time synchronization errors on localization deviation (m).

For NPW, the error increases linearly, reaching nearly 1,100 m at a 2-second mismatch. HGI also demonstrates severe degradation, while GA-NPW significantly mitigates this issue, limiting the error to under 170 m at 2 s. This resilience arises from the GA’s optimization of time alignment parameters as part of its search process.

Across all tested uncertainty scenarios—including ± 10% variation in wave speed, high operational noise (normalized value 1.0), flow rate changes from 60% to 120% of nominal, and sensor synchronization errors up to 2 s—the GA-NPW method maintained markedly higher robustness than conventional NPW and HGI techniques. Under wave speed deviations, GA-NPW retained sub-7% error compared to 16–21% for other methods. Even at extreme noise levels, error increased by only 2% from baseline, and under flow variability, accuracy remained between 5% and 7%. For severe synchronization offsets, GA-NPW limited location deviation to less than 170 m, while NPW exceeded 1,000 m. These results, drawn from Figs. 7, 8, 9 and 10; Table 3, collectively illustrate the method’s resilience to operational variability, a critical factor for reliable leak detection in field conditions.

Real-time detection response and computational efficiency

Timely leak detection is critical to minimize environmental damage and operational downtime. The system’s responsiveness was assessed by analyzing the delay between leak occurrence and detection signal generation. As shown in Fig. 11, traditional methods such as NPW and HGI exhibit detection delays of 30–40 s on average. These delays stem from the need for manual or post-processed interpretation of sensor signals. In contrast, the GA-NPW system generates a detection alert in approximately 10 s, owing to its real-time optimization and integrated data filtering capabilities.

Fig. 11.

Detection delay after leak occurrence.

In addition to response time, the computational efficiency of each method was evaluated. Figure 12 illustrates the average processing time required per leak detection cycle. While GA-NPW exhibits slightly higher computational overhead (320 ms) compared to NPW (150 ms) and HGI (230 ms), it remains within acceptable limits for real-time applications. This modest increase in processing time is justified by the significant gains in accuracy and robustness.

Fig. 12.

Average computation time per leak detection cycle.

Scalability with pipeline length

To evaluate the scalability of each method, leak localization accuracy was analyzed across different pipeline lengths ranging from 50 to 300 km. As shown in Fig. 13, both NPW and HGI methods exhibit a gradual increase in localization error as pipeline length increases, reaching errors of 17% and 27% respectively at 300 km. This degradation is attributed to cumulative uncertainties in wave speed, pressure loss, and sensor synchronization over longer distances.

Fig. 13.

Localization error (%) as a function of pipeline length for NPW, HGI, and GA-NPW methods.

The GA-NPW method, however, maintains low and stable error rates across all tested lengths. At 300 km, the GA-NPW approach reports an error of only 8%, demonstrating strong adaptability and resilience to scale-related challenges. This confirms the method’s suitability for large-scale pipeline networks, including those operating under diverse environmental and boundary conditions.

The scalability of the GA-NPW method was confirmed by its ability to maintain low localization error rates across pipeline lengths from 50 km to 300 km without any algorithmic reconfiguration, demonstrating inherent adaptability to network expansion. Even at 300 km, error increased only modestly to 8%, compared to 17% for NPW and 27% for HGI. Real-time feasibility was validated through detection delays of approximately 10 s, a three- to fourfold improvement over conventional methods. The GA optimization process required just 320–350 ms per detection cycle on standard industrial-grade hardware, comfortably within the processing window for 200 Hz SCADA data streams. This combination of low computational overhead, rapid detection, and consistent scalability confirms the method’s suitability for deployment in large-scale, real-time pipeline monitoring without the need for specialized high-performance computing resources.

Conclusion

This study introduced a hybrid leak detection framework that integrates Genetic Algorithm optimization into the Negative Pressure Wave method, achieving real-time refinement of wave speed, fluid velocity, and leak position. Compared with conventional NPW and HGI methods, GA-NPW reduced average localization error from 11% to 18% to 5%, maintained accuracy under challenging operational uncertainties, and improved detection speed from 30 to 40 s to approximately 10 s. These improvements were consistently observed across both field and simulation testing, confirming the method’s robustness and adaptability to diverse pipeline operating conditions. The method was evaluated through ten leak scenarios simulated and tested along a 175-kilometer oil pipeline segment. The results confirmed the advantages of using GA for parameter optimization, including wave speed and leak location estimation, yielding significant improvements in both accuracy and robustness.

Unlike conventional methods that struggle with variability in operational conditions, the GA-NPW framework demonstrated adaptability, low error rates, and real-time responsiveness. By optimizing critical parameters based on both experimental and simulated data, the method effectively reduced error and improved detection speed, even under noise, flow fluctuations, and pipeline length scaling. Key Findings are listed below:

• The GA-NPW method reduced the average localization error to 5%, compared to 11% for NPW and 18% for HGI.

• The system maintained reliable detection performance under high sensor noise conditions, showing only a marginal increase in error, while NPW and HGI degraded significantly.

• Across flow rates ranging from 60% to 120% of nominal, GA-NPW sustained high accuracy, whereas traditional methods showed escalating errors.

• The method was less sensitive to synchronization mismatches, with error increasing modestly (less than 170 m at a 2-second mismatch), unlike NPW, which showed errors exceeding 1,000 m.

• The system achieved leak detection within approximately 10 s of occurrence, far faster than NPW and HGI (30–40 s).

• GA-NPW maintained consistent performance across increasing pipeline lengths up to 300 km, confirming its utility in large-scale networks.

• Although slightly more computationally intensive (average 320 ms per detection cycle), the trade-off for improved accuracy and real-time detection is acceptable for industrial applications.

From a practical implementation perspective, the GA-NPW system’s modular, SCADA-compatible design, sub-350 ms computational time per detection cycle, and tolerance to noise, flow variability, and synchronization errors make it readily deployable in existing industrial monitoring networks. While the present validation was conducted on a 175 km crude oil pipeline, the demonstrated scalability to 300 km indicates strong potential for use in larger transmission systems. Future enhancements may include integration with AI-driven predictive models to provide early leak probability alerts and coupling with adaptive sensor networks to further reduce detection delays. Additional long-term field deployments across different pipeline types and environmental conditions will further confirm the method’s reliability and operational benefits.

Limitations and future work

Although the GA-NPW method demonstrated significant improvements in accuracy, robustness, and detection speed, certain limitations remain. The optimization process introduces additional computational load compared with conventional NPW techniques, which was manageable in the present real-time framework but could require further refinement in very large-scale networks with extensive sensor arrays. The method also depends on the quality and continuity of sensor data; while noise suppression and synchronization correction mitigate many issues, prolonged sensor failures or communication disruptions could still impair performance. Moreover, the genetic algorithm’s performance is influenced by the selection of algorithmic parameters such as population size, mutation rate, and crossover rate, which may require tuning for different pipeline configurations. The present validation focused on a single long-distance oil pipeline and simulated extensions to 300 km, and additional studies are needed to assess performance in complex branched or looped pipeline systems.

Future research should explore the integration of AI-driven predictive models with the GA-NPW framework. Predictive algorithms, such as neural networks or reinforcement learning agents, could provide early warnings by modelling pipeline behavior under varied operational conditions, while the GA-NPW system could perform high-precision localization once a potential leak is identified. This combination would unite the strengths of predictive analytics and optimization, supporting faster and more reliable leak detection in large-scale, dynamic pipeline networks.

List of symbols

L

Total pipeline length (m)

a

Negative pressure wave speed (m/s)

v

Fluid velocity (m/s)

t

Time difference between wave arrivals at sensors (s)

x

Leak position (m)

K

Bulk modulus of fluid (Pa)

ρ

Density of fluid (kg/m³)

E

Elastic modulus of pipe material (Pa)

e

Pipe wall thickness (m)

D

Internal diameter of pipe (m)

AE

Acoustic emission

CFD

Computational fluid dynamics

CNN

Convolutional neural network

GA

Genetic algorithm

HGI

Hydraulic gradient intersection

LSTM

Long short-term memory

MAE

Mean absolute error

MFL

Magnetic flux leakage

ML

Machine learning

NPW

Negative pressure wave

RMSE

Root mean square error

SCADA

Supervisory control and data acquisition

SVM

Support vector machine

Author contributions

Ali Sharifi: Conceptualization, Methodology, Supervision, Writing – Original Draft.Seyyed Faramarz Ranjbar: Investigation, Data Curation, Validation, Writing – Review & Editing.Seyyed Amirreza Mousavi Alamdardehi: Software Development, Simulation, Visualization.Naser Aslani: Experimental Design, Resources, Project Administration.Reza Zarezadeh: Formal Analysis, Statistical Evaluation, Review & Editing.Hamid Majidi: Instrumentation Setup, Data Collection, Field Testing.Fatemeh Asadi: Literature Review, Technical Writing, Figures and Illustrations.

Data availability

All data generated or analyzed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.