Lamb-Wave-Based Structural Health Monitoring for Surface Crack Detection in Pipelines

Abstract

Pipelines play a vital role in transporting oil, gas, water, and other critical resources across vast distances. However, they are often exposed to harsh environmental conditions, aging, corrosion, and mechanical stresses that can lead to structural degradation or failure. Structural health monitoring (SHM) offers a proactive solution for ensuring the integrity and safety of pipeline systems through continuous or periodic assessment using advanced sensing technologies and analytical methods. This paper presents the use of Lamb waves to find surface cracks in pipelines. Finite element software, ABAQUS/CAE 2017, is used to simulate intact and damaged pipes. The Time of Flight (ToF) method is applied with two techniques. The first is based on the difference between the received waves for damaged and intact pipelines, while the second is based on the difference between two sensor reads in damaged pipelines. The effectiveness of SHM systems in detecting anomalies and guiding maintenance decisions is evaluated. The results demonstrate the potential of SHM to enhance pipeline reliability, reduce downtime, and support condition-based maintenance strategies. This research contributes to the development of smarter, safer, and more efficient pipeline monitoring systems.

1. Introduction

Pipelines are critical components of modern infrastructure, used extensively to transport oil, gas, water, and other fluids across vast and often remote areas. Due to their strategic importance, the structural integrity and operational safety of pipelines are of paramount concern. Over time, pipelines are subjected to a variety of stresses, including internal pressure fluctuations, environmental loading, corrosion, mechanical damage, and material fatigue. These factors can significantly degrade the structural performance of pipelines, increasing the risk of leaks, ruptures, and catastrophic failures that can lead to severe environmental, economic, and human consequences.

To mitigate such risks, there is a growing emphasis on the development and deployment of structural health monitoring (SHM) systems. SHM involves the use of sensors, data acquisition systems, signal processing, and computational models to monitor the condition of structures in real time or at scheduled intervals. By continuously or periodically assessing the pipeline’s response to operational loads and environmental conditions, SHM enables early detection of defects, assessment of damage severity, and informed decision-making for maintenance and repair. This shift from traditional time-based inspection to condition-based monitoring helps improve safety, reduce unplanned downtime, and optimize maintenance costs.

Damage detection involves comparing current signals with baseline signals from a healthy state. Ultrasonic guided wave (UGW) technology was commonly used to generate signals for monitoring the structural integrity of pipeline systems, as described by Farrar and Worden (2007) [1] and Lowe et al. (1998) [2].

However, there was typically a trade-off between sensitivity to detection of small defects and the ability to cover a broad area with a single sensor. Lower frequencies were used for larger structures to allow for longer wave propagation distances, although this reduced the sensitivity to smaller defects. Guided waves were often applied in a screening mode to identify potentially damaged regions rather than providing detailed defect characterization. They served as an early indication of damage severity, offering initial assessments of structural health [3].

Ultrasonic guided waves (UGWs) were commonly used for structural health monitoring (SHM) and non-destructive testing (NDT). They offered an efficient way to identify damage in structures such as rails, aircraft, and composite materials due to their ability to propagate over long distances and interact with structural defects. Damage identification using guided waves typically involved multiple stages, as shown in Figure 1.

Guided-wave-based damage detection and health monitoring technologies have produced a multitude of research results over a long period of development. Gazis solved harmonic guided propagation along an infinite hollow tube by the use of the elastic theory, successfully explaining the dispersion effect and multi-mode episode of the guided waves from a theoretical view, which marked the start of guided wave research [4]. Greenspon systematically investigated cylinder shell dispersion curves and displacement fields [5,6]. Silk and Bainton successfully categorized guided waves in a cylinder shell into the symmetric longitudinal mode L (0, m), torsional mode T (0, m), and antisymmetric flexural mode F (n, m), and the categorization is currently in use [7]. Lowe et al. derived guided waves dispersion equations in a layered cylinder shell [2,8]. Aristegui et al. and Chen et al. studied guided waves propagation issues in pressured water pipelines, focusing on boundary influences on the frequency dispersion and mode transformation [9,10], and Elvira further explored the travelling attitude of guided waves in a circular cross-section pipe filled with viscous liquid [11]. Yan et al. experimentally validated the dispersion effect and multi-mode of guided waves [12,13].

Figure 1. Ultrasonic guided wave damage identification stages [14].

Figure 1. Ultrasonic guided wave damage identification stages [14].

Although finite element analysis (FEA) methods have played an important role in guided-wave-based SHMs and guided wave technology is improving, there are also some challenges with FEA in pipe structures [2,8,15,16]. One of the issues is the boundary effect on the echo signal due to inappropriate PZT transducer arrangement and frequency selections, inducing a superposition near the boundary range and making the identification very complicated [14].

Despite the advancements in SHM technologies for pipelines, several challenges remain. One major challenge is the high cost and complexity of implementing an SHM system over large-scale pipeline networks. The installation and maintenance of sensors, as well as the need for continuous data collection and processing, can be resource-intensive, especially for pipelines in remote or harsh environments.

Another challenge is the data interpretation problem. SHM systems generate vast amounts of data, and extracting meaningful information from this data requires sophisticated algorithms and models.

Finally, the integration of various SHM technologies and the development of standardized protocols for data collection, analysis, and reporting are still areas that need further exploration. A unified approach that combines different sensing techniques and simulation tools could lead to more comprehensive and reliable SHM systems for pipelines.

This study aims to address some of the aforementioned gaps by employing a combination of finite element simulations, sensor-based monitoring, and data-driven analysis to assess pipeline integrity. By integrating the advanced capabilities of ABAQUS with real-world SHM data, this research seeks to enhance damage detection capabilities and contribute to more effective pipeline maintenance strategies.

This paper investigates the use of propagation waves for detecting and characterizing surface cracks in pipelines. It focuses on determining the location and width of cracks by analyzing wave behavior. The study employs signal processing techniques to interpret wave reflections and scattering caused by crack-induced discontinuities. Numerical methods validate the approach, demonstrating high sensitivity and accuracy in identifying surface damage. The findings highlight the potential of wave-based diagnostics for real-time monitoring and early fault detection in pipeline systems. This research contributes to enhancing pipeline safety, minimizing failure risks, and improving maintenance strategies.

2. Modeling and Methodology

This section outlines the approach used to assess the structural health of pipeline systems through a combination of numerical modeling and sensor-based monitoring techniques. The methodology integrates finite element analysis using ABAQUS with principles of structural health monitoring (SHM), enabling the simulation and detection of damage under operational scenarios.

A three-dimensional model of a pipeline segment was developed using ABAQUS/CAE 2017. The pipe used was 2000 mm long and had an outer diameter of 70 mm and a thickness of 4 mm.

In the real tube, the type of steel is carbon steel, for which the mechanical properties were obtained from the production certificate of the pipe factory. The mechanical property parameters of the used steel material are shown in

Table 1. Mechanical property parameters of steel material.

Density (kg/m3)	Young’s Modulus (GPa)	Poisson’s Ratio
7850	210	0.32

.

The geometry is discretized using C3D8R (8-node linear brick, reduced integration) for solid elements. The mesh density is adjusted to divide the model into elements with a maximum edge length of 5 mm. This size balances accuracy and computational efficiency, allowing the model to capture detailed stress and strain variations without excessive computational load. A 5 mm mesh is particularly beneficial for simulations requiring precise local analysis, providing a finer resolution to accurately represent the model’s geometry and material response under loading conditions, as shown in Figure 2.

The simulation is carried out using ABAQUS/Standard for ABAQUS/Explicit to take the dynamic effects into consideration.

To emulate SHM, virtual sensors (strain gauges) are placed on the finite element model in a circular pattern, as shown in Figure 3, to investigate the effect of sensor location with respect to cracks on the efficiency of the damage detection technique.

2.1. Damage Detection Algorithm

The Time of Flight (ToF) method is widely used as a non-destructive technique for detecting damage in structures. It is used in this research to detect damage in pipelines. It involves sending ultrasonic waves along the pipe and measuring the time it takes for the waves to travel between a transmitter and a receiver. Any defects such as corrosion, cracks, or wall thinning alter the wave path or velocity, resulting in measurable delays or distortions in the signal. The ToF method is applied with two techniques. The first is based on the difference between the received waves in sensors for damaged and intact pipelines, while the second is based on the difference between two sensor reads in damaged pipelines. The ToF method is suitable and effective for long-range inspection due to its ability to detect internal and external flaws without requiring access to the entire pipeline length.

To apply the ToF technique on the pipeline structure, a force is applied to the pipe starting edge, and a hair crack is assumed to be 950 mm away from the starting point. Sensors are put 400, 900 mm and 1100 mm apart to track how the waves spread on the pipe’s surface, as shown in Figure 4.

To measure the accuracy of the damage detection techniques, the error in damage detection is measured as the difference between the estimated crack distance and the actual distance with respect to the actual distance, as follows:

$$\%error={\displaystyle \frac{estimateddistance-accuratedistance}{accuratedistane}}$$

2.2. Validation

To verify the wave propagation behavior in the simulated pipeline structure, as shown in Figure 5, finite element analysis was performed using ABAQUS and compared with experimental results. Guided wave propagation was simulated by applying an ultrasonic pulse at one end of the pipeline and monitoring the response at a location along its length. The selected sensor was 1000 mm from the pipe starting point. The material properties, boundary conditions, and excitation parameters in the model were carefully matched to those used in a previous experimental study [14]. As shown in Figure 6. The displacement time history at the pipe start point is shown in Figure 7 for the simulated and experimental tests respectively. The displacement time history for these pipe sensors located 1000 mm from the start point is shown in Figure 8. The simulation results are closely aligned with the experimental data, confirming the accuracy of the numerical model.

2.3. Selection of Excitation Signals

This research looks at choosing the right signals to study how waves move through steel pipes. Different categories of excitation signals are studied (by a HANNING window function) to show how they can effectively detect and evaluate problems like cracks or corrosion in pipelines. The aim is to find signals that make wave transmission better for accurately monitoring the pipeline’s condition. In the time domain, a normalized waveform involves changing a signal’s amplitude to a standard range, usually between −1 and 1, as presented in Figure 9. This process keeps the waveform shape the same but adjusts its values so that signals from various sources can be compared and analyzed more easily.

2.4. Time Increment Selection

The time interval affects the numerical results when using a finite element model. The choice of analysis step and time increment for the guided wave pipe structural simulation depends on the properties of the structure, damage, detection signal sampling interval, and frequency. For a big analysis step and longer time increment, using FEA calculations can save time. However, the chosen detection signal may not be sensitive enough to find small damage, which could lead to inaccurate results.

On the other hand, using a smaller analysis step and shorter time increment is better for finding tiny damage efficiently, but this approach may require more time and end up costing more when using SHM technology in engineering. In the ABAQUS/Standard module, dynamic explicit analysis is chosen to study pipe structure damage. The time step and increment are based on previous research to achieve convergence. As per the Newmark time increment scheme [17], the maximum time increment should be smaller than 1/20 of the excitation signal’s period at the highest frequency. This is represented by Equation (1).

$$∆t < {\displaystyle \frac{1}{20Fmax}}$$

(1)

where Δt is the time increment and Fmax represents the highest frequency of the excitation signal. In this research, the highest frequency of the excitation signal is 70 kHz, so it can be determined that the time increment should be less than 0.7 µm when employing Equation (1). Considering the accuracy of the analytical results, 0.05 µm is chosen as the time increment. The output settings in ABAQUS are mainly composed of field output settings and history output settings. The simulation analysis results are selected from time history curves by extracting voltage and displacement signals in the corresponding nodes in the model.

2.5. Damage Cases

To investigate the propagation behavior of a guided-wave-based signal in a damaged pipe structure, typical damage along the circumferential direction is introduced on the surface of the pipe. Shear-type piezoceramic elements are used in the simulation of PZT transducers. Circumferential damage with radial angles of 22.5, 45, 67.5, and 90 degrees, a maximum depth of 3 mm, and a longitudinal width of 2 mm, which is located at a distance of 950 mm from the PZT actuators (50 mm from the PZT sensors), is arranged. Two damage cases are selected for each damage radial angle, as shown in

Table 2. Cases of cracks.

Damage Angle Size	Abaqus Simulation	Case (1)	Case (2)
22.5°
45°
67.5°
90°

.

2.6. Wave Velocity in Steel Pipeline

To use the ToF technique for damage detection in pipelines, it is required to calculate the velocity of the guided wave in the steel pipes. To determine the wave velocity, the pulse test is performed many times, and the velocity is calculated based on the time between two successive sensors. Figure 10 shows the received wave at sensors 17 and 33 at distances of 900 and 1100 mm from the pipe starting point for healthy and damaged pipelines respectively. Moreover, the acceleration response is employed as the sensor output due to its high sensitivity. From the time of the corresponding points in the received waves, the estimated velocity in the steel pipe equals approximately 5431 m/s.

3. Results and Discussion

This section presents the outcomes of the finite element analysis and simulated SHM implementation on the pipeline model. The results focus on the detection of damage using sensor data and the performance of the SHM system in identifying early signs of failure.

3.1. Damage Location Detection

The ToF method is applied with two techniques. The first is based on the difference between the received waves for damaged and intact pipelines, while the second is based on the difference between two sensor reads in damaged pipelines. Firstly, the two techniques are applied on the first damage case when the damage is between sensors 17 and 18.

3.2. First Technique

For the first technique, the received wave accelerations at the sensor (S17) for healthy and damaged pipelines are shown in Figure 11. It is noticed that in the first 0.2 ms, the two time histories are identical, and then there is a small deviation between them. The reason for this deviation is that the wave in the damaged pipeline collides with the crack and is then reflected to the sensor.

It is important to pay attention to the first arrival of the wave at this sensor, as shown in Figure 12. A clear deviation between the received waves in the healthy and damaged pipelines is observed. The difference between these received waves is shown in Figure 13. To detect the time of the first valuable deviation between the two waves, the absolute difference between them, as shown in Figure 14, is plotted, the maximum absolute difference is detected, and the corresponding time (in thousandths of a second) is recorded, as shown in Figure 14.

Calculating the distance of the wave’s travel from the first deviation time and the wave speed leads to 1004.7 mm, while the actual distance is 1000 mm in total to reach to this sensor after reflection from the crack that is 950 mm from the pipeline starting point and 50 mm from the sensor. The accuracy of this technique is 0.47%, which indicates its high efficiency in damage detection, but this high accuracy is expected because sensor 17 faces the damage. However, in real cases, the damage is unknown, and it is not necessary to place the sensor facing the damage. When the other sensors (G2) are used with the same procedure to detect the damage location, the accuracy of this technique is reduced, as shown in Figure 15. It is found that when the sensor location is near the crack, the error of this technique reaches 9.7%, which is a reasonable value. This error can be reduced by installing two sensors in the pipeline and taking the minimum damage distance from them. However, the two sensors should be carefully selected to ensure they are sufficiently far apart. In such a case, the error does not exceed 5.2%.

When these procedures are repeated for sensor group G1), which are 400 mm from the pipeline starting point, i.e., sensors S1 to S16, it is found that the accuracy of this technique is increased, as shown in Figure 16. It is noted that for sensor group G2, the accuracy is decreased for the sensors that are on the opposite side of the crack (S25), while for sensor group G1, the accuracy is increased for sensors that are on the opposite side of the crack (S8) because the reflected waves from the crack did not reach the sensor (S25) due to its small distance from the crack, while the reflected waves from the crack reached the sensor (S8) due to its long distance from the crack.

When these procedures are repeated for sensor group G3, which are 1100 mm apart from the pipeline starting point, i.e., sensors S33 to S48, it is found that the calculated distance for first difference between the time histories of the healthy and cracked pipelines is matches the sensor location (i.e., 1100 mm from the pipeline starting point) because the sensor group lies after the crack, which means that the wave was not reflected back to these sensors; rather, the observed difference results from the reduced wave energy passing the crack compared to the healthy pipeline, due to partial reflection at the crack.

The same procedures are repeated for all damage cases. The error in the damage distance detection obtained when using sensor group G1 is shown in

Table 3. Error of first technique for damage distance detection obtained using sensor group G1.

Damage Angle Size	Case (1)	Case (2)
22.5°
45°
67.5°
90°

, while the error obtained when using sensor group G2 is shown in

Table 4. Error of first technique for damage distance detection obtained using sensor group G2.

Damage Angle Size	Case (1)	Case (2)
22.5°
45°
67.5°
90°

. It is found that the error in the damage detection obtained using sensor group G1 did not exceed 0.84%, while that obtained using sensor group G2 did not exceed 9.7%. It is also noted that the accuracy of this technique is improves for larger damage sizes because the amount of reflected waves is larger.

3.3. Second Technique

For the second technique, the received wave accelerations at sensor group G2 for the damaged pipeline are shown in Figure 17. It is noted that in the first 0.2 ms, all the sensor time histories are identical, and then there is a small deviation between them because the reflected waves from the crack reached some sensors before others with respect to their distance from the crack. By selecting two opposite sensors in this group (S17 and S25), the absolute difference between these time histories is obtained, as shown in Figure 18. When searching for the time corresponding to one thousandth of the maximum value, it is found at 0.185 ms, which corresponds to a distance of 1005 mm with an error of 0.5%. When these procedures were repeated with sensor S17 with the other sensors in the same group except for the two adjacent sensors (S18 and S32), the error in detecting the crack location did not exceed 0.72%, as shown in Figure 19, which highlights the efficiency of this technique.

When this technique is applied to sensor group G1, i.e., sensors S1 to S16, the error in detecting the crack location using S1 with the other sensors is obtained, as shown in Figure 20, which shows a larger error than that obtained for sensor group G2. The maximum error in detecting the crack location is still at an acceptable level.

To increase the accuracy of the second technique, the difference between three sensor reads is used to detect the damage location. The absolute difference between each of the two sensors is used to calculate the distance, and the minimum distance is taken into account, as shown in

Table 5. Error of second technique for damage distance detection obtained using sensor group G1.

Damage Angle Size	Case (1)	Case (2)
22.5°
45°
67.5°
90°

for sensor group G1and

Table 6. Error of second technique for damage distance detection obtained using sensor group G2.

Damage Angle Size	Case (1)	Case (2)
22.5°
45°
67.5°
90°

for sensor group G2. It is noted that the error obtained when using three sensors is smaller than that obtained when using two sensors only.

To conclude the previous results,

Table 7. Max error of damage distance detection.

Sensors	G1				G2
Case	1		2		1		2
Technique	First	Second	First	Second	First	Second	First	Second
Crack Angle
22.5	0.94	1.98	0.96	2.09	9.68	2.62	9.68	1.94
45	0.78	2.09	0.76	2.01	8	0.91	8	1.04
67.5	0.55	1.9	0.55	1.96	6.48	1.02	6.48	1.02
90	0.53	1.89	0.53	1.92	5.85	0.77	5.85	1.26

shows the maximum error in damage detection in the pipeline obtained using the two techniques when sensor groups G1 and G2 are used. It is found that the first technique delivers more accurate results when sensor group G1 is used, while the second technique delivers more accurate results when sensor group G2 is used. It is found that the maximum error for the first technique decreased when the size of the crack increased.

3.4. Detection of Crack Center

To determine the center of the crack on the pipe circumference, a group of sensors is distributed before the crack location that was detected in the first stage, and the test is repeated to receive the wave after being reflected from the crack, and the error of the crack location detection is calculated based on the first technique, as shown in Figure 21. Then, this is repeated for another cycle on the pipe circumference, as shown in Figure 22, the distance separating the two detected peaks is evaluated, as shown in Figure 23, a parabolic fitting is constructed, and the equation of the fitted curve is concluded, as shown in Figure 23. The location of the fitted curve vertex indicates the angle of the crack center on the pipe circumference. The center of the crack is indicated by the flat area on the original curve shown in Figure 23. This procedure is applied in the eight damage cases, and the fitted curves and concluded equations are shown in

Table 8. Fitted curves and concluded equations for damage extent using sensor group G2.

Damage Angle Size	Case (1)	Case (2)
22.5°
45°
67.5°
90°

.

The accuracy of this technique for all cases is summarized in

Table 9. Error of damage center detection.

	Equation Parameters			θ Center
Case	A	B	C	Estimated	Exact	Error (%)
22.5 Case1	0.0346	−25.672	4793.2	370.9827	371.5	0.14
22.5 Case2	0.0346	−27.223	5386.6	393.396	393.75	0.09
45 Case1	0.0235	−22.241	5306.6	473.2128	472.5	0.15
45 Case2	0.0235	−24.345	6352.5	517.9787	517.5	0.09
67.5 Case1	0.0212	−22.418	5963.1	528.7264	528.75	0
67.5 Case2	0.0195	−9.1094	1112.8	233.5744	236.25	1.13
90 Case1	0.0174	−7.8121	917.62	224.4856	225	0.23
90 Case2	0.0174	−10.94	1761.6	314.3678	315	0.2

. It is found that this method detects the center of the crack accurately in all damage cases.

3.5. Identification of Multiple Cracks in “Steel Pipe”

Description of the Pipeline

The pipe used in the test was 2000 mm long, and it had an outer diameter of 70 mm and a thickness of 4 mm. There were multiple cracks, located 500 and 1350 mm away from the starting point. Sensors were put 400, 900, and 1100 mm apart to track how the waves spread on the pipe’s surface, as shown in Figure 24. A force was applied at the starting point of the pipe. The location of the two cracks on the pipe circumference is shown in Figure 25 and in the finite element model in Figure 26.

By applying the two previous techniques that were used in detecting a single crack, the first crack was detected accurately. After detecting the first crack, a finite element model was prepared with the detected crack, as shown in Figure 27, and the results of this model were used as a baseline for detecting the second crack, and so on.

The difference between the received waves at sensor S33 for pipeline with two cracks and the simulated single crack that was treated as a healthy pipeline is shown in Figure 28. It is shown that in the first 0.3 milliseconds, the two received waves were identical because the wave did not reach the second crack. The difference appeared after this time because the wave was reflected in the second crack, while in the simulated single-crack pipeline, no reflection occurred. The time of this difference was used to determine the distance of the second crack, and this was compared with that of the real crack distance. This procedure was repeated using a single sensor only from sensor group G3, and the error of the damage detection was calculated, as shown in Figure 29. It is shown that the maximum error was 3.5%, which indicates the feasibility of this technique. When sensor group G2 was used to detect the second crack, the error was less than that for sensor group G3, as shown in Figure 30, because the reflected wave was spread over wide area when passing a long distance. When sensor group G2 was used to detect the second crack, the error increased, as shown in Figure 31, because the reflected wave from the second crack passed the first crack and was reflected again to sensor group G2, and the wave passed to sensor group G1 was very small.

4. Conclusions

This study presented a comprehensive approach to the structural health monitoring (SHM) of pipelines by integrating finite element modeling using ABAQUS with simulated sensor-based monitoring and damage detection techniques. The key objective was to evaluate the structural integrity of pipeline systems under realistic operational conditions and to assess the effectiveness of SHM methods in identifying early signs of damage. The Time of Flight (ToF) method was applied with two techniques. The first is based on the difference between the received waves for damaged and intact pipelines, while the second is based on the difference between two sensor reads in damaged pipelines. The location of damage on the pipe circumference was detected using curve fitting. When a pipe contains many cracks, a recursive procedure is suggested to detect these cracks.

From the research results, the following conclusions are drawn:

•

The first technique delivers more accurate results for farther sensors than near sensors, where the maximum error in the two cases is 0.96% and 9.68% respectively.

•

The second technique delivers accurate results for near and far sensors, where the maximum error in the two cases is 2.62% and 2.09% respectively.

•

The technique used for detecting the center of the damage on the pipe circumference delivers accurate results, where the maximum error is 1.13%.

•

Detecting many cracks in a pipeline by the recursion procedure delivers accurate results for far and near sensors, where the maximum errors are 2.5% and 3.5% respectively.

The SHM system, supported by data analysis, proved to be highly accurate in distinguishing between healthy and damaged pipeline states. These findings highlight the potential of combining numerical modeling with real-time monitoring technologies for proactive pipeline management. The results also align with the existing literature, reinforcing the validity of this integrated approach.