Experimental Study on the Quantitative Relationship between the Non-contact Magnetic Signal and Detection Height of Ferromagnetic Pipelines

The non-contact magnetic detection technology has good application prospects in the detection of buried steel pipelines. However, the variation of non-contact magnetic signal and measured height is unknown. The application of the technology in pipeline burial inspection is restricted. Therefore, this article conducts non-contact magnetic signal experimental testing on full-size steel pipelines. The collection method, pipe diameter, internal pressure, measurement height, and the non-contact magnetic signal are quantitatively analyzed. And the propagation factor f G was defined to quantify the degree of influence of measurement height on the non-contact magnetic signal. The results indicate that when the measurement height increases from 0.1 m to 2.0 m, the variation amplitude of the magnetic gradient modulus obtained by the parallel acquisition method is the largest, with a change rate of - 0.35. The amplitude and linear rate of change of the propagation factor f G increase with the pipe diameter and internal pressure. The amplitude and linear rate of change of the propagation factor f G increase with the pipe diameter and internal pressure. In the range of pipe diameters from 355.6 mm to 1016 mm, the amplitude of f G variation is 0.53, and the rate of change is 0.26. Furthermore, the amplitude of f G change due to a unit increase in internal pressure is 0.022, with a corresponding rate of change of 0.0114.


Introduction
Buried pipelines often pass through mountainous areas with complex geological structures.Furthermore, the increase in pipeline service life leads to changes in the thickness of the pipeline's overburden layer.The additional stress of the pipeline caused by the increase of the overburden layer is highly susceptible to fault accidents in the pipeline [1][2][3][4].Therefore, it is essential to detect the buried depth of the pipeline.
At present, several usual burial depth detection methods are a direct method, geological radar method [5], electromagnetic method, and AC potential Gradient method (ACVG) [6].But traditional detection methods and equipment still have certain limitations.These methods cannot work in situations where conditions change.The non-contact magnetic detection method uses Earth's magnetic field as the excitation source of the ferromagnetic pipeline.And without external current, the signal strength does not change with mileage.The problem of unstable signal values in traditional detection methods is solved.Furthermore, there is no need to install devices such as transmitters and receivers in pipeline magnetic signal detection.It is more convenient than traditional burial depth detection methods such as PCM.
The key to detecting the buried depth of pipelines using non-contact magnetic detection methods is to understand the variation of the magnetic signal of the pipeline with the detection height.He et al. studied the variation of non-contact magnetic signals in 0.1 m -1.0 m detection height by a hydraulic pressure test.The results indicate that the non-contact magnetic signal exhibits a second-order exponential relationship with the detection height [7].Xu et al. tested the magnetic field strength and gradient in a defective Q345 steel plate sample.The results indicate that the deeper the defect, the smaller the magnetic field intensity and gradient [8].Yao et al. tested the magnetic signal of prefabricated defective steel plates under axial tensile load and obtained that the magnetic signal width is proportional to the detection height [9].Liu et al. quantitatively analyzed the variation of the normal and tangent components of the magnetic signal with the detection height and obtained that the tangential signal decays rapidly with the increase of the detection height, while the normal signal remains stable [10].He et al. constructed a spatial analytical model to quantify changes in non-contact magnetic detection signals above pipelines.And proposed a signal correction method to correct magnetic signals [11].Chau et al. proposed a new method to determine the buried depth of the pipeline by remote magnetic field measurement with a ground magnetometer.The calculation results are verified through experimental research and on-site experiments [12].Wang et al. use Poisson's equation to deduce the theoretical calculation model of the all-field Magnetic anomaly (TMAs) to the submarine pipeline.The calculation results indicate that the amplitude of TMA is inversely proportional to the square of the detection height h.The width of the Magnetic anomaly is approximately positively correlated with h [13].Karimi et al. used the amplitude of the magnetic field component and the Analytic signal of its first derivative to detect the depth of the magnet.A new anti-noise method with higher accuracy in calculating depth, the depth averaging method, has been proposed [14].
Most of these studies are focused on specimens or small-diameter pipes.The impact of pipe diameter and internal pressure on magnetic signal is not considered.Therefore, this article conducts experimental research on magnetic signals at different heights and quantitatively analyzes the effects of variable collection methods, pipe diameters, and internal pressures on magnetic signals.

Experimental Subjects
According to on-site research, 355.6 mm, 813 mm, and 1016 mm pipelines were selected as experimental objects, and experiments were conducted on the influence of sensor position and pipe diameter on magnetic signals using atmospheric pipelines.When studying the effect of internal pressure on pipeline magnetic signals during operation, a 355.6 mm pipeline was used for sealing and pressurization.

Experimental System Design
This experiment is divided into two parts: an unpressurized experiment and a pressurized experiment.An experimental testing system is established to accurately test the magnetic signal data at different detection heights above the pipeline as shown in figure 1.The pressure testing system consists of an air compressor, a pipeline magnetic gradient measurement system, and a sealed pipeline.Both ends of the experiment pipeline are sealed with welded blind flange and set up injection and exhaust holes.The injection hole connects the sealed pipe to the air compressor to pressurize the test pipe.The exhaust hole is used to exhaust high-pressure gas from the experimental pipeline to relieve pressure in the pipeline.

Experimental Equipment
Figure 2 depicts the self-developed pipeline magnetic gradient measurement system.This system is specifically designed to evaluate the gradient modulus G of experimental pipelines.The key experimental components comprise a magnetic gradiometer, a data collector, and an engineering host computer.The pipeline's magnetic gradient measurement system is capable of automatically sensing the spatial magnetic signal and transmitting it wirelessly to the host computer via the data collector's builtin router.Two high-precision three-axis fluxgate sensors are positioned at both ends of the magnetic gradiometer to capture the three components of the spatial magnetic flux density.The signals measured by the two sensors undergo differential processing to derive a gradient signal.The measurement system's testing accuracy is 0.01 nT, with a range of ±100 μT.
The magnetic detection software interface displayed in figure 3 is hosted on the computer system.This interface allows for the real-time display, playback, and storage of magnetic field data.The test results primarily encompass the three components of the magnetic gradient and its modulus.

Experimental Methods 1)
Research on the influence of the relative position of sensors Three testing methods were designed based on the relative position of the center line of the magnetic gradient and the pipeline axis: (1) The magnetic gradient meter is located directly above the pipeline, and the centerline is perpendicular to the pipeline axis.This method is called the vertical detection method.(2) The magnetic gradient meter is located directly above the pipeline, and the centerline is parallel to the pipeline axis.This method is called the parallel detection method.(3) The left edge of the magnetic gradient meter is located directly above the pipeline, and the centerline is perpendicular to the pipeline axis.This method is abbreviated as the deviation detection method.
2) Research on the influence of pipe diameter Experimental objects include 355.6 mm, 813 mm, and 1016 mm pipelines.Variation curves of magnetic gradient signals are tested within a range of 0.1 m -2 m above the pipeline (with an interval of 0.1 m).
3) Research on the effect of internal pressure The experiment object is a 355.6 mm pipe.The pipe is pressurized with an air compressor.The pressure rose from 1 MPa to 3 MPa, with a single increase of 0.5 MPa.Under set of pressure conditions, Magnetic signal variation curves within a distance of 0.9 m -2.8 m (with an interval of 0.1 m) from the pipeline are measured.According to the on-site research results, the burial depth of the pipeline is set to 0.8 m.Store the data after the test.Repeat the measurements three times for each group of experiments to avoid single-test errors.
To eliminate the influence of pipeline surface gradient modulus and better quantify the amplitude of magnetic signal changes, the propagation factor fG is defined as: where G is the magnetic gradient modulus test values at various test heights, nT/m; Gmax refers to the maximum magnetic gradient modulus in the vicinity of the pipeline's surface, nT/m.

Backdrop Magnetic Field Test Results
A testing speed of less than 0.1 m/s is used to test the backdrop magnetic field in the test area.The statistical dispersion of the backdrop magnetic field test value is less than 0.05.Background magnetic field has little interference with experimental results.In the case of a 355.6 mm pipe, it can be seen that the overall trend of propagation factors in different detection methods is the same.The change curve is divided into two stages: the approximately linear stage and the stable stage.As the detection height increases, the propagation factor fG rapidly decreases and gradually stabilizes.Therefore, the burial depth can be well measured within the range of 0.1 m to 1 m.The propagation factor fG decreases from 1 to 0.67 in the parallel method, from 1 to 0.72 in the vertical method, and from 1 to 0.8 in the deviation method.The change rates of fG corresponding to parallel, vertical, and offset testing methods are -0.35,-0.32, and -0.24.The change rate corresponding to the parallel testing method is about 1.2 times that of the other two testing methods.The respect stable fG values are 0.67, 0.72, and 0.79.

Sensor-pipe Relative Position Affects the Test Result
Within a range of 2 m, the variation trend of 813 mm and 355.6 mm pipelines remains consistent.But the variation of the 1016 mm pipeline tends to be linear.Taking parallel connection as an example, when changing from 0.1 m to 2 m, the fG decreases by 0.33, 0.71, and 0.72 for 355.6 mm, 813 mm, and 1016 mm pipelines, with respect change rates of -0.35, -0.77, and -0.35.In summary, for pipelines with different pipe diameters, the parallel measurement method has the highest amplitude and rate of change.Therefore, the parallel measurement is employed to collect noncontact magnetic signals when conducting experiments on the impact of pipe diameter and pressure from the experimental pipeline.

Influence of Pipe Diameter Variation on the Magnetic of Pipeline Buried Depth
The curve depicts the changes in magnetic gradient modulus and propagation factor within the range of 0.1 m -2 m detection height is shown in figures 7 and 8.It can be seen from the figure that the magnetic flux density and propagation factor under different pipe diameters is gradually decreasing with the increase of detection height.The variation curves of the propagation factor of magnetic characteristic parameters for 355.6 mm and 813 mm pipelines can be divided into approximately linear and stable.As the detection height increases, the propagation factor fG rapidly decreases.When h > 0.9 m, the decline rate of the propagation factor significantly slows down and gradually stabilizes.The 1016 mm pipeline exhibits a linear relationship.
The gradient modulus values of 355.6 mm and 813 mm pipe diameters are similar, with a variation of only 2%.However, there is a sudden change in the gradient modulus G between 813 mm and 1016 mm pipe diameters, with an average increase of 84%.It can be seen that the trend of propagation factor fG variation for different pipe diameters is the same.As the detection height increases, fG decreases, and the average rate of fG decrease increases with the increase of pipe diameter.
Table 1 shows the reduction amplitude and average decrease rate of propagation factors for different pipe diameters within the detection height range of 0.1 m -2.0 m.The propagation factor fG of 355.6 mm, 813 mm, and 1016 mm pipelines decreased by -20%, -53%, and -73%.The respect average fG decrease rate of -0.10, -0.26, and -0.36.

The impact of variations in internal pressure on the Magnetic Signal of Pipeline Burial Depth
The graphs depicting the changes in magnetic gradient modulus and propagation factor under varying internal pressures within the detection height range of 0.9 meters to 2.8 meters are displayed in figures 9 and 10.The magnetic gradient modulus G decreases exponentially with the detection height and increases with increasing pressure.At the same detection height, the decrease in fG positively correlates with internal pressure, while the attenuation of magnetic signals negatively correlates with pipeline working pressure.Under the internal pressures of 1 MPa, 1.5 MPa, 2 MPa, 2.5 MPa, and 3 MPa, the propagation factor fG decreased by -14.1%, -15.2%, -16.6%, -17.8%, and -18.3%, respectively, the average decline rates of fG are -0.070,-0.076, -0.083, -0.089, and -0.092, respectively.

Conclusions
The optimal acquisition method for non-contact magnetic detection in pipeline buried depth detection was determined by detecting the curve of non-contact magnetic signals and the height of detection fullsize steel pipes.Quantitative analysis was conducted on the impact of pipe diameter and internal pressure on non-contact magnetic signals.The conclusion is as follows: (1) Within the detection height of 0.1 m -1 m, the propagation factor is more accurate for buried depth detection.The parallel measurement method has been determined as the best method for measuring pipeline burial depth, with the decrease in propagation factor as the indicator.
(2) The magnetic gradient modulus G and propagation factor fG exhibit second-order exponential changes with measurement height.It can be divided into similar linear declines and stable stages.
(3) The average decrease rate and change amplitude of the propagation factor fG increased with the pipe diameter and internal pressure.The detection height increased from 0.1 m to 2.0 m, and the decrease in propagation factor fG of the 1016 mm pipeline is -73%, with an average decrease rate of -0.36.At 3 MPa, the fG of the propagation factor fell -18.3%, and the average decrease rate was -0.092.

Figures 4 to 6
show the change curve of the magnetic gradient modulus signal at the different sensor relative positions for 355.6 mm, 813 mm, and 1016 mm pipes within the detection height of 0.1 m -2 m.

Figure 4 .
Figure 4. Comparison of magnetic signal data for 355.6 mm pipeline testing.

Figure 5 .
Figure 5.Comparison of magnetic signal date for 813 mm pipeline testing.

Figure 6 .
Figure 6.Comparison of magnetic signal data for 1016 mm pipeline testing.

Figure 7 .
Figure 7. Gradient modulus G curve under pipe diameter variation conditions.

Figure 8 .
Figure 8. Distribution of propagation factor fG curve under Pipe diameter variation conditions.

Figure 9 .
Figure 9. Gradient modulus G curve under internal pressure variation conditions.

Figure 10 .
Figure 10.Distribution of propagation factor fG curve under internal pressure variation conditions.