Simulation and Experimental Study of a Rotating Electromagnetic Field Probe for Nondestructive Testing
Article information
Abstract
Maintaining the integrity of pipelines that are used to transport natural gas and petroleum products is of utmost importance. In this study, a novel probe that uses the rotating electromagnetic field measurement method to detect cracks in the inner walls of pipelines is proposed. This paper investigates the probe based on the rotating electromagnetic field, identifies periodic changes in the rotating electromagnetic field, deduces the magnetic induction intensity of the arc-shaped excitation coil, and establishes static detection simulation models. The distribution of the magnetic field near the crack under arc excitation is analyzed, and experimental conditions consistent with the simulation model are established. Furthermore, experiments are conducted to assess the probe’s detection capabilities, and its quantitative detection performance is evaluated. In addition, the principles and functions of the rotating electromagnetic field tool are elucidated. The results demonstrate that the proposed probe exhibits exceptional capabilities for crack inspection in pipe walls, potentially serving as a technical reference for early warning systems and ensuring the long-term safe operation of metal structures.
I. INTRODUCTION
During the transportation of crude oil and natural gas, pipelines are subjected to immense fluid pressure and various external forces. Accidental pipeline failures not only result in significant economic losses but also lead to major environmental hazards and pose potentially life-threatening risks. Consequently, regular and effective pipeline inspection is crucial for preventing such failures, as well as for ensuring safe production and efficient transportation [1–6].
Electromagnetic non-destructive testing methods, such as magnetic flux leakage testing, eddy current testing, and AC electromagnetic field testing, can rapidly detect pipeline defects. However, these methods often exhibit inconsistent detection sensitivity to defects in different directions. To address this problem and ensure the effective detection of defects in all directions by probes, rotating electromagnetic field detection technology has been proposed. Along these lines, prior research [7–9] has suggested the mechanical rotation of eddy current probes around fastener sites for flaw detection in all directions. However, the involvement of mechanical rotation increases probe complexity. Moreover, such methods require additional post-processing to combine multiple sets of measurements for identifying the crack angle. To address this challenge, the use of rotating electromagnetic field detection technology integrated with an excitation coil has been proposed. An example of this technique is the eddy current—giant magneto resistive sensor system, which uses orthogonal planar coils and excitation currents characterized by a 90° phase shift. This sensor system is used to detect cracks in thick, riveted multilayered structures of various orientations. In this context, He et al. [10] proposed three kinds of pulsed eddy current differential hall/coil probes to detect defects, further emphasizing that defects between the third and fourth layers of a specimen can be easily detected using the two-stage differential coil probe.
In this paper, a rotating electromagnetic field detection system suitable for pipelines is presented. Rotating electromagnetic field detection technology involves two-phase or multi-phase AC electric fields that are layered on top of one another to form a stable induced electromagnetic field of constant amplitude, whose direction changes with the excitation current. The schematic of the principle behind rotating electromagnetic field detection is shown in Fig. 1. When the induced current is perpendicular to the defect, the distortion is most significant, and the detection sensitivity is highest. Furthermore, if the induced current rotates periodically, the crack will be perpendicular to the induced field for a period of time, regardless of the angle, allowing for the detection of defects at arbitrary angles. In this study, a circular rectangular core is employed to generate the rotating electromagnetic field by winding two orthogonal 90° phase-difference alternating current excitation coils around it. The coil along the X-direction is termed Excitation X, and the one along the Y-direction is termed Excitation Y. Excitation X and Excitation Y are energized by alternating currents ix(t) and iy(t), defined as follows:
Principle of the REFM method.
where I0 and ω refer to the amplitude and frequency of the alternating current, respectively, and α0 is the initial phase. Notably, the two excitations had the same amplitude and frequency, along with an initial phase difference of 90°.
According to the principle of electromagnetic field propagation, assuming that the depth of the surface of the conductor Z = 0, the induced electromagnetic field in the conductor decays exponentially and rapidly with depth Z . Therefore, under time-varying conditions, the strength of the magnetic fields Hx (Z, t) and Hy(Z, t) in the conductor induced by Excitation X and Excitation Y can be expressed as follows:
where d refers to the skinning depth, Hp denotes the magnitude of the primary magnetic field’s strength, and k is the ratio of the magnetic field on the conductor surface to the total primary field.
Combining the equations for magnetic field strength with Maxwell’s equations, the current densities induced by Excitation X and Excitation Y—Jex(Z, t) and Jey(Z, t), respectively—can be formulated as follows:
Notably, the induced AC current density Je (Z, t) is a superposition of the orthogonal components Jex(Z, t) and Jey(Z, t). Thus, the amplitude AJ(Z) and phase θJ(Z) of Je (Z, t) can be calculated using the following equations:
According to Eqs. (8) and (9), the induced current in a conductor decays exponentially with increasing depth. Moreover, at the same depth, the amplitude of the induced current density remains constant, while the phase rotates periodically at the same frequency.
A detailed calculation of the formula for the induced magnetic field of an arc coil is presented in Section II. In Section III, the mechanical structure of the proposed rotating electromagnetic field measurement (REFM) probe, the finite element method (FEM) model for analyzing the probe, and the distribution of the magnetic flux density around the crack are demonstrated. This is followed by a description of the detection experiment conducted using the REFM probe and an evaluation of the quantitative detection performance of the probe in Section IV.
II. INDUCED MAGNETIC FIELD OF THE ARC COIL
Upon maintaining the same size and excitation conditions, the distance between the rectangular coil and arc coil from the surface of the pipe was observed to be different. Moreover, since the arc coil was positioned closer to the pipe wall, it resulted in a smaller lift-off distance and greater detection sensitivity. In this study, an arc-shaped current loop was employed in the REFM probe, as illustrated in Fig. 2. However, since there is limited information on the magnetic induction intensity of arc-shaped coils, a formula for estimating the same at any position in space was devised based on coil characteristics.
Simplified drawing of the circular arc rectangular coil: (a) schematic diagram of the original structure of the coil, (b) schematic diagram of the original structure of a single-layer coil, (c) original structure of the single-layer coil, and (d) schematic diagram of the side view of the coil.
The parameters considered in this study are described in Table 1. Fig. 3 shows that the central angle of arc BC is at point O, with the coils symmetrically distributed along the z-axis on the YOZ plane. The arc-shaped coil is decomposed into four current-carrying segments—AB, BC, CD, and AD. Drawing on the limit theory, the arc is decomposed into n straight wires. When n approaches infinity, the shape is considered an arc. First, the magnitude of the magnetic induction generated by the current-carrying segment AB at point N was calculated. Assuming that the projection of AB on the y-axis is point P and the distance from point N to AB is NP, the length of NP is a2, which was calculated based on the following geometric relationship:
Parameter explanation
Outlined dimensions of the circular arc rectangular coil: (a) schematic diagram of the circular arc rectangular coil dimensions and (b) spatial distribution of magnetic induction intensity generated by a circular arc rectangular coil.
Upon substituting the above equations with the mathematical relationship
Based on the above formula, it is concluded that the components of magnetic induction intensity B generated by the coil ABCD can be expressed as follows:
III. DESIGN AND SIMULATION
The detection device is the main tool used to determine metal loss in pipelines. In such a device, the probe remains directly in contact with the inner wall of the pipeline while the magnetic field distortion signal is collected by magnetic sensors. A new type of REFM detection device is presented in Fig. 4. The device has a segmented structure, and consists of two instrumental compartments equipped with a power supply and electric circuits. Notably, the circuits were employed to generate the induced magnetic field, collect physical data, and carry out real-time positioning. The device is sealed and pushed forward in the pipeline by a difference in fluid pressure. Furthermore, to allow the probe to adapt to different pipe diameters and smoothly pass through deformations, its arms are evenly distributed across the circumference of the device to maintain continuous contact with the pipeline walls by means of springs. Thereby, the safe, stable, and efficient operation of the detection device is ensured.
Detection device based on REFM: (a) three-dimensional model of detection device and (b) practical application scenarios of the detection device.
To obtain a uniform rotating magnetic field, two current loops at 90° angles are wound around the arc-shaped magnetic core. As shown in Fig. 5, the simulation model established in Multiphysics software includes simplified probes (the arc magnetic core and loops), ducts, a crack, and air areas. The crack is located under the magnetic core, while alternating current with a phase difference of 90° passes through the two current loops.
Simulation model: (a) simplified simulation model of the probe and (b) the relative position of the crack and the probe.
Typical excitation frequencies used to rotate electromagnetic fields are usually in the range of a few kHz. Since the depth of penetration of induced current within metallic material (especially ferromagnetic materials) is very small, it can basically be assumed that the current is distributed across the surface of the metallic material, i.e., the induced current tends to converge on the surface of a workpiece. In this context, skin depth can be calculated using the following formula:
where σ refers to the electrical conductivity, μr indicates the relative magnetic permeability, μ0 denotes the vacuum permeability, and f is the frequency. In the proposed model, σ = 5×106 S/m, μr = 850, f = 6 kHz, δ = 0.1 mm. Since the skin depth (0.1 mm) was very small relative to the thickness of the workpiece, it was assumed that the skin depth is 0 and that the induced currents flow only over the surface of the workpiece. As a result, the impedance boundary condition on the surface of the pipe was accounted for when calculating the magnetic field distribution, thereby excluding the inner part of the workpiece from the solution domain and focusing the analysis on the surface of the workpiece only.
To ensure that the simulation results are closely align with actual working conditions, it is imperative to simulate the change in magnetic field at the location of the magnetic sensor when the detection device moves along the direction of the defect length, i.e., the parameter sweep. Since the magnetic sensor in the proposed structure is located in the middle of the two excitation coils and its relative position to the detection device is fixed, the parameter sweep was estimated from a simulation of the change in magnetic field at the center of the detection device when it is moving.
To simulate the relative motion of the device and the pipeline, the relative horizontal positions of the core center and the defect center are defined as Position. A parameter sweep was established for Position with a scanning interval of (−10 mm, 10 mm), with the step size set to 1 mm. The magnetic field for each value of Position was calculated for a total of 21 times (one calculation is performed for every 1mm of movement, totalling 21 calculations), thereby acquiring the magnetic field distribution at the position of the magnetic sensor when the detection device is in motion. The model for the parameter sweep is illustrated in Fig. 6.
Parameter sweep model: (a) schematic diagram of the detection device's working principle and (b) finite element simulation.
Fig. 7 depicts the isograms of the horizontal and vertical magnetic induction near the crack. The isograms indicate that the magnetic induction intensities related to the cracks at axial angles of 0°, 30°, and 90° have some common characteristics. Concentrated parts of the isograms appear at the two endpoints of the cracks, which denote the places exhibiting a larger magnetic induction intensity. In contrast, the sparse parts of the isograms appear in the middle of the cracks, indicating the location where the magnetic induction intensity is small.
Isogram results: (a) the isograms of the horizontal and vertical magnetic induction related to the cracks at axial angles of 0°, (b) the isograms of the horizontal and vertical magnetic induction related to the cracks at axial angles of 30°, and (c) the isograms of the horizontal and vertical magnetic induction related to the cracks at axial angles of 90°.
By comparing the peaks and valleys of the magnetic field distortion signals pertaining to different cracks, as presented in Table 2, it is evident that the probe achieved the best detection effect for cracks at 90°, while detection effects for the cracks at 0° and 30° were not as accurate. However, the probe successfully identified obvious magnetic field distortion signals to detect cracks featuring varying orientations.
Details of the extracted lines
IV. DETECTION EXPERIMENT
An experiment was conducted to test the detection ability of the probe when included in a device. The organization of the experimental platform is depicted in Fig. 8. A signal amplifier was employed to output sinusoidal alternating current signals with adjustable frequency, voltage, and initial phase. The magnetic field intensity generated by the probe and the induced magnetic field were collected by the magnetic sensor and converted into voltage information. Subsequently, the collected voltage data were amplified by the data acquisition circuit board and then transmitted to the computer for data processing.
The setup for the experiment.
To verify the feasibility of the proposed method, cracks of different sizes and at different angles were inspected. We chose to include cracks that were not in the normal and axial directions to demonstrate that the proposed method can be employed to inspect cracks in any direction. The size of the workpiece tested in this experiment—an arc-shaped Q235 steel plate—was 500 mm × 100 mm × 10 mm. Meanwhile, the cracks—16 mm in length, 3 mm in width, and 3.6 mm in depth—were processed using a computer numerical control milling machine. The axis angles of the four cracks on the steel plate were 0°, 30°, 60°, and 90°, respectively, as shown in Fig. 9.
Design of the defective steel plate.
In this experiment, the distance between the probe and the steel plate was maintained at 1 mm. The probe was fixed on a lifting platform, which was responsible for driving the translation platform. The movement speed of the probe was 2.97 mm/s. A signal generator supplied 4,000 Hz alternating currents with a phase difference of 90° to the coil. The two pulsating magnetic fields generated by the two sets of alternating currents ultimately synthesized a stable rotating magnetic field. The results of the experiment are presented in Fig. 10.
Experimental results: (a) the original signal of horizontal component of magnetic induction intensity and (b) the original signal of vertical component of magnetic induction intensity.
V. Experimental Data Analysis
Friction between the experimental equipment due to slippage of the contact surface and attachment surface, environmental noise, and vibration of the translation table inevitably added noise to the magnetic induction intensity signal. To address this, a combination of the one-dimensional wavelet noise reduction and quadratic moving average methods was employed to reduce the noise in the acquired magnetic field signal and to achieve a substantial noise reduction effect. First, 3-layer wavelet decomposition of the signal was carried out to obtain the high- and low-frequency components of each layer. Notably, the low-frequency components retained the basic trend of the signal curves. Furthermore, it was observed that the higher the number of decomposition layers, the more obvious the contour of the low-frequency components. Meanwhile, hard and soft thresholding methods were implemented to process the high-frequency components of Layer 3. The noise reduction results are shown in Fig. 11, indicating that the noise of the signal was significantly reduced after wavelet noise reduction processing, with the signal filtered by soft thresholding being smoother in some sections of the curve.
Signals filtered by hard and soft thresholding: (a) the noise reduction result of magnetic induction intensity, (b) the noise reduction result of horizontal component of magnetic induction intensity, and (c) the noise reduction result of vertical component of magnetic induction intensity.
Furthermore, a method based on empirical mode decomposition (EMD) was applied to process the magnetic field signals. The EMD algorithm draws on the time-scale characteristics of magnetic field signals for signal decomposition, thereby smoothening them to obtain the multiple different intrinsic mode functions (IMFs) that characterize the signals. In this study, the EMD of noise reduction was conducted on the original experimental signal. The IMF results of the decomposed magnetic induction signals for the horizontal and vertical components are shown in Figs. 12 and 13, respectively. As shown in Figs. 12, c1–c7 denote the magnetic induction signals for the horizontal component, representing the eigenmode function component r, which refers to the residual signal. In the case of the vertical component, c1–c6 represent the eigenmode function component. Fig. 12 also shows that the magnetic induction intensity of the horizontal component was decomposed into seven eigenmode function components. The results obtained after noise reduction are shown in Fig. 14. Meanwhile, the vertical component was decomposed into six eigenmode function components, and the results after noise reduction are presented in Fig. 15. Overall, the results confirm that the noise of the signal was reduced significantly after EMD noise reduction processing.
IMF components of the horizontal signal.
IMF components of the vertical signal.
Noise reduction results for the horizontal component: (a) the signal before noise reduction of the horizontal component and (b) the signal after noise reduction of the horizontal component.
Noise reduction results for the vertical component.: (a) the signal before noise reduction of the vertical component and (b) the signal after noise reduction of the vertical component.
VI. CONCLUSION
This study presents the design of a novel arc-excitation probe structure for the efficient and accurate inspection of cracks on the inner surface of pipelines, and deduces a formula for calculating the space magnetic induction intensity of arc coils. A FEM model of the probe was constructed to model the distribution of the magnetic field near the crack. Based on this model, a dynamic parameter sweep model was established to simulate the scanning process as the detection probe and the magnetic sensor moved along the pipeline axis. Furthermore, experiments were carried out to verify the probe’s detection capabilities. The simulation and experimentation results verified that the proposed probe can quickly and efficiently induce a uniform magnetic field on pipe walls, and thereby collect the horizontal and vertical component signal of the magnetic induction intensity pertaining to cracks in different directions.
Although rotating electromagnetic field detection is currently used only for in-pipe detection, this technology can also be employed to detect defects in other metal structures and mechanical equipment. Moreover, to further improve detection accuracy, research must be conducted on the method’s applicability for detecting different kinds of objects.
Notes
This work is supported by Project “High weatherability and Reliability Testing Technology for Photovoltaic Systems and Modules (Grant No. 2021YFB1507204)” of National Key Research and Development Program of China.
References
Biography
Yijing Feng, https://orcid.org/0000-0001-9743-5980 received her Ph.D. degree from the China University of Petroleum-Beijing in 2019. Since 2023, she has been an associate researcher at the Institute of Electrical Engineering, Chinese Academy of Sciences. Her research interests include mechanical fault diagnosis and non-destructive testing.
Haitao Liu, https://orcid.org/0009-0007-4019-7556 is the China Lead Expert of the IEA PVPS T13 Working Group. Since 2014, he has been an associate researcher at the Institute of Electrical Engineering, Chinese Academy of Sciences. His research interests include photovoltaic modules, system testing, and non-destructive testing.
Yibo Wang, https://orcid.org/0009-0003-0526-5876 is the director of the renewable generation systems research department at the Institute of Electrical Engineering, Chinese Academy of Sciences. His research interests include PV modules and system testing.
Xianjie Qiu, https://orcid.org/0009-0005-5428-4445 holds a master’s degree in mechanical engineering. His research interests include mechanical fault diagnosis and non-destructive testing.