Design of differential probe with harmonic magnetic field and its data process method

To identify the condition of steel pipelines beyond the line of sight during operation, this study presents a design methodology for a differential probe, along with a harmonic magnetic field excitation technique and its corresponding data processing methodology. The coaxial arrangement of the excitation coils in a planar configuration generates a potent induced magnetic field, ensuring a sufficient standoff distance. Under the influence of harmonic excitation, the magnetic permeability of the pipeline surface decreases, resulting in an increased detection depth. Periodic alterations in the magnetic permeability of the pipeline surface enhance the amplitude of defects. Adjusting the position of the induction coil minimizes interference from the excitation magnetic field, thereby obtaining a pure induced magnetic field. Differential processing is applied to the two induction coils to counteract interference from the background magnetic field. Finally, the effectiveness and reliability of this probe are validated through three experiments: pipeline positioning, weld seam inspection, and damage detection.


Introduction
The transportation of pipelines is favored for its cost-effectiveness and economic advantages.However, due to the presence of corrosive and acidic substances in the transported media and exposure to harsh working conditions characterized by high pressure and humidity, pipelines inevitably develop various forms of defects.Failing to promptly detect and repair pipeline damage often leads to catastrophic consequences.Therefore, conducting regular inspections on pipelines is of paramount importance.
Typically, pipelines, in addition to being coated with anti-corrosion layers, may require an insulation layer (either for thermal retention or cooling) or burial underground [1].Presently, such pipelines are often subjected to manual inspections and visual examinations.However, these inspection methods exhibit a degree of uncertainty and randomness, making it challenging to achieve a scientific evaluation.To address this, Wang et al. [2] have devised a method for crafting flexible probes coupled with harmonic magnetic field detection technology.This approach effectively focuses the excitation magnetic field and penetrates the pipeline's outer insulation layer, enabling the detection of defects such as cracks, grooves, and through-holes at a standoff distance of up to 100 mm.Yang et al. [3] designed a three-phase array probe with a zero-flux position for placing TMR sensors to counteract interference from the excitation magnetic field, thereby enhancing probe lift-off distance.Zhao et al. [4] have introduced an arrayfocusing detector to increase the energy density of the excitation magnetic field on the pipeline.Hu et al. [5] improved the accuracy of large-area corrosion measurement by adding Mn-Zn ferrite magnetic cores to the receiving probes.Ona et al. [6] have optimized the distance between the transmitting and receiving coils through numerical analysis and experimental testing to enhance the probe's lift height.
Nevertheless, detecting defects in pipelines at high lift-off poses a tricky problem [7]: small damage characteristic signals are often too weak to be effectively captured in the acquired induced magnetic field signals.Differential sensors, as a design approach for probes, can effectively address this issue.Ona et al. [8] have designed an improved pick-up coil structure by combining it with a Maxwell bridge as a magnetic field measurement sensor, further enhancing the probe's standoff distance.Zhang et al. [9] have introduced a planar three-phase array probe, in which the output of the probe is only proportional to the size of the damage.
Reliable damage target identification algorithms are equally crucial.Existing target extraction algorithms, include Empirical Mode Decomposition [10], Variational Mode Decomposition [11], Independent Component Analysis [12], and Stochastic Resonance [13], employ time-frequency analysis tools combined with filtering to separate and extract target signals.These algorithms are effective for noise reduction.However, due to the shared time-frequency characteristics between background magnetic fields (the induced magnetic field at non-defective locations and the excitation magnetic field) and target magnetic fields (variations in the induced magnetic field at pipeline defect locations), these methods cannot eliminate the background field from the measured signal.This paper presents a harmonic magnetic field excitation method and a differential probe fabrication method to achieve noncontact detection of pipeline damage.The harmonic magnetic field excitation method systematically alters the magnetic permeability of the pipeline surface, enhancing the amplitude of damage targets.Two coaxially arranged excitation coils in a planar configuration provide a sufficiently strong excitation magnetic field to achieve a significant lift-off distance.The pick-up coil is positioned at a zero-flux location to mitigate interference from the excitation magnetic field.By matching damping resistors, the induction coil operates in a critical damping state to reduce noise interference.Combining a differential amplifier ensures that the system output is solely related to abnormal changes in the pipeline's induced magnetic field.Simultaneously, a data processing method is proposed to denoise, target frequency extraction, and defect characteristic identification.
The remaining sections of this paper are outlined as follows: Section II provides an introduction to the detection method, encompassing the principles of harmonic magnetic field detection and the operational principles of the probe.Section III delves into the fabrication of the probe, the method for matching damping resistors, and the experimental setup.Section IV, in conjunction with experimental data, elucidates denoising, target frequency extraction, and damage characteristic identification methods.Experimental verification is also conducted in this section.Finally, Section V summarizes this paper.

Harmonic excitation sources
As elucidated in reference [14], the high magnetic permeability of steel pipes is a crucial factor leading to the under-detection of small defects.High magnetic permeability generates a strong induced magnetic field, and the magnetic field variation at the defect location causes minimal disturbance to the measured magnetic field.Consequently, short yet deep defects are challenging to detect.In light of this issue, we have improved our harmonic excitation source based on previous work, represented as follows: where A represents the fundamental amplitude, B signifies the peak harmonic amplitude, n denotes the number of harmonics, and f represents the fundamental frequency of the harmonics.
In this work, where n is 4 and f is 100 Hz, the excitation waveform is illustrated in Figure 1(d).Under the influence of the high-frequency magnetic field, the magnetic field strength varies as a→b→a→c→a, as depicted in Figure 1(a).The magnetic permeability of the pipeline continuously changes in response to the high-frequency magnetic field, as shown in Figure 1(b).When the amplitude of the excitation field reaches point c in Figure 1(a) (H0+HLwo+HHigh), the permeability of the pipeline is minimized.

Probe design
Theoretically, it should be feasible to separately measure the excitation magnetic field and then subtract it from the measurement results obtained from the test sample.However, the change in the induced magnetic field caused by damage is minute and requires amplification to ensure an adequate resolution.The presence of a large excitation magnetic field restricts the dynamic range of the signal amplifier, limiting the capability to identify the extent of damage.
The pick-up coil indirectly measures the magnetic field by detecting the rate of change of magnetic flux and is not affected by the static magnetic field.Placing the pick-up coil at the zero-flux position of the excitation coil can eliminate the excitation magnetic field.Based on this approach, a differential detection probe has been designed.The probe comprises an excitation coil, an adjusting coil, and two pick-up coils, as illustrated in Figure 2. The excitation coil and the adjusting coil share the same winding direction.The excitation coil generates the primary magnetic field for detection, while the adjusting coil provides an auxiliary excitation field for magnetic field focusing.Two pick-up coils are symmetrically arranged on the circumference of the excitation coil, measuring changes in magnetic flux density along the z-axis direction.In practice, it is not possible to eliminate the excitation magnetic field.Thus the magnetic flux in each pick-up coil is the vector sum of the induced magnetic field and the excitation magnetic field and can be represented as follows: where ΦP is the magnetic flux of the pick-up coils, n is the pick-up coil measurement direction vector, SP is the pick-up coil area, and BEC, Bexc, and Badj are the induced magnetic field, excitation magnetic field, and adjusting magnetic field in the pick-up coils, respectively.Then, the electric potential of a pick-up coil is where np is the turns of a pick-up coil.There are two design approaches for the two induction coils.One is adding the outputs of the two sensors within the same group, doubling the sensitivity of the sensors.The other is the differential of the outputs between the two coils.The essence of pipeline damage detection is to highlight the magnetic field variations at the damage location as effectively as possible.The differential design approach is better suited for removing interference from the background magnetic field and expanding the dynamic range of the subsequent circuitry.Therefore, the probe adopts a differential design approach, and its output is represented in Eq. ( 4).
where EPI and EPII are the electric potentials of two pick-up coils, respectively.

Probe fabrication and testing
The framework of the probe is a 3D-printed model, has grooves, and guides in the excitation coil frame and the pick-up coil frame to facilitate the adjustment of the relative positions between the excitation coil and the pick-up coil.The excitation coil and tuning coil are connected in series with the same winding direction, as depicted in Figure 3

Damping resistance matching
The pick-up coil can be equivalently modeled as an RLC circuit, as illustrated in Figure 4(a).Its mathematical model takes the form of a second-order differential equation, as shown in Eq. ( 5).In this equation, ξ represents the damping coefficient, as indicated in Eq. ( 6), and ω is the resonant frequency of the circuit.When ξ is greater than 1, the pick-up coil is in an overdamped state, resulting in a sustained phase lag in the induced voltage signal.When ξ is less than 1, the system becomes unstable, leading to increased coil output noise.Therefore, to ensure that the pick-up coil operates at critical damping, the matching resistance R is calculated to be 45.557 kΩ using Eq. ( 7). Figure 9(b) depicts the modulation circuit for the pick-up coil, where the matching resistance R is connected in parallel with the pick-up coil.The induced voltage of each pick-up coil is obtained by the differential amplifier AD8276.

Experimental instruments
The schematic diagram of the experimental setup, as shown in Figure 5, comprises a harmonic excitation source, a detection probe, signal modulation circuitry, a data acquisition system, and a PC.Within the harmonic excitation source, the signal generator module generates four sets of sinusoidal reference signals with frequencies f, 3f, 5f, and 7f.These reference signals are synthesized into a harmonic reference signal through harmonic modulation circuitry, where the fundamental amplitude A is set to 1, and the highest harmonic amplitude B is 0.75.The reference signal is then amplified by a power amplification module to drive the coil, generating the harmonic magnetic field.The data acquisition system adjusts the frequency of the harmonic excitation magnetic field by controlling the frequency.

Signal analysis
Due to circuit bias in the operational amplifier circuit and the incomplete removal of unnecessary harmonic components by the band-pass filter, original data exhibits deviations and significant noise.We employ an integrated data preprocessing algorithm to enhance the signal-to-noise ratio for accurate damage target identification.This preprocessing algorithm includes the elimination of even-order harmonic and the extraction of the highest-order harmonic components, as depicted in Figure 7(a).
Restore the periodic data Half frequency noise 1) Removal of even-order harmonic: As depicted in Figure 7(b), the process begins by summing the data over a period and taking the average.Then, the data from the latter half of a cycle is reversed within one cycle and averaged with the data from the first half of the cycle.Finally, the half-cycle data is restored to the full-cycle data.
2) Extraction of the highest-order harmonic component: As illustrated in Figure 7(c), the process begins by determining the number N of the highest-order harmonic component within one harmonic cycle.Subsequently, the harmonic signals within one cycle are divided into N groups.Finally, the data corresponding to each group is accumulated and averaged to extract the highest-order harmonic signal.
3) Orthogonal phase-sensitive detection technique: First, two orthogonal reference signals are constructed for the target frequency f harmonic and denoted as ( ) sin 2 ( ) cos2 where f is the frequency of the target harmonic.The cross-correlation function between the differentialinduced voltage signal and the reference signals can be represented as where T = 1/f is the period of the target harmonic, λ is the amplitude of the differential signal, and ψ is the phase angle of the differential signal.The variation in the amplitude λ of the target harmonic component can be calculated as 2 Using this method, the amplitude of the pipeline's induced magnetic field can be calculated.This allows for the determination of the position of the characteristic magnetic field signal associated with damage during the detection process.

Experimental research
In this section, the effectiveness of the proposed probe and data processing methods were validated through two laboratory test cases: pipeline routing and weld seam inspection, as well as an engineering demonstration case: pipeline defect detection.
Case 1. Pipeline positioning experiment The test pipeline consists of two 45# steel pipes with an outer diameter of 76 mm and a wall thickness of 3 mm, as shown in Figure 8(a).The two pipes are placed parallel to each other with a spacing of 300 mm.The total detection distance is 250 cm, and the lift-off height h is 450 mm, approximately 6 times the pipe diameter.During detection, the probe is moved horizontally along the detecting guideline while the magnetic field data is collected, and then the collected data is processed (Figure 7).The results, as shown in Figure 8(b), reveal clear amplitude variations in the induced voltage of the differential probe, indicating effective pipeline localization.However, it is not possible to determine the number of pipes and the distance between parallel pipes based solely on amplitude information.Therefore, gradient processing is applied to the amplitude data, and the results are shown in Figure 8(c).The gradientprocessed results indicate that there are two parallel pipes, and the spacing between them is approximately 303 mm, as determined from the distance between two zero-crossing points of the oscillation.

Case 2. Welding detection experiments
The test pipeline and process are the same as the localization experiment.There is a circumferential weld seam at the center of the pipe.The probe's centerline is kept directly above the pipe, and the probe is moved horizontally along a detection guideline for weld seam inspection, as shown in Figure 9(a).
The total distance of the detection path is 300 cm, and the lift-off height h is 300 mm, approximately 4 times the pipe diameter.The detection results are displayed in Figure 9(b), where a significant amplitude is observed around the 140 cm position, deviating approximately 9 cm from the actual weld seam position.The reasons for this positioning error include: 1) Data preprocessing algorithms causing the loss of front-end data; 2) Inconsistent movement speed while manually moving the probe.

Conclusion
This work proposed a method for detecting external pipeline damage using a differential probe fabrication technique and harmonic magnetic field excitation.The probe provides a sufficiently strong excitation magnetic field.Two pick-up coils are placed near the zero magnetic flux position, and a differential circuit and matching resistors are designed to reduce noise and background magnetic field interference.The improved harmonic magnetic field excitation method helps enhance the identification of damage targets.Test results demonstrate that this method can be effectively used for pipeline localization, weld seam detection, and pipeline wall thickness loss detection.In summary, this work provides an effective approach for pipeline damage detection, with the potential for practical engineering applications.

Figure 1 .
Figure 1.The detection principles of harmonic magnetic field.

Figure 3 .
Figure 3. Detection probe and its impedance diagram The two pick-up coils are symmetrically arranged near the zero-flux position with a radius of 435 mm. Figure 3(b) represents one of the pick-up coils, and each pick-up coil has an inner diameter of 200 mm with a total of 200 turns and a resistance of 32.7 ohms.Figure 3(c) displays the frequency response curve of the pick-up coil, with the first resonant frequency at 72.992 kHz.From this, it can be inferred that the inductance value of the pick-up coil is 196.992mH, and the capacitance value is 0.24 nF.

Figure 4 .
Figure 4. Induction coil equivalent circuit and its matching circuit.

Figure 5 .
Figure 5. Schematic diagram of the testing instrument.

Figure 6 .
Figure 6.Schematic diagram of constant current source.

Figure 8 .
Figure 8. Pipeline positioning experiment and results.