Keywords

1 Introduction

In the last few decades, the number of subsea oil and gas key equipment, such as platforms and deepwater pipelines, has increased dramatically with the development of subsea oil and gas exploitation industries [1]. The development of underwater equipment makes it important to develop an intelligent and accurate cracks detection technology and system for discovering the defects and eliminating hidden dangers in underwater structures [2,3,4].

The conventional ACFM is used to detect and size the crack in offshore welded structures [5, 6]. The theoretical model of ACFM is shown in Fig. 1. The ACFM probe induces alternating current into the surface of the metal slab. If a surface-breaking crack is present, the current flows around ends of the crack. The changed current disturbs magnetic field above the crack. The magnetic field component, denoted as Bx (parallel to the slab), produces a deep trough in X direction, which contains depth information of the crack. Meanwhile, the magnetic field component, denoted as Bz (perpendicular to the slab), shows a peak and trough to the ends of the crack, which is indicative of the crack length [7, 8]. Because of the advantages of non-contact, fewer requirements of surface preparation, fast defects recognition and quantification, ACFM has become a promising alternative non-destructive test (NDT) technique for the conventional magnetic particle and penetrant testing methods [9].

Fig. 1
A schematic diagram of A C F M. The labels include magnetic field, electric field, current lines far apart gives B X trough, current lines close together gives B X peak, anti-clockwise flow gives B Z peak, and clockwise flow gives B Z trough.

The theoretical model of ACFM

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Since the oil exploitation advances to abyssal sea, the demand for precise and high reliability underwater ACFM probe is increasing sharply [10]. For the existing challenges like signal attenuation and distortion in long-distance transmission [11], other interfering signals in the sea [12] and the lag of signal comparing with scanning speed for complex processing program [13], they are all critical factors to test the underwater crack precisely. Although ACFM does not need calibration, detection accuracy is still a big challenge in deepwater for interference signals [14]. In the last few years, commercially available ACFM technology has already offered visual results [15]. However, the conventional ACFM system cannot reconstruct the profile of crack visually and immediately, which brings difficulties to the operators to evaluate the test results [16].

In this work, a simulation model of underwater VACFM probe is built. The optimal excitation current, lift-off and structure are selected from simulation results. The underwater VACFM system is set up and tested by the crack inspection experiments in underwater environment. At the last part, a TCM is introduced to improve precision of the detected crack length.

2 Underwater VACFM

The schematic of underwater VACFM system is shown in Fig. 2. The system consists of two parts, underwater component and topside component. The underwater component of VACFM integrates excitation circuit, amplifier circuit, excitation coil, detecting sensor and conditioning circuit, which makes the system smaller and easier to handle. The topside component includes A/D acquisition card, DC power supply and personal computer.

Fig. 2
A schematic depicts the underwater V A C F M model. The underwater begins with the sample under test, followed by detecting sensor, conditioning circuit, A/D, P C, power supply, excitation circuit, amplifier circuit, excitation coil, and others.

The underwater VACFM system

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In order to reduce the signal attenuation in long-distance transmission between topside and underwater, the excitation circuit, amplifier circuit, excitation coil, detecting sensor and conditioning circuit (amplification and filtering) are encapsulated the underwater probe. The excitation circuit produces driving signals. Signals are transferred to excitation coil through the power amplifier circuit. The excitation coil induces alternating current into the surface of sample under test (SUT). The detecting sensor pikes up the distorted magnetic field above the SUT surface. The signals are sent to topside after signal conditioning by the conditioning circuit. Then the signals are converted into digital signals by a A/D acquisition card and sent to PC at last. The intelligent identification software in PC will display the signals and identify defects.

3 Analysis and Optimization for Probe Parameters

3.1 Model Development in ANSYS

To optimize parameters of underwater VACFM probe, a FEM model is set up using ANSYS software, as shown in Fig. 3a. The model includes an alternating current-carrying coil with a U-shaped ferrite core, encapsulation shell and metal slab. The medium in the shell is air while the outside surrounding medium is seawater. A rectangular crack is introduced on slab surface in X direction. The dimensions of the model are shown in Table 1 and the characteristic parameters are shown in Table 2.

Fig. 3
A set of three graphical illustrations. a. F E M model setup of V A C F M. b. The current density of the V A C F M. c. Magnetic field versus path. It has a peak in B X in the middle crack and a trough in B Z at the ends.

The results of simulation. a The FEM of underwater VACFM probe. b The current density on the surface of the slab. c The magnetic field above the crack

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Table 1 The size of the FEM
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Table 2 The characteristic parameters of the FEM
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The current density is extracted on slab surface, as shown in Fig. 3b. Two eddy areas appear right under the legs of the U-shaped ferrite core; meanwhile a uniform current area [17] is generated between two legs on the slab. The uniform currents gather at ends of the crack and become sparse in the middle of the crack. A path is defined along X direction above the crack at the height of 2 mm from −0.03 to 0.03 m. The magnetic field is picked up on the path with 100 points, as shown in Fig. 3c. There is a peak (the absolute value is a trough) in Bx and a peak and trough in Bz. The peak of Bx lies in the middle of the crack, meanwhile the peak and trough of Bz locate at ends of the crack.

3.2 Excitation Currents

The induced current intensity on SUT surface is affected by the excitation current. When the excitation current is weaker, the current intensity becomes smaller, which is unfavorable for detecting the signal. Due to the power constraints, the excitation current should not be too big. Figure 4a and b shows the Bz and Bx with different excitation current. It can be seen, the excitation current increases as the amplitude of Bx and Bz increases. The maximum distortion (\(\Delta Max\)) of Bx and Bz are showed in Fig. 4c respectively, which are both grow linearly with the excitation current. The sensitivity of Bx and Bz are given as follows [18].

$$ \xi_{x} = \frac{{\Delta Bx_{\max } }}{{Bx_{0} }} $$
(1)
$$ \xi_{z} = \frac{{\Delta Bz_{\max } }}{{Bx_{0} }} $$
(2)
Fig. 4
3 plots. A, B x amplitude versus X direction for currents 0.005 A to 0.1 A, with varying magnetic field strengths. B, B z amplitude versus X direction for the same currents, with distinct peaks. C, a linear plot of max changes in B x and B z versus magnetizing current.

The optimization for excitation current. a The Bx with different excitation current. b The Bz with different excitation current. c The \(\Delta {\varvec{Max}}\) of Bx and Bz against the excitation current

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\(\Delta Bx_{\max }\) and \(\Delta Bz_{\max }\) are the maximum distortion of Bx and Bz above defect. \(Bx_{0}\) is the amplitude of Bx signal without defects. \(\xi\) can reduce detection errors and improve the signal-to-noise ratio, which affects the measurement accuracy of the VACFM system [19]. The \(\Delta Max\) and sensitivity of Bx and Bz are showed in Table 3.

Table 3 The results of simulation with different excitation current
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As shown in Table 3, the \(\xi_{{\varvec{x}}}\) (40.0%) and \(\xi_{{\varvec{z}}}\) (36.7%) remain the same basically as the excitation current increases. Hence the sensitivity of detecting signal has no significant effect by the excitation current. However, the larger distortion signal can minimize other interfering signals. The maximum allowable continuous working current of circuit modules is 50 mA for the power constraints. In order to provide strong enough current intensity without the need for cooling the system, the excitation current is set as 40 mA here.

3.3 Fix Structure Lift-Off

Lift-off is the distance between the probe and the specimen; it influences the desired characteristics of the ACFM signals [20]. The magnetic field is weaker as the lift-off distance longer. However, the signals induced and received by ACFM probe are unstable when the lift-off is too small. A small variation of lift-off, which may be due to varying coating thickness, irregularities on sample surface or movement of probe, will lead to a large change in the signal response [21, 22]. As shown in Fig. 4a, b, Bz is an order of magnitude less than Bx. So the weaker Bz component is more susceptible to the lift-off. Simulations are performed to analyze the lift-off effects. Figure 5a shows that the amplitude decreases as the lift-off increases.

Fig. 5
Two graphs. A, Amplitude versus X direction with six plots starting at 0, peaking at 0.015, dipping to negative 0.015, and returning to 0 from negative 0.04 to 0.04. B, Sensitivity versus lift-off starting at 40%, decreasing to 10% from 1 to 6times 10 superscript negative 3.

The optimization for lift-off. a The Bz with diffreent lift-off. b The sensitivity of Bz against the lift-off

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As shown in Fig. 5b, the sensitivity of Bz drops steeply as the lift-off increases from 1 to 3 mm. For the uneven specimen or movement of probe, the lift-off value normally changes within ± 1 mm errors. The minimum relative rate of change in signal characteristic vectors is 22.9% with ± 1 mm lift-off variation when the lift-off is below 3 mm. When the lift-off is greater than 4 mm, the maximum relative rate of change is 18.7%. So when the lift-off is below 3 mm, a slight perturbation can result in significant error. Meanwhile, when the lift-off distance is greater than 4 mm, the sensitivity of Bz becomes smooth, which introduce smaller error. However, as the lift-off increases, the amplitude of Bz becomes weak, which is not conducive to detection. To balance the stability and strength of signal, 4 mm is the selected lift-off.

3.4 Probe Structure

The underwater VACFM probe consists of the excitation coil with a U-shaped ferrite core [23], detecting sensor, excitation circuit, amplifier circuit, conditioning circuit, cover, gland, shell, sealing ring and cable sealing joint, as seen in Fig. 6. These are encapsulated in the probe shell. The material of the shell is 316L (00Cr17Ni14Mo2), which is a kind of non-magnetic stainless steel. The cover of the probe is on the bottom of the shell, which uses non-Magnetic plexiglass. To keep the lift-off, the detecting sensor is fixed on the cover at the thickness of 3 mm (the lift-off of the sensor center is 4 mm). The U-shaped ferrite core, excitation circuit, amplifier circuit and conditioning circuit are fixed in the shell. To seal against the water pressure, the gland compresses the cover with a Sealing ring and all the signal wires pass through the cable sealing joint. The signals are transmitted via signal wires between the underwater and topside.

Fig. 6
A schematic diagram of underwater V A F C M probe. It consists of a gland, cover, shell, cable sealing joint, alternating current-carrying coil, U-shaped ferrite core, circuit modules, sealing ring, and detecting sensor.

The structure of underwater VACFM probe

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4 System Performance Testing

4.1 Experimental System

Figure 2 shows the experimental system of underwater VACFM. It consists of two main parts: the underwater probe, the topside signal acquisition and processing system. According to the results of simulations, the experiment parameters are adopted in Table 4.

Table 4 The experiment parameters of underwater VACFM
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The excitation coil consists of 500 turns of winding wire on the beam of U-shaped ferrite core with an excitation frequency 6 kHz and magnitude 1 V [24]. The detecting sensor is made up of two coils (the Bx coil is 150 turns and Bz coil is 200 turns) with one common magnetic core. The detecting planes of Bx and Bz coil are perpendicular to X-axis and Z-axis direction respectively.

The test piece is a mild steel specimen with three cracks. The defects are rectangular-shaped cracks with different lengths and same depth, length, which are artificially introduced using the electric discharge machine, as shown in Fig. 7a, the size of cracks are given in Table 5. The 3D scanner is driven by stepper motors and the test system is shown in Fig. 7b. By driving the underwater VACFM probe above the surface of crack (No.1 crack) on the slab at a certain speed in the water tank, the test results are showed on the PC, as shown in Fig. 7c, which includes the Bx and Bz, Butterfly plot and Inverse results. From the Bx and Bz, the crack length can be detected. Sometimes, the curves of Bx and Bz could not be distinguished for nonuniform scanning speed. At the moment, the butterfly plot is useful to identify the crack, in which Bx is plotted against Bz. A loop butterfly plot helps the operator to decide whether a crack is present or not for decreasing misdetection frequency [25]. The Bx signal with scanning speed is processed by the software to calculate the profile of crack. By this inversion operation, the crack profile can also be seen in the inverse results, which is described in previous studies [26]. Thus, the crack can be identified visually by the VACFM.

Fig. 7
A, Steel specimen with three cracks (66, 30, 48 millimeters). B, Photo of V A F-C M probe system with a 3-D sensor, underwater component, top-side component, and water tank. C, 3 graphs for amplitude versus length, B z versus B x, and depth versus length for rectangular crack and inverse results.

The specimen and test results. a The crack on the surface of the test piece. b The VACFM test system. b The test results

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Table 5 The size of cracks
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4.2 Accurate Measurements

Crack lengths are critical parameters for underwater structures safety estimation [27]. In the laboratory, the VACFM probe is drive by stepper motor and screws keeping a certain speed. The detecting signals from probe are sent to the topside and collected by A/D card and processed by software. In this process, the signal lags seriously. So there is a great error in the scanning time and the nominal time of the signal. What’s more, other interference factors cannot to be neglected for the detection precision of crack length.

To offset the error of the lag of signal processing and other interference factors, TCM is introduced using a compensation factor time-constant (\(\overline{t}\)). A specimen is calibrated before the test experiment, which has the same material with SUT. With the same material, the same scanning speed, the same interference factors and the same lag degree of signal processing, crack length can be sized accurately with the help of compensation factor \(\overline{t}\).

Firstly, the calibration crack is detected for several times at a certain speed to get a stable \(\overline{t}\). The lengths of the crack can be given as follows:

$$ \begin{aligned} & L_{1} = t_{1} VN_{1} \\ & L_{1} = t_{2} VN_{2} \\ & \cdots \cdots \cdots \\ & L_{1} = t_{6} VN_{6} \\ \end{aligned} $$
(3)

\(L_{1}\) is actual length (AL) of crack. V is scanning speed. N is the number of sampling points (NSP) between the peak and trough of crack, t is the time-constant. So the mean value of t can be given as:

$$ \overline{t} = \frac{{L_{1} }}{6V}\left( {\frac{1}{{N_{1} }} + \frac{1}{{N_{2} }} + \cdots + \frac{1}{{N_{6} }}} \right) $$
(4)

The scanning speed is calculated by the rotate speed of stepper motor and the transmission ratio of screws. So the scanning speed should be chosen at some special value only. The target crack is scanned at a certain speed and the measuring length (ML) of the crack is given as follows:

$$ L = \overline{t}VN $$
(5)

To get \(\overline{t}\), No.1 crack (48 mm length) is tested for 6 times at 3.81 mm/s (select a certain speed). The NSP between the peak and trough of the crack is shown in Table 6.

Table 6 The NSP between the peak and trough of No.1 crack
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The \(\overline{t}\) can be obtained from (4), \(\overline{t} = 12.29{\text{E}} - 3\) s. The No.2 (30 mm length crack) and No.3 (66 mm length crack) are also tested at 3.81 mm/s. According to (5), the length of No.2 and No.3 crack can be obtained, the test results and relative errors (\(\left| {{\text{AL}} - {\text{ML}}} \right|/{\text{AL}}\)) are shown in Table 7.

Table 7 The test results of No. 2 and No. 3 crack at 3.81 mm/s
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To analyze the effect of scanning speed on detection precision, No.1 crack (calibration crack) is tested at 4.52 and 5.08 mm/s and the No.2 and No.3 crack (target crack) are tested at the same speed respectively according to the TCM. The test results are showed in Table 8 and the relationships between the relative errors and the scanning speeds are displayed in Fig. 8.

Table 8 The test results of No. 2 and No. 3 crack at 4.52 and 5.08 mm/s respectively
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Fig. 8
A graph of relative error versus scanning speed. It includes two plots of number 2 and 3 cracks. The second crack begins with a 10% error and rises to 20% while the third crack begins with 1% and rises to 7%. The values are approximate.

The relative error against the scanning speed

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4.3 Results and Discussion

Comparing the results of the experiments and simulations, as seen in Figs. 3 and 7, a good agreement is shown in trends of Bx and Bz. The troughs of Bx (the absolute value of Bx presents a trough in the simulation result) lie in the center of the crack, meanwhile the peaks and troughs of Bz locates at the both ends of the crack.

As shown in Table 8, the relative error of the crack length increases as the scanning speed increase using the VACFM based on TCM. Meanwhile, comparing the results of No.2 and No.3 crack, the relative error of No.3 crack (66 mm length) is much less than that of No.2 crack (30 mm length). It shows that the VACFM is more accurate to longer crack. It means that, to get an optimum test results, the scanning speed should be slower. Of course, low efficiency of scanning speed will make it inadequacy in service. To meet the needs of detection precision in engineering, whose relative error should be less than 10%, the 3.81 mm/s can be selected as the optimum scanning speed.

5 Design Summary and Conclusion

In this work, the VACFM system has been built including the excitation coil, detecting sensor, probe structure, signal processing system and software system. To reduce the signal attenuation in long-distance transmission, the excitation and signal processing circuits (amplification and filtering) are encapsulated the underwater probe. The parameters (such as excitation current, lift-off and structure) of VACFM system are optimized by the modeling to achieve better sensitivity, stability and accuracy. Meanwhile, TCM is presented to improve the detection precision by reducing the effect of signal attenuation, interference factor and the lag of signal processing. According to TCM, the scanning speed is optimized.

The modeling and optimization of visual ACFM system are able to provide a high accurate and visual measurement for underwater structure cracks, which is tested and proved by real cracks inspection experiments. The results show that the underwater VACFM based on TCM can size the crack length and profiling the section of crack with the optimized system, which meets the needs of detect precision in engineering.

In a word, the underwater VACFM system provides a method for the intelligent and accurate detection of underwater structure cracks to keep subsea oil and gas equipment safety and reliability. The test results of the system are visual, which is convenient and simple for the inspector to evaluate the cracks. Furthermore, the underwater VACFM system presented this paper are applicable to other long-distance transmission test fields.

The performance of VACFM is still not robust for detection of complicated shape underwater defects. Moreover, further research needs to focus on detecting and reconstructing different type of underwater cracks and improving detection precision.