High Sensitivity Rotating Alternating Current Field Measurement for Arbitrary-Angle Underwater Cracks

Abstract

Alternating current field measurement (ACFM) technology has been used for sizing underwater structure cracks. However, conventional ACFM is more sensitive to cracks perpendicular to the induced current than cracks with other angles. In this paper, a rotating alternating current field measurement (RACFM) method and underwater test system are present for the detection of arbitrary-angle cracks with high sensitivity. The RACFM is proved by simulations and experiments. Arbitrary-angle cracks detection results obtained from ACFM and RACFM have shown that the RACFM method overcomes the limitation of directional detection of ACFM and effectively achieves high detection sensitivity for arbitrary-angle cracks on underwater structures.

1 Introduction

In the past few decades, with the development in offshore oil & gas exploitation industry, the demand for key equipment, such as offshore platforms and pipelines, has increased dramatically. During the equipment’s lifetime, they are suffering from a number of hazards including extreme storms, complex loads, and corrosions. Even a small crack will diminish the overall capacity of the key equipment significantly. In the past few years, several serious incidents were caused by key equipment failures in offshore oil and gas industry [1,2,3,4,5]. U.S. mineral management service reported that 1443 incidents occurred in offshore during 2001–2007.

According to the results of the industry and government research programs [6,7,8], it is important to prevent future failure of underwater structures by providing cracks information using inspection technologies in early stages. However, there are lots of challenges in underwater inspections, because the marine environment is always coming with physical, chemical, biological factors and the complex surface situations, such as attachments on underwater structures, which influence the operations and cracks inspection results [3, 9,10,11,12,13].

For underwater cracks inspection, visual inspection is a very useful and economical method, which relies on inspectors’ ability and experience [14, 15]. However, small and narrow cracks, such as stress corrosion cracks (SCC), are not visible to the unaided eye in most cases. Magnetic particle inspection (MPI) [16, 17] is the most widely used method for underwater surface cracks inspection. MPI uses small magnetic particles, such as iron filings, to reveal and locate the surface cracks. However, its effectiveness depends on the situation of structures surface, which is similar to liquid coupled ultrasonic inspection methods [18, 19]. But high levels of surface cleaning will be costly for underwater equipment. As a non-contact inspection technology, magnetic flux leakage (MFL) [20] technology doesn’t require high level surface cleaning before inspection. MFL is based on magnetizing the equipment and sensing the flux leakage. About 90% of metal loss detections for underwater pipelines are performed with MFL. But it is difficult to detect tight cracks as the flux will flow around these cracks without leakage. Eddy current testing (ECT) is widely used for the detection of surface and sub-surface flaws in conductive materials. Conventional ECT is highly sensitive to lift-off because of the variations in sensing coil’s impedance [21]. In the underwater environment, the surface of structures is often uneven due to coatings and attachments. Therefore, constant lift-off is difficult to achieve, which affects the accuracy and detectability of conventional ECT.

ACFM is originally developed by University College of London (UCL) for sizing underwater cracks as an alternative to MPI, which based on the alternating current potential drop (ACPD) [22] technology. When the measurement is performed, the induced uniform alternating electromagnetic field will be disturbed by crack on structures. As shown in Fig. 1, two components of the disturbed magnetic field are measured to calculate the crack depth and length via mathematical models. The magnetic field in X direction (B_x) shows a reduction for the decrease of current density, which reflects the crack depth, while magnetic field in Z direction (B_z) shows a negative and positive peak at both end of the crack, which indicates the crack length [23, 24]. With the advantages of high tolerance to lift-off, no or little surface cleaning and accurate mathematical model, ACFM has been widely used for sizing cracks on underwater structures without calibration in the offshore oil and gas industry [25, 26].

Fig. 1

Perturbations of electric field and magnetic field around a crack and ACFM signals obtained

There is a signal excitation coil driven by AC current to induce alternating current and magnetic field on metal surface in conventional ACFM technology, as shown in Fig. 2. The induced current perturbation will be the maximum when the crack is perpendicular to the induced current (known as perpendicular crack in this paper). But it will be the minimum when the crack is parallel to the induced current (known as parallel crack in this paper), as shows in Fig. 3. Due to this phenomenon, the sensitivity of conventional ACFM is directional, high sensitivity for perpendicular cracks and low sensitivity for other angle cracks and almost no signal for parallel cracks. Therefore, traditional ACFM has to scan the same area several times along different directions to avoid missing the cracks, which significantly increases the cost of underwater inspections. In our previous work, an optimized double U-shaped orthogonal inducer is present to detect perpendicular crack with sensor array. In this paper, a rotating alternating current field induced by the double U-shaped orthogonal inducer and an underwater test system are present for the detection of arbitrary-angle cracks on underwater structure with one pass scanning.

Fig. 2

Induced AC current and Magnetic field using a signal excitation coil in traditional ACFM a around the excitation coil, and b on the metal surface

Fig. 3

Inducted AC current field perturbation caused by, a perpendicular crack, and b parallel crack

This paper is organized as follows: Sect. 2 shows the theoretical model of RACFM and FEM analysis of rotating alternating electromagnetic field. The RACFM system is described in Sect. 3. Arbitrary-angle underwater cracks detection experiments are conducted and discussed in Sect. 4. Conclusion is made in Sect. 5.

2 Induced Rotating Alternating Current Field

2.1 RACFM Theoretical Model

According to the ACFM principle, it is sensitive to the perpendicular crack as the distortion of induced alternating current field is most significant when the perpendicular crack presents, as shown in Fig. 3. If the induced alternating current rotates periodically, the arbitrary-angle cracks in any direction will be perpendicular to the induced field at one moment in a period, which makes it possible to have high detection sensitivity for arbitrary-angle cracks. A rotating magnetic field can be constructed using two orthogonal excitation coils with 90° phase difference alternating currents [27, 28]. In this way, two same excitation coils winding on the U-shaped MnZn ferrite yokes are placed orthogonally along X direction (excitation X) and Y direction (excitation Y) as the double U-shaped orthogonal inducer of RACFM [29], as shown in Fig. 4. Excitation X and excitation Y are driven by one pair alternating currents, i_x(t) and i_y(t) respectively, which are defined as follows

$$i_{x} \left( t \right) = I_{0} \sin \left( {\omega t + \alpha_{0} } \right)$$

(1)

$$i_{y} \left( t \right) = I_{0} \sin \left( {\omega t + \alpha_{0} + 90^\circ } \right)$$

(2)

Fig. 4

Structure of double U-shaped orthogonal inducer of RACFM

where I₀ is the amplitude of the alternating current, ω is the frequency of the alternating current, and $\alpha_{0}$ is the initial phase of the i_x (t). Amplitudes and frequencies of them are the same, while the initial phases are with 90° delay.

The time varying conditions of RACFM are given by Maxwell’s equations as follows

$$\left\{ {\begin{array}{*{20}c} {\nabla \times E = - \frac{\partial B}{{\partial t}}} \\ {\nabla \times H = J_{e} + \frac{\partial D}{{\partial t}}} \\ {\nabla \cdot B = 0} \\ {\nabla \cdot D = \rho } \\ \end{array} } \right.$$

(3)

where E is the electric field, B is the magnetic flux density, D is the electric displacement, H is the magnetic field intensity, ρ is the charge density and J_e is the current density. And the displacement current ∂D/∂t is negligible compared to the current density for the relatively low operating frequency (below 10 MHz), such as the 6k Hz frequency applied in this paper.

The constitutive relations for an isotropic, linear and homogeneous medium are given as

$$\left\{ {\begin{array}{*{20}c} {B = \mu H} \\ {D = \varepsilon E} \\ {J_{e} = \sigma E} \\ \end{array} } \right.$$

(4)

where μ is the magnetic permeability in Henrys per meter (H/m), ε is the electric permittivity in Farads per meter (F/m), and σ is the electric conductivity in Siemens per meter (S/m).

According to the Ampere’s Law, when the length of excitation coil is much bigger than its radium, the alternating primary magnetic flux densities, B_x(t) and B_y(t), induced by the excitation X and Y, are given as follows

$$B_{x} \left( t \right) = \mu ni_{x} \left( t \right) = \mu_{0} \mu_{r} nI_{0} \sin \left( {\omega t + \alpha_{0} } \right)\vec{X}$$

(5)

$$B_{y} \left( t \right) = \mu ni_{y} \left( t \right) = \mu_{0} \mu_{r} nI_{0} \sin \left( {\omega t + \alpha_{0} + 90^\circ } \right)\vec{Y}$$

(6)

where μ₀ and μ_r are free space and relative magnetic permeability, n is the number of turns of each coil. $\vec{X}$ and $\vec{Y}$ just mean the directions of the primary magnetic field along X and Y directions respectively.

When the double U-shaped orthogonal inducer is closed to the conductor surface, the alternating eddy currents will be induced in the conductor. Because the double U-shaped orthogonal inducer is very close to the surface of conductor, the conductor will be assumed as a half-infinite plate. According to the principle of electromagnetic field propagation, the induced electromagnetic fields in the conductor rapidly decay exponentially with depth z, and z = 0 at the conductor surface. The magnetic field intensity in the conductor induced by the excitation X and excitation Y, H_x(z, t) and H_y(z, t), is found for time varying conditions as follows

$$H_{x} \left( {z,t} \right) = \sqrt 2 kH_{p} {\text{e}}^{{ - \frac{z}{d}}} \cos \left( {\omega t + \alpha_{0} - \frac{z}{d}} \right)\vec{X}$$

(7)

$$H_{y} \left( {z,t} \right) = \sqrt 2 kH_{p} {\text{e}}^{{ - \frac{z}{d}}} \cos \left( {\omega t + \alpha_{0} + 90^\circ - \frac{z}{d}} \right)\vec{Y}$$

(8)

$${ }d = \sqrt {2/\omega \sigma \mu }$$

(9)

where d is the skin depth, H_p is the amplitude of primary magnetic field intensity and k is the ratio of the magnetic field on the surface of conductor to the total primary field.

As shown in Fig. 5, combining the magnetic field intensity with Maxwell’s equations, the current densities induced by the excitation X and excitation Y, J_ex(z, t) and J_ey(z, t) [30], are given as follows.

$$J_{ex} \left( {z,t} \right) = \frac{{2kH_{p} }}{d}{\text{e}}^{{ - \frac{z}{d}}} \cos \left( {\omega t + \alpha_{0} - \frac{z}{d} + \frac{\pi }{4}} \right)\vec{Y}$$

(10)

$$J_{ey} \left( {z,t} \right) = \frac{{2kH_{p} }}{d}{\text{e}}^{{ - \frac{z}{d}}} \cos \left( {\omega t + \alpha_{0} - \frac{z}{d} + \frac{3\pi }{4}} \right)\vec{X}$$

(11)

Fig. 5

Induced alternating current on the surface of ample by excitation X and excitation Y respectively

The induced alternating current density, J_e(z, t), can be combined with these two orthogonal components, J_ex(z, t) and J_ey(z, t). In this way, the amplitude and phase of J_e(z, t), A_J(t) and θ_J(t), are calculated as follows

$$A_{J} \left( z \right) = \sqrt {J_{ex} \left( {z,t} \right)^{2} + J_{ey} \left( {z,t} \right)^{2} } = \frac{{2kH_{p} }}{d}{\text{e}}^{{ - \frac{z}{d}}}$$

(12)

$$\theta_{J} \left( z \right) = \arctan \left( {\frac{{J_{ex} \left( {z,t} \right)}}{{J_{ey} \left( {z,t} \right)}}} \right) = \omega t + \alpha_{0} - \frac{z}{d} + \frac{3\pi }{4}$$

(13)

According to Eqs. (12) and (13), the combined induced alternating current in the conductor also decays exponentially with depth. At a given depth, the amplitude of the induced current density is constant, while the phase is rotating periodically at the same frequency with driving alternating current of double U-shaped orthogonal inducer, as shown in Fig. 6.

Fig. 6

The theory analysis results for induced alternating current field in the conductor, and T is the period

According to the theoretical model, the rotating alternating current field is induced in the conductor using the double U-shaped orthogonal inducer and the set of driving currents have been presented in this paper. Thus, there is no directional limitation for crack detection using RACFM.

2.2 FEM Modeling and Analyzing

To verify the RACFM theoretical model proposed above, a FEM model of the double U-shaped orthogonal inducer is set up and analyzed by using transient analysis method in ANSYS. The simulation model consists of a double U-shaped orthogonal inducer wound with excitation coils above a mild steel sample, as shown in Fig. 7. Each coil is wound by 500 turns 0.15 mm enameled copper wire. Other structural parameters of the model are given in Table 1. To simulate the real underwater environment, the computational domain of the FEM model is set to sea water. The material characteristic parameters of both model and environment are shown in Table 2 [31, 32]. The excitation coils X and Y carry the alternating currents with 1V amplitude, 6 k Hz frequency, and the 0° and 90° initial phases respectively.

Fig. 7

The FEM model of RACFM

A complete period is divided into 4 transient steps equally. And the transient induced current densities on the surface is simulated and analyzed. Simulation results show that the direction of induced current field at the uniform area revolves periodically at 6k Hz frequency, whose direction is negative Y at t = 0, and negative X at t = 0.25 T, and positive Y at t = 0.5 T, and positive X at t = 0.75 T, as shown in Fig. 8.

Fig. 8

The FEM simulation analysis results for induced AC field on the surface at different transient time, a t = 0, b t = 0.25T, c t = 0.5T, and d t = 0.75T

The average amplitudes of induced magnetic flux densities are almost constant at the approximate uniform area on the surface at different transient times, as shown in Table 3. The biggest relative change of average amplitudes is only 4.27%. Comparing Fig. 6 with Fig. 8, it can be seen that the uniform rotating alternating current field is induced by the double U-shaped orthogonal inducer with constant amplitude and periodically revolving direction, which matches the results of RACFM theory analysis.

Summarizing the results from theoretical analysis and FEM simulation, the uniform rotating alternating current field induced by the double U-shaped orthogonal inducer meets the requirement of overcoming the limitation of directional inspection by conventional ACFM and achieves high sensitive detection for arbitrary-angle cracks with one pass scanning.

3 RACFM System for Arbitrary-Angle Cracks Measurement

3.1 RACFM System

The underwater RACFM system consists of two parts, underwater component and topside component, as shown in Fig. 9. The topside component includes power supply, data acquisition (DAQ) module and PC. The underwater component consists of signal processing hardware including signal generator, power amplifier, 90° phase shifter and condition circuit. The RACFM probe includes double U-shaped orthogonal inducer and detecting sensor.

Fig. 9

The underwater RACFM system

The power supply provides 12V DC for the signal processing hardware. The signal generator provides a sine exciting signal (6k Hz and 1 V) as the initial driving signal. The initial driving signal and the orthogonal driving signal provided by the 90°phase shifter are used to drive the excitation coils of double U-shaped orthogonal inducer. The RACFM probe scans the surface of sample and the detecting sensors pick up the distorted magnetic field above the cracks. After signal amplification and low pass filtering, these analog signals are transformed to digital signals and sent into the PC using the DAQ module. The real-time curves of B_x and B_z are plotted and the cracks can be determined.

3.2 RACFM Probe

The underwater RACFM probe consists of the double U-shaped orthogonal inducer and detecting sensors, as shown in Fig. 10a. According to theoretical model and FEM model, the double U-shaped orthogonal inducer is built by two orthogonal U-shaped MnZn ferrite yokes wound with 500 turns excitation coils of 0.15 mm enameled copper wire respectively. As shown in Fig. 10b, the detecting sensors are made up of two detection coils (B_x coils and B_z coils), which are wound on a common yoke. The planes of the two detection coils are perpendicular to X direction and Z direction for picking up the B_x and B_z respectively.

Fig. 10

Photo of RACFM probe

3.3 RACFM Waterproof Shell

The RACFM probe and the signal processing hardware are fixed together and encapsulated in a waterproof shell, as shown in Figs. 11 and 12. The shell material is non-magnetic stainless steel (00Cr17Ni14Mo2) and the bottom of the shell is made of non-magnetic Perspex. The detecting sensor is installed on the cover of probe at a 4 mm lift-off above the specimen. To seal against the water pressure, the gland and the sealing ring are used to compress the bottom cover together with the shell and all the signal wires pass through the cable sealing joint. The signals are transmitted via signal wires between the underwater component and topside component.

Fig. 11

Photo of the RACFM underwater component

Fig. 12

Assembling of RACFM underwater component

4 RACFM System Testing and Discussing

4.1 Experiment System

To further verify the effectiveness of RACFM method and underwater test system present in this paper, arbitrary-angle cracks on underwater sample detection experiments are conducted with a high precise 3D scanner, as shown in Fig. 13. A water tank filled with seawater is used to simulate the seawater environment. The RACFM underwater components and the sample are placed in water tank as in the FEM simulation. The sample under test (SUT) is a Q235 mild steel sheet with a 45mm length and 7mm depth artificial rectangular crack produced by the electric discharge machining (EDM).

Fig. 13

RACFM experiment system

To simulate the arbitrary-angle cracks detection, the probe scans the crack with 10 different paths accurately controlled by the scanner. The angles between the scanning paths and crack change from 0° to 90° with 10° step, as shown in Fig. 14. The 0° angle crack indicates that the scanning path is along the crack, while the 90° angle crack indicates that the scanning path is perpendicular to the crack.

Fig. 14

Experiment sample and scanning path

4.2 Discussion

In order to compare the detection sensitivity of different angle cracks using RACFM and conventional ACFM [33, 34], the same crack on underwater structure detection experiments have been conducted along different scanning paths using the RACFM probe and a U-shaped ACFM probe respectively. Furthermore, to keep the electromagnetic field signals picked up by different probes comparable, the excitation signal of the ACFM probe are the same as the excitation X of the RACFM probe. Meanwhile the detecting sensors of these two probes are the same.

When the probes scanning over the surface of sample, two components of the disturbance magnetic field, B_x and B_z, are picked up and drawn in real–time by the software after both hardware signal processing and digital signal processing. Figure 15a–d show the 0, 30, 60, 90 degree angle cracks detection experimental results using the RACFM probe and traditional ACFM probe respectively. Comparing Fig. 15a with Fig. 1, it is clear that the B_x and B_z signals obtained from experiments are in accordance with the principle of ACFM, which proves the capability of RACFM system for detection of cracks on underwater structure [34].

Fig. 15

B_X and B_Z signals from experiments using the RACFM probe and traditional ACFM probe for, a 0 degree crack detection, b 30 degree crack detection, c 60 degree crack detection, d 90 degree crack detection

Comparing these experimental results of RACFM with traditional ACFM at 0 degree angle crack detection, as shown in Fig. 15a, it is apparent that the B_x and B_z distributions agree with the principle of ACFM. Meanwhile, the perturbations of B_x and B_z caused by the crack are similar using both ACFM and RACFM. When the angle is increased to 30°, as shown in Fig. 15b, the perturbations of ACFM experimental results are far smaller than those of RACFM, although both the B_x and B_z distributions can also describe the presence of the crack using both RACFM and ACFM. When the angle is increased to 60°, as shown in Fig. 15c, the B_x and B_z distributions of RACFM experimental results are still in accord with the principle of ACFM and the perturbations are big enough for recognizing the crack. However, the B_x and B_z perturbations of ACFM experimental results are small and almost covered by noise, which cannot be used to determine the crack. Finally, when the scanning path is perpendicular to the crack (90°), as shown in Fig. 15d, the crack can be recognized by B_x and B_z distributions of RACFM experiments results perfectly, while there are no perturbations caused by the crack in ACFM experimental results.

According to the principle of ACFM, the perturbations of B_x and B_z are analyzed to determine and recognize the crack. The detection sensitivities (S_x and S_z) are given as follows to describe the maximum distorted signals above the crack [32].

$$\left\{ {\begin{array}{*{20}c} {S_{x} = \frac{{MX_{max} }}{{MX_{0} }} \times 100\% } \\ {S_{z} = \frac{{MZ_{max} }}{{MX_{0} }} \times 100\% } \\ \end{array} } \right.$$

(14)

where MX₀ is the amplitude of B_x signal without crack, and MX_max and MZ_max are the maximum perturbations of B_x and B_z caused by crack respectively.

Table 4 shows the sensitive parameters (S_x and S_z) from the experimental results of RACFM and traditional ACFM. When detecting cracks using traditional ACFM probe, the fixed direction induced electromagnetic field can be mostly disturbed by 0 degree angle crack, and the sensitive parameters decrease sharply with the increasing of the cracks’ angle as shown in Fig. 16a. When the angle reaches 40 degree, the S_x and S_z are only 2.9% and 6.6%, which are less than 10% of the maximum sensitivity. Compared with traditional ACFM experimental results, the rotating alternating current field induced by the double U-shaped orthogonal inducer is disturbed by arbitrary-angle cracks. There is a little decrease of detection sensitivity for different angle cracks, as shown in Fig. 16b. The minimum sensitivities of S_x and S_z for detecting different angle cracks are still as high as 27.3% and 59.7%, which are almost 80% of the maximum sensitivity. It is apparent that the RACFM system proposed in this paper can solve the problem of directional detection and achieve high detection sensitivity for arbitrary-angle underwater cracks.

Fig. 16

Inspection sensitivity for different angle of cracks using, a traditional ACFM probe, and b RACFM probe

5 Conclusion

In this paper, the RACFM technique based on the induced rotating alternating current field is proposed to solve the directional detection problem of traditional ACFM. The rotating alternating current field is proved by the FEM simulations. Based on theoretical and simulation results, the underwater RACFM test system and encapsulated probe are present for the detection of arbitrary-angle cracks. The performance and efficiency of the RACFM system is clearly demonstrated by arbitrary-angle cracks detection experiments.

Comparing the experimental results of RACFM system with traditional ACFM system, the detection sensitivity of RACFM system does not decay too much for the non-perpendicular crack. It is clear that the RACFM overcomes the limitation of directional detection of traditional ACFM. Comparing with traditional ACFM, the RACFM system almost achieves a relatively high sensitivity for the detection of arbitrary-angle cracks on underwater structure with one pass scanning. The RACFM system can help to prevent future failures of key equipment during their whole lifetime and keep the safety of offshore oil & gas exploitation systems.

Table 1 The structural parameters of the FEM model

Table 2 Material Parameters of the FEM model

Table 3 The FEM simulation result at different transit time

Table 4 The sensitivity of RACFM and ACFM experiments