Signal enhancement of rectangular wave eddy current testing via compensation using digital-to-analog converter

Abstract

Rectangular wave eddy current testing (RECT), which is performed using a rectangular wave excitation current, can simultaneously obtain multiple datasets. However, the high-frequency harmonic signal detected by the detection coil interferes with the low-frequency signal based on Faraday’s law of induction. The method proposed in this study is a type of electronic bridge, wherein a compensation method is implemented to enhance the low-frequency signal of the RECT using a digital-to-analog converter (DAC). The compensation wave generated by the DAC is determined such that the output signal becomes zero when the probe does not detect any flaws. A 12 mm thick aluminum plate with flat-bottom drill holes on the backside is used as the specimen. The holes have a diameter of 3 mm and depths of 2, 4, and 6 mm, respectively. The results demonstrate that the flaw signal cannot be detected without compensation. However, the flaw signal can be successfully detected around these holes with compensation.

Keywords

Eddy current testing low frequency rectangular wave eddy current testing digital-to-analog converter electronic bridge

1. Introduction

The maintenance of industrial infrastructure is crucial for rapid economic growth. The inspection methods employed in the maintenance of this infrastructure must be accurate, simple, and time-efficient. Industrial infrastructure is primarily composed of thick metals. Among the non-destructive testing methods, eddy current testing (ECT) is a promising technique for detecting defects because it does not require a sensor for fast detection [1]. Generally, metal plates with thicknesses exceeding 10 mm are used for large infrastructure. However, this results in the occurrence of the skin effect, and defects cannot be detected when the excitation frequency is high. Therefore, the frequency of ECT must be sufficiently low to examine the backside defects of a thick metal specimen [2–8].

In general, ECT employs a sinusoidal excitation current. A multifrequency ECT can be used to simultaneously obtain multiple datasets [1,9]. A rectangular wave ECT (RECT) was proposed in a previous study to simplify the excitation circuit of an ECT in the low-frequency range [10,11]. The RECT uses a rectangular wave current or voltage for excitation. In our previous studies, we demonstrated that the RECT can detect front and back side flaws on thick metal plates [12]. Moreover, the harmonic and fundamental signals can be simultaneously obtained. Essentially, the RECT can obtain additional information compared to the conventional ECT.

The excitation current of the RECT contains both fundamental and harmonic waves. However, the harmonic signal detected by the detection coil increases with an increase in the frequency, that is, the harmonic order, based on Faraday’s law of induction. Consequently, the harmonic component interferes with the amplification of the low-frequency component.

By contrast, in our previous study, the sinusoidal waveform for compensation was generated using a digital-to-analog converter (DAC) to suppress the interference. Specifically, an electronic bridge circuit was developed, and the detection coil successfully detected small voltage changes [13]. In this study, an improved compensation method is applied to the RECT using a DAC to address this problem. It is worth mentioning that the compensation waveform in our previous study [13] was sinusoidal wave, and only the amplitude and the phase were changed for compensation. In contrast, the compensation waveform in this study is a pulsed waveform because the excitation current waveform is not sinusoidal. Therefore, we enhanced the compensation method as follows. First, a rectangular wave current was fed to the excitation coil to generate an eddy current in the specimen. Second, the generated flux was detected using a differential detection coil. Third, the compensation waveform was determined from the measured voltage waveform of the detection coil such that the output signal became zero when there was no flaw under the probe.

2. Methods

Figure 1 presents an overview of the experimental setup of the developed LF-RECT system, which is based on the system reported in [12].

Fig. 1.

Experimental setup of the RECT system.

2.1. Control and measurement system

Figure 1 illustrates the developed RECT system. A rectangular wave current was fed into the excitation coil to generate an eddy current in the specimen.

A rectangular wave, v_DAC0(t), was generated using a DAC (National Instruments Corporation NI 9260, 24 bit, 51.2 kS/s). The signal was amplified using a bipolar power supply (NF Corp., BA4610). A resistance of 10 Ω was connected in series to the excitation coil. If the resistance is sufficiently larger than the impedance of the excitation coil, i (t) can be expressed as follows: $\begin{eqnarray}\displaystyle i(t)=\frac{4I_{0}}{{\pi}}\left(\sin {\omega}_{0}t+\frac{1}{3}\sin 3{\omega}_{0}t+\frac{1}{5}\sin 5{\omega}_{0}t+\cdots \hspace{-1.5pt}\right), & & \displaystyle\end{eqnarray}$ (1) where I₀ denotes the amplitude of the rectangular voltage wave, and ω₀ =2πf₀ (f₀: frequency). Subsequently, a differential detection coil was utilized to detect the magnetic flux generated by the eddy current. A 100 μF capacitor was connected to the resistance, and a 2 μF capacitor was also connected to the detection coil to reduce unnecessary harmonic voltage. A shunt resistor (1 mΩ) was connected in series to the excitation coil to measure the current. The shunt voltage was amplified using an isolation amplifier (NF Corporation 5325).

The probe was simultaneously moved by 5 mm for 1 s using two-axis motorized stages (OSMS26-300(XY), Sigma-koki Co., Ltd.) in the range ${\Omega}\in \{x,y|-100∼\text{mm}\leq x\leq 100∼\text{mm},-50∼\text{mm}\leq y\leq 50∼\text{mm}\}$ . An analog-to-digital converter (ADC, National Instruments Corporation NI 9239, 24 bit, 50 kS/s) was used to measure the voltages of the detection coil and shunt resistance, and v_coil(t) and i (t) were obtained. The DAC and ADCs were installed in the CompactDAQ chassis (National Instruments Corporation cDAQ-9174), and the modules and motorized stage controller (SHOT-304GS, Sigma-koki Co., Ltd.) were controlled using the LabVIEW software.

The compensation waveform, v_DAC1(t), was determined such that the output signal became zero when the probe did not detect any flaw. The differential voltages of v_coil(t) and v_comp(t) were amplified using an instrumentation amplifier, and the voltage, v_amp(t), was measured using the ADC. Subsequently, the n-th harmonic voltage, $\dot{V}_{n}$ , and current, ${\dot{I}}_{n}$ , were calculated by using a fast Fourier transform (FFT) to v_amp(t) (or v_coil(t)) and i (t), respectively. Here, the phase of ${\dot{I}}_{n}$ was considered as a reference phase. Ultimately, G was successfully magnified and set to 500 when compensation was used.

2.2. Generation of compensation wave

This subsection presents a detailed description of the method used to determine the compensation waveform, v_DAC1(t). First, the relay was turned off to protect the instrumentation amplifier and v_coil(t) was measured for 1 s using an ADC (CH 2) with a sampling rate of 50 kHz, when no flaw was detected by the probe. The measured data, v_coil(t), includes noise. Subsequently, the moving average and addition average were applied to v_coil(t), to obtain a new waveform, v _coil (t), to reduce the noise. v_comp(t) must be equal to v _coil (t). Finally, the relay was turned on and the waveform of the v_DAC1(t) was determined by considering that the voltage divider circuit is connected to the DAC (CH 1) to reduce the noise generated from the DAC. The sampling rates between the ADC and DAC are different; therefore, upsampling (i.e., sampling frequency conversion) was performed.

2.3. Probe

Figure 2 presents the detailed specifications of the excitation and detection coils. The detection coils are placed above and below the excitation coil and are differentially connected. The upper detection coil was used to cancel the direct magnetic flux generated from the excitation coil. The excitation coil has 50 turns, an inner diameter of 20 mm, an outer diameter of 30 mm, and a height of 5 mm. Each detection coil has 600 turns, an inner diameter of 20 mm, an outer diameter of 30 mm, and a height of 5 mm.

Fig. 2.

Specifications of the probe.

2.4. Specimen

Figure 3 shows the structure of the specimen used in this study. A 12 mm thick aluminum plate with flat-bottom drill holes was used as the specimen. In this study, non-magnetic materials were used for the specimen for simplicity. The diameter of the holes was 3 mm, and the depths of the holes were 2, 4, and 6 mm; these flaws were on the back side of the specimen.

Fig. 3.

Specimen structure and dimensions.

2.5. Control and measurement system

The output amplitude of the voltage, E, was set to approximately 10 V. The resistance connected to the excitation coil in series was sufficiently large (10 Ω). Therefore, the output current amplitude, I₀, was approximately 1 A. The frequency, f₀, was set to 10 Hz.

3. Results and discussion

Figure 4 presents the results of the waveforms of i (t) and v_coil(t) when the position of the probe is (−100 mm, −50 mm), that is, there are no flaw detected by the probe. The shape of the waveform of current, i (t), is an impulse, and v (t) changes sharply with the change in i (t). The maximum value of v (t) is approximately 0.17 V. The range of the ADC is ±10 V, and the limit of the gain is 10∕0.17 ≈ 50.

Figure 5 presents the results of the waveforms of i (t) and v_amp(t). v_amp(t) can be measured without saturation of the instrumentation amplifier using the proposed method, as shown in the figure. The absolute value of the measured voltage lies within ±2 V, which is less than the range of the ADC (i.e., ±10 V).

Fig. 4.

Waveforms of the excitation current i (t) and voltage of detection coil v_coil(t).

Fig. 5.

Waveforms of the excitation current, i (t), and amplified voltage of detection coil, v_amp(t).

Figure 6 presents the result of the real part of the voltage of the detection coil, v_coil(t). Here, the fundamental, 5th, and 15th harmonics are presented as examples. The signal from the flaws cannot be observed because the signal is completely offset by the noise. Therefore, it is difficult to detect 2–6 mm depth holes.

Figure 7 illustrates the results of the real part of the voltage of the detection coil, v_amp(t). In contrast to the results in Fig. 6, the flaw signal is enhanced by the compensation, and it appears around 4 and 6 mm depth holes.

Fig. 6.

Real part of the voltage of the detection coil, v_coil(t). (a) Fundamental, (b) 5th, and (c) 15th harmonics.

Fig. 7.

Real part of the amplified voltage of the detection coil, v_amp(t). (a) Fundamental, (b) 5th, and (c) 15th harmonics.

The flaw signal can also be observed in Fig. 7; however, it is deteriorated by an edge effect (particularly, in the 2 mm and 6 mm depth holes around x = −100 and 100). The median value is subtracted along the x and y directions to suppress the edge effect in a simple manner. Figure 8 presents the results of the subtraction. Evidently, the flaw signal appears more clearly around the holes with depths of 4 mm and 6 mm. Furthermore, the flaw signal also appears slightly around the holes at a depth of 2 mm, as shown in Fig. 8(c) (the result of the 15th harmonic). Therefore, the proposed method can enhance the flaw signals obtained using the RECT, and flaws can be easily detected by performing further signal processing, that is, subtraction of the median value. The phase of the magnetic field from the flaw changes with the increase in the frequency. The flaw signal decreases, as shown in Figs. 8(a) and (b), whereas the signal increases, as shown in Fig. 8(c).

Fig. 8.

Real part of the voltage of the detection coil, v_coil(t) with subtraction of median value. (a) Fundamental, (b) 5th, and (c) 15th harmonics.

These results indicate that the flaw signal becomes clearer because the compensation method can increase the gain of the instrumentation amplifier to 500. However, the differential voltages of v_coil(t) and v_comp(t), that is, the differential voltage of the non-inverted (positive) and inverted (negative) terminals of the instrumentation amplifier, still remain. This is attributed to the delay of the conversion, the low sampling rate of the DAC and ADC, and the moving average. The flaw signal will become clearer, with a higher gain, if the compensation method is improved. In a future study, we will focus on improving the compensation method.

4. Conclusion

In this study, we applied a compensation method to the RECT using a DAC to address the problem of interference of the harmonic component with the amplification of the low-frequency component. The voltage of the detection coil was amplified with high gain via the proposed compensation method. Consequently, the signal from the back side flaws (𝜙3 mm × 2 mm, 4 mm, and 6 mm) on a 12 mm thickness aluminum plate could be detected. These results demonstrate that the proposed method can effectively enhance the flaw signals obtained using the RECT.

Footnotes

Acknowledgements

This study was supported in part by the Iron and Steel Institute of Japan (ISIJ) Research Promotion Grant.

References

Blitz

, Electrical and Magnetic Methods of Non-Destructive Testing, Chapman & Hall, London, UK, 1997.

Dogaru

and Smith

S.T.

, Giant magnetoresistance-based eddy-current sensor, IEEE Trans. Magn.37 (2001), 3831–3838, doi:10.1109/20.952754.

Krause

H.-J.

and Kreutzbruck

M.v.

, Recent developments in SQUID NDE, Physica C368 (2002), 70–79, doi:10.1016/S0921-4534(01)01142-X.

Hesse

and Pankratyev

, Usage of magnetic field sensors for low frequency eddy current testing, Meas. Sci. Rev.5 (2005), 86–93.

Tsukada

Hayashi

Nakamura

Sakai

and Kiwa

, Small eddy current testing sensor probe using a tunneling magnetoresistance sensor to detect cracks in steel structures, IEEE Trans. Magn.54 (2018), 6202205, doi:10.1109/TMAG.2018.2845864.

Sasayama

Ishida

Matsuo

and Enpuku

, Thickness measurement of an iron plate using low-frequency eddy current testing with an HTS coil, IEEE Trans. Appl. Supercond.26 (2016), 9001305, doi:10.1109/TASC.2016.2535366.

Yoshimura

Tanaka

Sasayama

and Enpuku

, Detection of slit defects on backside of steel plate using low-frequency eddy-current testing, IEEE Trans. Magn.54 (2018), 6202505, doi:10.1109/TMAG.2018.2847729.

Yoshimura

Sasayama

and Enpuku

, Optimal frequency of low-frequency eddy-current testing for detecting defects on the backside of thick steel plates, IEEE Trans. Magn.55 (2019), 6201205, doi:10.1109/TMAG.2019.2896590.

D.F.

Shiwa

Jia

J.P.

Takatsubo

and Moriya

, Multi-frequency ECT with AMR sensor, NDT&E International44 (2011), 438–441, doi:10.1016/j.ndteint.2011.04.004.

10.

Sasayama

and Enpuku

, Eddy current testing using square-wave inverter for thickness inspection of steel plate, Sensors and Materials31 (2019), 3023–3032, doi:10.18494/SAM.2019.2318.

11.

Sasayama

Yoshimura

and Enpuku

, Rectangular wave eddy current testing using for imaging of backside defects of steel plates, Int. J. Appl. Electromagn. Mech.64 (2020), 255–262, doi:10.3233/JAE-209329.

12.

Sasayama

, Classification of corrosion flaws on front and/or back surfaces of non-magnetic metal plates using a rectangular wave eddy current testing system, Journal of JSNDI71 (2022), 215–221, doi:10.11396/jjsndi.71.215.

13.

Sasayama

Okamura

and Yoshida

, Sensitivity improvement of magnetic nanoparticle imaging by compensation with digital-to-analog converter, IEEE Trans. Magn.57 (2021), 9159546, doi:10.1109/TMAG.2020.3014375.