Thickness measurement for non-ferromagnetic metal under the large liftoff based on the last peak point of differential pulsed eddy current signals

Abstract

Pulsed Eddy Current Testing (PECT) has been used to measure the wall thickness of ferromagnetic metallic component with thick insulation. However, for the non-ferromagnetic metallic component, there is still the problem to be solved. The main purpose of this study is to find an effective feature, to measure wall thinning of the non-ferromagnetic metallic component under the large liftoff, and further expand application of the PECT technology. Hence, the time to the last peak point (TLPP) is proposed based on the analytical predicted signals. Furthermore, the influence of the variable liftoff is studied, and the error caused by the liftoff is within the acceptable range. Two sets of experiments are conducted to test the performance of the TLPP under various liftoffs. The results show that when the wall thickness is reduced by more than 40%, the measurement error based on the TLPP is within 11%.

Keywords

Pulsed eddy current testing LNG pipeline non-ferrimagnet liftoff time to the last peak point

1. Introduction

In recent years, with the rapid growth of global demand for clean energy, the utilization of liquefied natural gas (LNG) has been rapidly developed and improved, thus the LNG pipeline is being set up in large areas of China [1]. The LNG pipeline, made of stainless steel, is covered with nearly 200 mm insulation foam and a protective layer of galvanized steel [2], so it is difficult for conventional NDT methods to measure the wall thinning caused by the erosion and corrosion of gas. Pulsed Eddy Current Testing (PECT) has been proved to be an effective method to measure the wall thickness of ferromagnetic metallic component without removing the insulation and cladding [3], which is a favorable method for LNG pipeline inspection. Therefore, research on PECT method to test of the LNG pipeline is imperative for continuous safe operation.

PECT technology has been widely studied in the detection of ferromagnetic materials, at the same time, many PEC signal features are proposed to assess the wall thickness of ferromagnetic metals. The signal slopes was found to be linearly correlated with the wall thickness, and has been widely used in the evaluation of the wall thinning of ferromagnetic materials for several years [4]. Recently, Wen found that the liftoff intersection (LOI) points in frequency domain can accurately evaluate the wall thickness of ferromagnetic samples regardless of the influence of liftoff distance [5,6]. In the meantime, there are also some signal features for non-ferromagnetic metal. The time to zero-crossing (TZC) and LOI points in the signals of non-ferromagnetic materials was studied [7,8]. However, these signal features for non-ferromagnetic metal are on the condition of a small liftoff (usually a few millimeters), while LNG pipeline is coated by thick insulation, which is a typical large liftoff condition. Therefore, the signal features mentioned above might be inapplicable, and new signal features should be proposed to adapt to the non-ferromagnetic metallic component under the large liftoff conditions.

The theoretical calculated signals of non-ferromagnetic materials have been widely studied The electrical conductivity of the specimen mainly affects the early signal, while the relative magnetic permeability plays an important role in the late signal. On the other hand, with increasing of liftoff, the amplitude of the signal decreases and the signal change rate increases [9]. Thus for non-ferromagnetic metal, especially under the large liftoff, the PECT signal decays more rapidly and with smaller amplitude. Therefore, unlike ferromagnetic metal or non-ferromagnetic metal under small liftoff, it is difficult to extract the signal features mentioned above from the PECT signal of the LNG pipeline.

This paper proposes a new signal feature named the time to the last peak point (TLPP) based on the characteristics of the analytically predicted PEC signals of non-ferromagnetic metal. Different from the above-mentioned features appearing in the early or late stage the TLPP appears in the middle of the PECT signal and is linear with the wall thinning within a certain range. It is an easy-to-obtain and effective signal feature for measuring the wall thinning of the LNG pipeline. And it was confirmed by experiments that the TLPP of differential signals turns out to be a reliable feature. The rest of this paper is organized as follows. In Section 2, analytically predicted signals of the LNG pipeline are given, and the TLPP is proposed and proved to be theoretically applicable for the detection of wall thinning of non-ferromagnetic metal. In Section 3, experimental verification is conducted, and the PEC signals under various conditions are obtained. The influencing factors to the linear relationship between TLPP and wall thinning is explored to verify the favorable performance of TLPP under different conditions. Finally, a brief conclusion is given in Section 4.

2. Analysis

2.1. The analytical predicted signal

There are various specifications of LNG pipelines, and this paper focuses on the low-pressure pipeline with an outside diameter of 38 inches (965 mm) and a wall thickness of 0.5 inches (12.7 mm). Due to the large curvature of the pipeline, it can be simplified into the five-layer flat model as shown in Fig. 1 [10].

Fig. 1.

Analytical model of PECT.

In Fig. 1, from bottom to top, the mediums represent respectively the inner air, the pipe wall, the thermal insulation, the cladding and the outer air. These mediums are assumed to be linear, homogeneous and isotropic. Their magnetic permeability and electrical conductivity are denoted by μ_ri and σ_i (i = 1, 2, 3, 4, 5), respectively. And the structure simulates the real LNG pipeline. The material of the pipe is 304 stainless steel, which is a non-ferromagnetic metal, and the conductivity is 1.35 × 10⁶ S/m, and the thickness of pipe wall is approximately set to 12 mm. The insulation is made of a 3-layer flame-retardant poly isocyanate foam with a thickness of 60/60/60 from the inside to the outside, a total of about 180 mm. And the outer cladding is an aluminized steel sheet with a thickness of 0.5 mm, the material of which is generally 304 stainless steel, so the conductivity of the cladding is approximately 1.35 × 10⁶ S/m. The probe adopted is the coaxial coils commonly used in the PECT, and the parameters of the driver and pickup coil are shown in Table 1.

Table 1

Parameters of driver coil and pickup coil

	Inner radius	Outer radius	Height	No. of
	r₁ (mm)	r₂ (mm)	l₂ − l₁ (mm)	turns n
Driver coil	10	30	40	800
Pickup coil	76	79	3	400

According to the previous study [10], the expression of the induced voltage under harmonic excitation was given by Eq. (1) based on the closed solution by Dodd and the Truncated Region Eigen function Expansion (TREE) method by Theodoulidis. $\begin{eqnarray}\displaystyle {\rm\Delta}U & = & \displaystyle \frac{j2{\pi}{\omega}{\mu}_{0}n_{d}n_{p}I({\omega})}{(r_{2d}-r_{1d})(l_{2d}-l_{1})(r_{2p}-r_{1p})(l_{2p}-l_{1})}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \times ∼\mathop{\sum }_{n=1}^{Ns}\frac{\mathit{Int}({\alpha}_{n}r_{1d},{\alpha}_{n}r_{2d})\mathit{Int}({\alpha}_{n}r_{1p},{\alpha}_{n}r_{2p})}{{\alpha}_{n}^{5}[({\alpha}_{n}h)J_{0}({\alpha}_{n}h)]^{2}}(e^{-{\alpha}_{n}l_{2d}}-e^{-{\alpha}_{n}l_{1}})(e^{-{\alpha}_{n}l_{2p}}-e^{-{\alpha}_{n}l_{1}})R_{1,2}^{\prime }({\alpha}_{n})\end{eqnarray}$ (1) Where j is the imaginary unit. The discrete eigenvalue 𝛼_n is the n-th positive root of first order Bessel function J₁(𝛼_nh) = 0, while Int (x₁, x₂) can be obtained by the following formula $\begin{eqnarray}\displaystyle \mathit{Int}(x_{1},x_{2})=\int _{x_{1}}^{x_{2}}xJ_{1}(x)dx & & \displaystyle\end{eqnarray}$ (2)

I (ω) is the amplitude of the applied harmonic current, and ω is the angular frequency of the excitation. The peak value of the excitation square wave signal is set to 4 A, the rise time and fall time are 2 ms, and the duty cycle is 0.5. r₁, r₂ respectively represent the inner and outer radius of the coils, while n denotes the number of the coil turns, and the subscripts d and p label the driver and pickup coil, respectively. h is the truncation radius, and h = 200 ∗ r_2p. Ns is the number of accumulation, and Ns = 150. $R_{1,2}^{\prime }$ can be derived by the following iterative equations. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{i,i+1}^{\prime }=\frac{R_{i,i+1}+R_{i+1,i+2}^{\prime }e^{-2{\beta}_{i}(z_{i-1}-z_{i})}}{1+R_{i,i+1}R_{i+1,i+2}^{\prime }e^{-2{\beta}_{i}(z_{i-1}-z_{i})}}\quad i=1,2,3,4\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{i,i+1}=\frac{{\mu}_{r(i+1)}{\beta}_{i}-{\mu}_{ri}{\beta}_{i+1}}{{\mu}_{r(i+1)}{\beta}_{i}+{\mu}_{ri}{\beta}_{i+1}}\quad i=1,2,3,4\end{eqnarray}$ (4) Where, $R_{i,i+1}^{\prime }$ is the generalized reflection coefficients from the inner layer to the i-th layer, while R_{i, i+1} is the reflection coefficient between the i-th layer and the (i +1)-th layer.

The PECT signal can be obtained by superimposing the signals of the harmonic excitation according to the Fourier Transform. Therefore, the induced voltage signal of PECT can be derived. $\begin{eqnarray}\displaystyle {\rm\Delta}U[k]=\frac{1}{N}\mathop{\sum }_{m=1}^{N}e^{j\frac{2{\pi}}{N}(k-1)(m-1)}{\rm\Delta}U[{\omega}_{m}] & & \displaystyle\end{eqnarray}$ (5) Where, N is the number of sampling points, while k = 1,2, … , N.

Obviously, the induced voltage signal is the function of the relative permeability, conductivity and thickness of the pipe wall, as well as the liftoff. The induced voltage derived above is calculated by Matlab R2017a to obtain the analytical predicted signal of the LNG pipeline. At the same time, the signal of the same condition but under small liftoff is calculated. And the effects of liftoff on the original signal and the differential signal can be seen from Fig. 2a and Fig. 2b respectively.

Fig. 2.

Analytical predicted signal.

Compared with the small liftoff condition, both the original and differential signal under the large liftoff condition show distinct characteristics. Their peak values are obviously smaller, and their change rate are much faster. Therefore, signal features like signal slopes in the original signal or peak amplitude (PA) in the differential signal are more difficult to extract. However, the shapes of both the signals under large or small liftoff are always similar. That is, although the liftoff has significant effect on the amplitude, there is no obvious advance or lag of the signal, which means some signal features of time are still applicable. The time features in the early stage, such as TPA and TZC, are too small to ensure the accuracy, so the time features in the middle stage is focused. Based on the analysis above, the TLPP is selected as a signal feature to assess the wall thinning of non-ferromagnetic metallic component under large liftoff as shown in Fig. 3.

Fig. 3.

The TLPP in the differential PECT signal.

Fig. 4.

The relationship between the TLPP and the wall thinning.

2.2. The characteristic of the TLPP

Since the thickness of insulation is not a constant value in practical detection, the relationships between the TLPP and the wall thinning are studied when the liftoff varies between 160 and 200 mm. The differential signals is obtained according to the analytical simulation based on a reference wall thickness of 12 mm, In addition, the TLPP feature is extracted from the differential signal, and the relationship between the TLPP and the percentage of the wall thinning is shown in Fig. 4. There is a good linear relationship between the TLPP and wall thinning under various liftoff conditions. It also can be seen that the linear relationship changes with the liftoff. Therefore, wall thinning calculation based on a certain liftoff will be inaccurate, and errors will be inevitably produced due to the changeable liftoff.

Fig. 5.

Errors caused by liftoff.

As mentioned above, the actual liftoff value will be varied approximately between 160 and 200 mm, so the median value of 180 mm is adopted for wall thickness measurement to reduce the overall error. The theoretical measurement errors of TLPP caused by liftoff are calculated, and the results are shown in Fig. 5. As the wall thickness thinning increases, the error caused by liftoff gradually decreases. And when the wall thickness thinning exceeds 30%, the error is limited to ±30%, and reaches the maximum at the liftoff of 160 mm and 200 mm, which is acceptable for rough testing without removing the coating [11]. According to the analysis above, the TLPP is indeed a theoretically effective feature to measure the wall thinning of non-ferromagnetic metal under large liftoff conditions.

3. Experiments and discussion

In order to further test the practical feasibility of the signal feature in the wall thinning measurement and the performance under various liftoff, a series of PECT experiments were carried out. The experiment approximates the actual working conditions of the LNG pipeline and makes a slight adjustment according to the existing equipment. The experiment approximates the actual working conditions of the LNG pipeline and makes a slight adjustment according to the existing equipment. The cladding adopts a sheet with size of 450 mm * 450 mm, material of 304 stainless steel and thickness of 0.5 mm. A number of plastic plates are superimposed to simulate the insulation layer. The specimens used in the experiment were 304 stainless steel with a size of 500 mm * 500 mm. There are 5 plates of different thickness, 6, 8, 10, 12 and 14 mm respectively, of which the reference thickness is 14 mm, and plates with other thickness are used to simulate the uniform wall thinning.

On the basis of the above general experimental setup, the changeable liftoff conditions of the LNG pipeline detection are simulated by further changing the experimental conditions. According to the above analysis, the linear relationship between the TLPP and wall thinning is affected by the liftoff, but when the liftoff varies between 160 and 200 mm, the detection of specimen with wall thickness reduction of more than 30% can be realized, and the measurement error reaches maximum when the liftoff is 160 or 200 mm. Therefore in order to study the actual maximum measurement error of TLPP, the total thickness of the plastic plate is set to 160 and 200 mm in the experiment. And a total of two groups of experiments were divided. In the first set of experiments, the thickness of the insulation is 160 mm. In the second set of experiments, the thickness of the insulation is set to 200 mm, and all the other experimental settings are the same as above. Figure 6 shows the original signal and differential signal of all the 2 sets of experiments.

Fig. 6.

Original experimental signals.

There is few information in the original signals, thus the detailed discussion about the performance of TLPP will be developed. Based on the above experimental results, the differential PECT signals of the two sets of experiments can be obtained by differentiating the reference signal as shown in Fig. 7. It can be seen from the figure that, consistent with the analysis of the simulation results, the signal changes quickly so that the accuracy of the early signal features can be poor. Therefore, the TLPP has a great advantage over these features.

Fig. 7.

Differential experimental signals.

Furthermore, in order to study the measurement error of wall thickness, the TLPPs of each plate are extracted from the differential signals, and the theoretical wall thinning is calculated according to the analytical linear relationship between the TLPP and wall thinning. And the measurement errors are shown in Table 2.

Table 2

Wall thinning measurement based on TLPP

Liftoff	Actual wall	Percentage of	TLPP	Theoretical calculated	Errors
(mm)	thinning (mm)	wall thinning	(ms)	wall thinning (mm)
	4	28.6%	2.714	6.44	61%
160	6	42.9%	2.714	6.44	7.33%
	8	57.1%	2.560	7.49	6.38%
	4	28.6%	2.765	6.08	52%
200	6	42.9%	2.714	6.44	7.33%
	8	57.1%	2.611	7.14	10.75%

As shown in the table, when the wall thinning is less than 30%, the measurement result is not reliable due to the large error caused by liftoff. But it doesn’t indicate TLPP can not be used to measure the wall thinning. It also can be seen that when the wall thinning is increased by more than 40%, the measurement of wall thinning is obviously improved. And according to the above analysis, the error reaches the maximum when the liftoff is 160 or 200 mm. Therefore, when the liftoff changes between 160 and 200 mm, the measurement error based on TLPP will not exceed to 10.75%, the maximum error in the experiments in this paper. Therefore, for the non-ferromagnetic metal under large liftoff condition, like LNG pipeline, the TLPP can be regarded as an effective feature to measure the wall thinning.

4. Conclusion

This work has investigated the PECT method of LNG non-ferromagnetic metal pipeline under the large liftoff condition. Based on the analysis of the analytical predicted PECT signals of the non-ferromagnetic pipeline with thick insulation, an effective signal feature TLPP is proposed to evaluate the wall thinning. First, the PECT signal is approximately predicted by analytical solution. According to the characteristics of signal amplitude and attenuation rate, the TLPP in the differential signal is found to be easy to get and linearly related to the wall thinning. Further calculation is conducted to analyze the impact of the changeable liftoff conditions on the performance of the TLPP, and it is proved that the liftoff effect on the TLPP is within an acceptable range. Finally, the performance of TLPP is tested by experiments, and the results show that when the relative wall thinning is more than 40%, the measurement error based on TLPP can be controlled within 11%. The new signal feature TLPP found in this work is an efficient signal feature for evaluating the wall thinning for non-ferromagnetic metal under large liftoff.

Footnotes

Acknowledgements

This work was supported by the National Key Research and Development Program of China (grant no. 2017YFF0209701).

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