Evaluation of detection capability of eddy current probes with stochastic decision threshold for inspecting pits on austenitic stainless steel welding

Abstract

It is still a big challenge to calculate the probability of defect detection for inspecting pits on austenitic stainless steel welding using traditional POD models. Because we determine the decision threshold, the POD curve has a lot of changes as the decision threshold changes, there is no clear reason to insist which threshold is reasonable. This study proposes a new probability of detection (POD) model to quantitatively assess the detection capability of eddy current probes for inspecting pits on austenitic stainless steel welding. The experimental results show that the proposed model is more reasonable than traditional ones. The novel POD model was employed to analyze three eddy current probes, uniform, TR, plus-point probes on austenitic stainless steel welding. The results reveal that the uniform eddy current probe has the best detection capability for inspecting pits on among the three probes.

Keywords

Eddy current testing probability of detection stochastic decision threshold austenitic stainless steel welding

1. Introduction

Pressure vessels is one of the important components in various industries and widely used in chemical and nuclear power plants [1]. The corrosion of steel is one of the most common degradations in various pressure vessels, causing huge loss every year [2,3]. Thus, the inner surface of pressure vessels is usually covered with austenitic stainless steel cladding to protect it from corrosion [4]. Austenitic stainless steel exhibits high corrosion resistance in an oxidizing environment and has excellent toughness at low and high temperatures while the steel is prone to pitting corrosion in the presence of chloride ions [5–7]. When pitting corrosion occurs at the welding, it is difficult to be found due to the roughness and unevenness of the surface, which will cause great safety hazards. Therefore, Non-destructive testing (NDT) is particularly important to check the integrity of the inner surface of the pressure vessel and the safe operation of the device.

Eddy current testing (ECT) is a potential non-destructive testing method to inspect such corrosion pits on austenitic stainless steel welding [8,9]. ECT can perform non-contact detection when detecting defects on or near the surface of the workpiece, with high detection sensitivity and a good linear indication within a certain range [10,11]. However, high levels of noise will be generated during ECT inspection due to the rough surface of the austenitic stainless steel welding. When the flaw size is small, the noise signal will cover the defect signal, resulting in errors in the inspection results. In order to more accurately assess the detection probability of defects. Therefore, it is necessary to quantify the detection ability of ECT more probabilistically for subsequent analysis.

In order to solve this problem, the probability of detection (POD) was proposed, which represents the ability of non-destructive testing methods to detect defects probabilistically [12,13]. The main concept of a POD is to express the probability that a flaw with a size, a, is detected using a probabilistic function, POD (a), to quantify the capability of a non-destructive testing method. The POD contributes not only to the quantification of non-destructive testing methods but also to the risk-based maintenance [14,15]. The main task of the conventional POD model calculation method is to find a decision threshold ( $\hat{a}$ value) to maximize the separation of noise and signal and minimize false alarms caused by noise. But the noise is very large and non-uniform during the inspection process due to factors other than defect size (a), when we determine the decision threshold, the POD curve has a lot of changes as the decision threshold changes, there is no clear reason to insist which threshold is reasonable. Therefore, this article proposes a novel POD model that is not limited to a given decision threshold ( $\hat{a}_{th}$ ) to evaluate the POD curve, but uses stochastic decision threshold to calculate the POD curve more probabilistically based on $\hat{a}$ versus a approach and hit/miss approach.

In this study, two models, a conventional model and the proposed model, were adopted to conduct POD analysis of ECT for inspecting corrosion pits on austenitic stainless steel welding. Plate samples covered by austenitic stainless steel welding were prepared to simulate the inner surface of large pressure vessels and 43 holes of different size were artificially drilled on the plate samples to simulate corrosion pits. Compared with the results generated by the traditional POD model, the POD curve produced by the proposed model is not affected by objective factors and shows higher detection capability for small defects. In addition, the detection capabilities of uniform, plus point and TR probes were evaluated by using the proposed model. The results show that the uniform probe has better detection capability for inspecting pits on austenitic stainless steel welding among the three types of probes.

2. Materials and methods

2.1. Fabrication of plate samples

This study prepared plate samples cladded by austenitic stainless steel to simulate the wall of a large-scale pressure vessel, which is illustrated in Fig. 1. Base metal of the plate samples is steel plate (SM490 or ASTM A387 Gr22) with a length of ranging from 251 to 401 mm and a width of ranging from 112 to 175 mm. The cladding was applied by electric slag welding method with plural welding beads whose material was US-B309L and number depends on the dimension of the plate samples; the welding beads had a width of 50–70 mm and a thickness of about 5 mm at the center; Cylindrical holes characterized by diameter and depth were artificially fabricated by drilling on the welding beads of 6 plate samples to simulate corrosion pits, the drilled holes position is the centerline of each welding bead; The pitch between neighboring holes on the same bead was 30 mm as illustrated in Fig. 1, thus, the number of drilled holes on a welding bead is 2-3,which depends on the dimension of the bead. Table 1 lists the number of drilled holes corresponding to each pair of diameter and depth, and totally 85 drilled holes were prepared. For POD analysis, 3 defect-free plate samples were prepared to obtain inspection noise of ECT. This study prepared defect-free plate samples (as illustrated in Fig. 2). The length of the plate sample ranges from 251 to 401 mm, and the width ranges from 115 to 150 mm. The cladding had a thickness of approximately 5 mm; the width of a weld bead was 115–150 mm.

Fig. 1.

Schematic diagram of the sample prepared for this study (unit: mm).

Table 1

The number of drilled holes corresponding to each pair of diameter and depth (unit: mm)

	depth = 0.3	depth = 0.5	depth = 1.0	depth = 3.0	depth = 4.0	depth = 7.0
diameter = 0.5	2	2	2
diameter = 1.0	2	1	9	5	9	4
diameter = 3.0			5	5	5
diameter = 4.0			4		4	4
diameter = 5.0				5	5
diameter = 10.0			4		4	4

Fig. 2.

Schematic diagram of the noise sample prepared for this study (unit: mm).

Fig. 3.

(a) Plus-point probe. (b) Uniform probe. (c) TR probe. The three eddy current probes utilized in this study. Upper image: side view, lower image: bottom view (unit: mm).

Fig. 4.

Experimental system of eddy current testing.

2.2. Eddy current inspection

Eddy current testing experiments used three different types of probes, including plus-point, uniform and TR (mutual-induction differential type pancake probe) probe, together with a commercial eddy current testing instrument (aect-2000N, Aswan ECT Co. Ltd., Osaka, Japan) to collect signals from the drilled holes on the plate samples. In order to compare the capability of different probes under basically the same conditions, appropriate probes of each type were selected so that they have the best performance when the excitation frequency is within 300–400 kHz. The excitation frequency was 400 kHz. The dimensions of the three probes and the moving direction of the probes were shown in Fig. 3, the sample placement position was that the welding line is parallel to the Y axis of the XYZ-stage. The plus-point probe was positioned in such a way that its coils and the welding bead line made 45 degree angle in order to reduce noise; The uniform and TR probe were placed that its coil and welding line are perpendicular (as illustrated in Fig. 3). Experimental system of eddy current testing was illustrated in Fig. 4. The probe was fixed on an XYZ-stage controlled by the PC with a lift-off of 1 mm, for two-dimensional scanned of the surface of plate samples. The ECT instrument, aect-2000N, was controlled using software running on the laptop. The signal was collected by the probe and output by the PC through the AD converters. The scanning area is a 30 mm × 30 mm square area (as illustrated in Fig. 1) centered at the drilled hole. The pitch of the scanning is 500 μm and 100 μm in the X and Y directions of the sample, respectively.

Before the experiments, the probe needs to be calibrated, signals were normalized so that the maximum signal due to an artificial slit whose length, depth and width are 20, 5, 0.5–0.6 mm, respectively, on a standard plate (Inconel 600) became 1.0 V and 0 degree. Then, the signal generated by the largest flaw is slightly less than 10.0 V. Thus, the maximum amplitude of the defect signal is controlled in a 10 mm × 10 mm square area surrounding a drilled hole. Noise was extracted in a similar way, all points on the defect-free plate samples compared with drilled holes were extracted noise. The scanning area starts from the white dot and gradually becomes a square area of 30 mm × 30 mm (as shown in Fig. 2). The pitch of the scanning is 500 and 100 μm in the X and Y directions of the sample, respectively.

2.3. POD analysis

This study adopted two POD models: a conventional POD model and a novel proposed POD model.

There are two conventional POD models, so called $\hat{a}$ versus a analysis and hit/miss analysis, to construct POD curves. The former is commonly used to calculate POD, because it is suitable when the number of test samples is small. This method assumes linearity between flaw size, a, and the amplitude of signals, $\hat{a}$ . However, the linearity is not always satisfied by the original data, therefore, log-transformation is usually applied to satisfy the linearity between them as represented in Eq. (1), $\begin{eqnarray}\displaystyle \ln (\hat{a})={\beta}_{0}+{\beta}_{1}\ln (a)+{\varepsilon} & & \displaystyle\end{eqnarray}$ (1) where ϵ is a noise term following a normal distribution with zero mean and constant standard deviation of σ. 𝛽₀, 𝛽₁ is the coefficient. After 𝛽₀, 𝛽₁, σ are obtained by maximum likelihood estimation using inspection data, POD (a) is calculated as the probability that the signal amplitude (â) exceeds a given threshold, $\hat{a}_{th}$ , POD $(a)=P(\hat{a}>\hat{a}_{th})$ . More specific procedures and details can be found in ASM and USDOD Handbook [12,13].

The hit/miss is based on binary results to construct POD curve where “hit” signifies the signal amplitude exceeds $\hat{a}_{th}$ , indicating the presence of a flaw and “miss” signifies the signal amplitude is below $\hat{a}_{th}$ , indicating the absence of a flaw. Then, POD can be calculated as the ratio of the number of “hit” to the sum of “hit” and “miss” for the flaws with a specific parameter.

In this study, considering the advantages and disadvantages of two conventional POD models, a novel method was proposed that uses stochastic decision thresholds instead of a fixed value to evaluate the POD for ECT inspection of corrosion pits on the cladding. Firstly, the proposed method evaluated the distribution of defect signal and noise, respectively. For example, the distribution of the defect signal (diameter = 1 mm) and the noise data of the uniform probe obeys the normal distribution (as shown in Figs 5–6). This method, like $\hat{a}$ versus a method, also assumes linearity between flaw size and the amplitude of signals. Then, obtaining a suitable expression to express the correlation, after obtaining 𝛽₀, 𝛽₁, and σ through a simple regression analysis, the distribution of noise and defect signal were obtained, respectively. Secondly, for a specific flaw size, sample one data from the distribution of signal amplitude and the distribution of noise randomly and individually. The hit/miss method is used to compare the amplitudes of the two sampled data to determine whether the defect is detected. If the defect signal is greater than the noise, it is recorded as “hit”, otherwise it is recorded as “miss”. Finally, under a flaw parameter, 1,000,000 times of sampling and comparison were conducted to calculate the ratio of “hit” to approximate the POD.

Fig. 5.

The distribution of defect signal (diameter = 1 mm).

Fig. 6.

The distribution of noise.

Fig. 7.

Results of regression and POD analysis (when the depth was used as a parameter).

Fig. 8.

Results of regression and POD analysis (when the diameter was used as a parameter).

Fig. 9.

Amplitudes of the measured ECT signal varies with depth.

Fig. 10.

Amplitudes of the measured ECT signal varies with diameter.

Fig. 11.

The results of the traditional POD analyses under different decision thresholds.

Fig. 12.

The result of the novel POD analyses for uniform probe.

3. Result and discussion

The results of the conventional POD analyses for the uniform probe are presented in Figs 7–8. The 95% quantile of noise was selected as the decision threshold. In this study, log-transformation was applied to make the relation between the diameter and depth of drilled holes and signal amplitude satisfies linearity, respectively. Linear regression between the diameter and depth of drilled holes and the signal amplitude is conducted, as shown in Fig. 7(a) and Fig. 8(a). Figure 7 reveals that POD as a function of the depth was not reliable because of this large confidence intervals. In contrast, Fig. 8 shows that POD has a much narrower confidence interval. Thus, it is implied that the diameter of drilled holes is more reasonable as a parameter. To further confirm whether it is reasonable to use the diameter of drilled holes as a single parameter, the degree of influence of parameters on the signal amplitude is evaluated.

Fig. 13.

The result of the novel POD analyses for plus-point probe.

Fig. 14.

The result of the novel POD analyses for TR probe.

Figures 9 and 10 show how the signal amplitude changes with the depth and diameter of drilled holes, respectively, where dots represent the signal amplitude of defect and the solid line represents the maximum amplitude of the noise. Figure 9 shows that when the diameter is fixed, the signal amplitude does not change significantly with the depth. Figure 10 presents the relationship between the signal amplitude and the diameter when the depth is 1 mm and 3 mm, respectively, which reveals that the diameter is linearly and positively related to the signal amplitude. Compared with the depth, the diameter is a more appropriate parameter and should be used for POD analyses. It should be noted that the final experimental results are also applicable to other probes. Therefore, it is sufficient to use diameter and amplitude to evaluate the probability of defects.

The results of the traditional POD analyses under different decision thresholds are summarized in Fig. 11. The results show that the traditional POD curves largely change as the decision threshold changes. The results of the novel POD analyses are shown in Fig. 12. The result of novel POD analyses based on stochastic decision threshold is exempted from the influence of subjective selection of decision thresholds, which suggests a better detection ability of the uniform probe than that indicated by the traditional POD analyses.

The novel POD model was also used to evaluate the detection capabilities of plus point and TR probes for inspecting pits. The results of the plus-point and TR probes are shown in Fig. 13 and Fig. 14, respectively. By comparing the detection capability characterized by the novel POD model, the uniform probe has a better detection capability for inspecting corrosion pits on austenitic stainless steel welding.

4. Conclusion

This study proposed a novel POD model based on stochastic decision threshold for quantifying the detection capability of ECT for inspecting corrosion pits on austenitic stainless steel welding. Compared with the traditional POD model which requires subjective selection of decision threshold, the novel model is exempted from the influence of subjectivity. Subsequently, the novel model was used to evaluate the detection capability of ECT with three different probes, including uniform probe, plus point probe and TR probe, for inspecting the corrosion pits. The results reveal that the uniform eddy current probe has better detection capability for inspecting pits on austenitic stainless steel welding among the three types of probes.

Footnotes

Acknowledgements

This work was developed at Tohoku University in Japan and it was supported by a grant from the Key Research and Development Program of Shandong Province, China.

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