Quantitative Investigation of Containment Liner Plate Thinning with Combined Thermal Wave Signal and Image Processing in Thermography Testing

Abstract

This study presents a process for the quantitative investigation of thinning defects occurring in the containment liner plate (CLP) of a nuclear power plant according to various depths with a combined thermal wave signal and image processing in a lock-in thermography (LIT) technique. For that, a plate sample with a size of 300 × 300 mm was produced considering the 6 mm thickness applied to an actual CLP. The sample was designed with nine thinning defects on the back side with defect sizes of 40 × 40 mm and varying thinning rates from 10% to 90%. LIT experiments were conducted under various modulation frequency conditions, and phase angle data was calculated and evaluated through four-point method processing. The calculated phase angle was correlated with the defect depth. Then, the phase image was binarized by the Otsu algorithm to evaluate defect detection ability and shape. Furthermore, the accuracy of defect depth assessment was evaluated through third-order polynomial curve fitting. The detectability was analyzed by comparing the number of pixels of the thinning defect in the binarized image and the theoretical calculation. Finally, it was concluded that LIT can be applied for fast thinning defect detection and accurate thinning depth evaluation.

1. Introduction

Non-destructive testing (NDT) is very valuable from a quality control perspective because it does not modify or destroy the component being tested. Additionally, it saves time and economic costs and improves reliability of equipment, parts, and materials. Equipment and facilities have standard design requirements and expected lifespans, and non-destructive testing is performed according to various requirements and standards for safety and reliability [1,2].

Recently, thermography testing (TT) has been receiving a lot of attention as an advanced technology that can quickly inspect large areas in a non-destructive manner with no contact [3]. Furthermore, due to its powerful advantages, its application field is expanding as an advanced technology that can inspect microscopic mineral crystallization processes, including macroscopic property inspection [4]. TT complements the limits of common NDT technologies such as visual testing (VT), penetrant testing (PT), magnetic particle testing (MT), eddy current testing (ECT), radiographic testing (RT), and ultrasonic testing (UT), and can be applied as an alternative technology [5].

The nuclear reactor containment building is a concrete building where the core facility, the nuclear reactor, and the reactor coolant system are installed. The reactor containment building of the Korea standard nuclear power plant (KSNPP) is a structure with a hemispherical roof and is a symbol of the nuclear power plant. As shown in Figure 1, a nuclear power plant containment building includes several layers of containment structures. The reactor containment building is made of reinforced concrete walls about 1.2 m thick, and the interior is sealed with a 6 mm steel plate called a CLP [6]. The concrete structure and CLPs are multi-layered protective walls that protect the internal reactor from external attacks in case of an emergency, prevent external leakage and exposure of radioactive materials in the event of an accident inside the dome, and perform the final protective function. When CLP is constructed, various structures (concrete, rebar, etc.) and additives are included inside and outside the CLP. The back of the CLP is attached to concrete, and voids may be created in this process. Corrosion defects are created on the back of the CLP due to voids in the concrete, which develop into thinning defects [7,8,9]. Ultimately, it reduces the strength of CLPs and concrete containment buildings and can lead to serious accidents [10,11]. Currently, non-destructive testing of the CLP of nuclear power plants in operation is mainly performed by examining the thickness of the CLP using local ultrasonic testing (UT) and visual inspection (VT) to check whether the CLP is penetrated or deformed [12]. However, the containment structure is very large and there are limitations due to the disadvantages of UT inspection (small inspection area, inspection result quality depending on operator proficiency, etc.). In addition, there is a method of estimating the concrete voids that cause CLP thinning through the striking sound of the CLP surface. Most techniques only apply inspection to the sidewall shell portion of the containment building, and only perform VT on the upper dome portion due to limited accessibility. These inspection techniques are mostly localized and have limitations in identifying CLP thinning or the shape of concrete voids. Recently, phased array ultrasonic testing (PAUT), acoustic resonance method (ARM), and CLP inspection techniques using automated scanners are being studied [6,12]. However, relatively complex mechanisms and signal processing are required to determine the shape of the defect. Therefore, if it is possible to evaluate CLP thinning defects using infrared thermography, quick and useful inspection will be possible.

Reviewing the existing literature, it can be seen that various thermographic testing studies that simulated thinning defects have been conducted [13,14,15,16,17,18,19,20]. Representative examples include pulse thermography (PT) and lock-in thermography (LIT) using a light source as an external energy source, as well as static eddy current thermography and dynamic eddy current thermal imaging-based online scanning using induction heating. However, when examining applicability to actual sites, pulse thermography, which applies heat from a high-power flash lamp in a very short period of time, may have limitations such as a somewhat small inspection area and complex signal processing techniques. Additionally, eddy current thermography (ECT) may have limitations that make it difficult to achieve uniform induction heating due to the complex structure. On the other hand, in the case of lock-in thermography using sinusoidal heating, it is advantageous to evaluate the time dependence between the input and output signals caused by the presence of defects and to control the influence of environmental factors [21,22]. In addition, it can be advantageous for field application because it is better at detecting, identifying, and quantitatively evaluating defects in complex structures. Therefore, in this study, a study on thinning defect evaluation was conducted by applying lock-in thermography.

In this study, in order to evaluate according to the depth of thinning defects, various depth conditions were considered while the defect size was constant. Similar previously published literature mainly focuses on the research of thinning detection and detection performance improvement algorithms and evaluation of defect size. In contrast, the novelty of this study combines signal processing and image processing to conduct defect depth evaluation as well as defect detection capability for CLP thinning. For the study, analysis was performed using phase data and phase images by applying the four-point signal processing technique, which is simple and excellent for improving detectability. The modulation frequency was applied to a low-frequency band that generates enough thermal contrast between the healthy part and the defective part by providing sufficient heat energy. An empirical equation was derived for depth estimation through the fitting of phase data. Additionally, the phase image was binarized using the Otsu algorithm. The defect detection was performed on the binarized image through an optimal threshold, and the results between thinning depth estimation accuracy and thinning detectability was finally presented by comparative analysis.

2. Theory

2.1. Four-Point Method for Phase Determination in LIT

LIT is one of the most widely used TT techniques [22]. LIT is a technology that simultaneously stimulates sinusoidal heat as a heat source across the entire surface of the object to be inspected and senses the IR signal emitted from the surface with an IR camera. Using sinusoidal waveforms results in the ability to preserve the shape and frequency, while the only deviation from the reference wave will be the magnitude and phase delay [23]. Defect detection is possible by demodulating this phase change and comparing and analyzing the difference between the sound area and the defective area. LIT modulates the heat source that stimulates the object in the form of a harmonic function and synchronizes the detection element to demodulate the phase change of the harmonic function. As a result of extracting phase changes using lock-in technology, even minute temperature changes on the surface can be detected even at low sampling, reducing the impact of uneven surface emissivity. In addition, inspectors can obtain good results by controlling the influence of environmental factors such as ambient temperature, measurement angle, and wind speed [24].

The phase shift method is a technique used to determine phase maps from different thermography raw images. The four-point method is one of the phase shift methods. It is calculated using the phase angle data of each pixel, then saved in a 2D matrix format, and displayed as a phase image. Figure 2 shows the processing process of the four-point method in LIT. If S₁, S₂, S₃, and S₄ are four equidistant thermal images, then the phase ($\mathrm{\varnothing }$) data can be expressed by Equation (1) [24,25].

$$\mathrm{\varnothing }\{\mathrm{x},\mathrm{y}\}={\mathrm{t}\mathrm{a}\mathrm{n}}^{-1}\left(\frac{S_1-S_3}{S_2-S_4}\right)$$

(1)

2.2. Otsu Algorithm Process for Binarization

Simplifying thermography images through binarization allows for intuitive evaluation of defects and characterizes automatic detection of various defects. Figure 3 shows the binarization process of the Otsu algorithm. As shown in Figure 3, the Otsu algorithm is a technology that finds the optimal threshold value through the histogram of the input image and performs binarization. This is a method to find an optimal threshold that minimizes the variance or maximizes the difference between classes when classifying pixels in an image into two classes [15].

Binary images obtained by Otsu’s processing of images are classified into two classes. In the two classified classes, ‘class 1’ refers to [0, k] based on the calculated threshold k, and ‘class 2’ refers to [k, 1]. The image of a 2D matrix can be expressed as a binary image through this series of processes and is useful for evaluating the characteristics of defects in the image. To obtain an appropriate binary image, the optimal threshold must be calculated [26,27,28]. The gray level of the M × N image with L intensity levels is [0, 1, …, L − 1]. The threshold t (0 ≤ t ≤ L − 1) splits pixels with intensity values into two classes: object (class 1) and background (class 2). The object class probability is ‘class 1’, and the background class probability is ‘class 2′, and can be expressed by Equations (2) and (3).

$${\mathrm{P}}_1\left(\mathrm{k}\right)={\sum }_{\mathrm{i}=0}^{\mathrm{k}}{\mathrm{P}}_{\mathrm{i}}$$

(2)

$${\mathrm{P}}_2\left(\mathrm{k}\right)=1-{\mathrm{P}}_1\left(\mathrm{k}\right)$$

(3)

The average intensity values of pixels classified into classes 1 and 2 are defined as Equations (4) and (5).

$${\mathrm{m}}_1\left(\mathrm{k}\right)=\frac{1}{{\mathrm{P}}_1\left(\mathrm{k}\right)}{\sum }_{\mathrm{i}=0}^{\mathrm{k}}\mathrm{i}{\mathrm{P}}_{\mathrm{i}}$$

(4)

$${\mathrm{m}}_2\left(\mathrm{k}\right)=\frac{1}{{\mathrm{P}}_2\left(\mathrm{k}\right)}{\sum }_{\mathrm{i}=\mathrm{k}+1}^{\mathrm{L}-1}\mathrm{i}{\mathrm{P}}_{\mathrm{i}}$$

(5)

There are mean intensity values up to the k level, which for all images is

$${\mathrm{m}}_{\mathrm{G}}={\mathrm{P}}_1{\mathrm{m}}_1+{\mathrm{P}}_2{\mathrm{m}}_2$$

(6)

In order to calculate the optimal threshold value, the Otsu algorithm should allow the concept of between-class variance. The equation of between-class variance is defined in Equation (7).

$${\mathsf{\sigma }}_{\mathrm{b}}^2=\frac{{\{{\mathrm{m}}_{\mathrm{G}}{\mathrm{P}}_1-\mathrm{m}(\mathrm{k}\left)\right\}}^2}{{\mathrm{P}}_1(1-{\mathrm{P}}_1)}$$

(7)

3. Methods and Samples

3.1. Thinning Defect Sample

The sample applied in this study was a square plate-shaped sample made of S275 material, which is used in CLPs. Figure 4 shows the geometric information of the thinning defect sample. The thinning defect sample is 300 × 300 mm, and the thinning size in subsurface of the sample is constant at 40 × 40 mm. The thickness of the sample considered was 6 mm, which is the CLP thickness of KSNPP, as described in Section 1. As for the thinning depth, 9 defects of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% of the total thickness of the specimen were considered. A rows A to C and columns 1 to 3 show the respective thinning defect identification information.

Table 1. Classification of each defect and its dimensional value.

Defect ID	Geometric Value
	Size (mm)	Depth (mm)	Thinning Rate (%)
A1	40 × 40	0.6	10
A2		1.2	20
A3		1.8	30
B1		2.4	40
B2		3.0	50
B3		3.6	60
C1		4.2	70
C2		4.8	80
C3		5.4	90

shows quantitative information for each defect ID. Figure 5 shows a picture of the sample. Figure 5a shows the front of the test sample, where matte black paint was applied to the surface to maintain the emissivity above 0.9, and Figure 5b shows the thinning defect generated on the back side.

3.2. Experimental Setup for LIT

Figure 6 shows the configuration of the LIT experimental device applied in this study. The IR camera was the FLIR SC655 long-wave infrared camera model with a wavelength range of 7.5 to 14 μm and a resolution of 640 × 480 pixels. The infrared camera has a FOV of 15°, and a lens with an aperture of f = 41.3 mm was applied. Sinusoidal heating was performed by applying two 1 kW halogen lamps as external heat sources which were controlled in synchronization with the function generator and power amplifier. In the LIT experiment, six excitation frequencies were applied: 0.1 Hz, 0.05 Hz, 0.04 Hz, 0.03 Hz, 0.02 Hz, and 0.01 Hz. The distance between the camera and the sample was approximately 1.5 m, and it was placed so that the sample on the screen could be filled as much as possible. The irradiance (radiation flux) of the sample plane by a halogen lamp with an output of 2 kW was irradiated in the form of a sinusoidal wave ranging from a minimum of 0 to a maximum of 11.1 kW/m². Raw data of LIT testing was acquired at 50 frames per second and analyzed using commercial software MATLAB 2022a coding.

Table 2. Details of LIT raw data to determine phase by 4-point method.

Frequency (Hz)	Frame/ Cycle	Frame Interval	Frame Considered
			1st	2nd	3rd	4th
0.1	500	125	125	250	375	500
0.05	1000	250	250	500	750	1000
0.04	1250	312.5	312	625	937	1250
0.03	1666	416.5	416	833	1249	1666
0.02	2500	625	625	1250	1875	2500
0.01	5000	1250	1250	2500	3750	5000

shows the raw data information of LIT considered to determine phase through the 4-point method.

4. Results and Discussion

4.1. Thinning Defect Detection

In this study, only phase images, which are less sensitive to non-uniform heating effects and surface emissivity, were considered for thinning rate evaluation. In the LIT experiment, an excitation frequency of two complete cycles was applied. To determine phase data using the four-point method, the raw data from thermography was computed for all pixels and converted to a phase image.

The phase image results processed by the four-point method for each of the modulation frequencies are shown in Figure 7. As can be seen in the phase image in Figure 7, the detectability of thinning defects with different thinning rates varies depending on the modulation frequency. Defect A1 (thinning rate: 10%) is not detected in the phase images of any applied modulation frequencies. In addition, defects A2 (thinning rate: 20%) and A3 (thinning rate: 30%) defects were detected in the phase images of all of the modulation frequencies, but their shapes were not clear. On the other hand, defects with a thinning rate of 40% to 90% were detected in all of the modulation frequency phase images, and the shape of the defect was also maintained. In particular, the A7 (thinning rate: 70%) defect, A8 (thinning rate: 80%) defect, and A9 (thinning rate: 90%) defect had good detection ability at all modulation frequencies, showed excellent phase contrast, and the defect shape was like a square.

Figure 8 shows the absolute phase contrast value of the C3 (thinning rate: 90%) defect between the defective area and the sound area. For defect areas in phase contrast calculations, the average value of 10 × 10 pixels was considered at each defect center. For the sound area, the average value of 10 × 10 pixels in the area adjacent to the defect was considered. As shown in Figure 8, the phase contrast improves as the modulation frequency decreases. The maximum phase contrast is 2.2006 radian at 0.01 Hz, and the minimum phase contrast is 0.86 radian at 0.1 Hz.

Figure 9 shows the trend of phase change according to thinning defect depth and modulation frequency. As can be seen in Figure 9, for all thinning defects, the phase angle tended to increase as the depth increased. In addition, it was found that as the modulation frequency increases from 0.01 Hz to 0.1 Hz, the phase change decreases and the phase difference between the sound area and the thinning area decreases.

To evaluate the performance of the proposed technique, the signal-to-noise ratio (SNR) values of phase data were calculated. The SNR value was calculated from the pixel value in the same area used when calculating the phase contrast. The SNR can be expressed by Equation (8).

$$\mathrm{S}\mathrm{N}\mathrm{R}=20{\log }_{10}\left(\frac{\left|\mathrm{D}\mathrm{R}\mathrm{O}{\mathrm{I}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}-\mathrm{S}\mathrm{R}\mathrm{O}{\mathrm{I}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right|}{\mathsf{\sigma }}\right)$$

(8)

where SROI is the average value of the sound area, DROI is the average value of the thinning area, and $\mathsf{\sigma }$ is the standard deviation of the thinning area.

Table 3. SNR calculation values of phase data according to modulation frequency.

Defect ID		Modulation Frequency (Hz)
		0.1	0.05	0.04	0.03	0.02	0.01
Phase SNR (dB)	B1	1.57	6.07	6.32	16.25	13.08	18.47
	B2	1.34	6.12	7.98	24.23	22.57	29.22
	B3	3.68	6.74	11.78	30.35	28.01	38.34
	C1	3.67	30.02	35.48	38.98	41.67	50.12
	C2	7.57	36.44	36.24	40.36	41.75	50.57
	C3	8.07	37.15	32.86	45.02	47.86	53.18

shows the SNR values for defects with a thinning rate of 40% or more according to each modulation frequency. As with phase contrast, it can be seen that SNR of good quality is shown according to thinning depth increases. Additionally, it can be seen that as the modulation frequency increases from 0.1 Hz to 0.01 Hz, the SNR improves. Considering the phase contrast results comprehensively, the low modulation frequency band is more advantageous for quantitative investigation than the high modulation frequency band.

4.2. Phase Image Banarization by Otsu Algorithm

Binarization was performed for low frequencies that showed sufficient phase contrast: 0.01 Hz, 0.02 Hz, and 0.03 Hz. Binarization processing was performed according to Equations (2)–(7). Figure 10 shows the binarization result of Otsu algorithm processing on the phase image for each modulation frequency. As shown in Figure 10, good detection potential was shown for thinning rates of 40% to 90%. However, as the frequency decreases from 0.01 Hz to 0.03 Hz, the shape becomes more blurred. Comprehensively, the modulation frequency of 0.01 Hz is the most advantageous.

4.3. Estimation of Thinning Depth

To evaluate defect depth evaluation effectiveness, empirical tests of lock-in thermography were conducted, and the depth was estimated by calculating the phase contrast. Figure 11 shows the variation in depth of defects (40% to 90% thinning) detected in the binarized image as a function of phase difference at a modulation frequency of 0.01 Hz. As can be seen, using the third order polynomial curve results in a good fitting of the defect depth with a coefficient of determination equal to $R^2$ = 0.9999. The third-order polynomial curve for expressing the defect depth as a phase angle is expressed as Equation (9).

Table 4. Defect depth prediction at 0.01 Hz using phase angle and related error.

Defect Depth (mm)	Thinning Rate (%)	Phase Angle (Radian)	Estimated Depth (mm)	Error (%)
2.4	40	0.5039	2.35	0.85
3.0	50	0.7472	2.90	1.76
3.6	60	1.0534	3.51	1.65
4.2	70	1.6067	4.42	−4.14
4.8	80	1.9097	4.86	−1.10
5.4	90	2.2006	5.26	2.60

shows the defect depth prediction results at 0.01 Hz calculated by Equation (9). It can be seen that the defect depth prediction shows good results of less than 4.14% for all detected defects. The maximum error was calculated to be −4.14% for a defect depth of 4.2 mm, and the minimum error was calculated to be 0.85% for a defect depth of 2.4 mm.

$$Depth=0.97277+3.10884\Phi -0.78949{\Phi }^2+0.11905{\Phi }^3$$

(9)

4.4. Evaluation of Defect Detecability

The resolution for identifying the size of the defect is determined by the resolution of the IR camera, the distance to the inspection target, and the field of view (FOV). By converting the surface distance of the inspection target corresponding to one pixel (surface distance per unit pixel), the size of the defective area can be calculated through the number of pixels in the defective area. The size was estimated by calculating the ratio of the actual defect size and image resolution and can be expressed as Equation (10).

$$Size=\mathrm{M}\times \frac{\mathrm{L}}{\mathrm{P}}$$

(10)

where M is the number of pixels occupied by the defective area in image, P is the fraction number corresponding to the length of the measuring device, and L is the length of the actual sample through measurement.

Table 5. Calculation of the number pixels and error for defect depth in binarization image.

Defect ID	Pixels		Error (%)
	Real Pixel	Estimated Pixel
B1	1995	5504	−63.75
B2	3179		−42.24
B3	3795		−31.05
C1	5589		1.54
C2	6153		11.79
C3	6427		16.77

shows the number of pixels in the image for defects with thinning rates of 40% to 90% at 0.01 Hz and the number of pixels calculated by Equation (10). A defect indicating 40 × 40 mm in a real sample becomes 86 pixels and 64 pixels in a 640 × 480 resolution image. Therefore, thinning defect can be estimated as 86 × 64 = 5504 pixels in the binary image. As can be seen in Figure 10 and Table 5, the deeper the defect depth and the closer the defect is to the surface, negative errors change into positive errors. This is because the higher the thinning rate, the more external energy heating occurs on the surface, and the excessive heat conduction phenomenon becomes active due to the thickness difference between the sound area and the defective area. Conversely, as the thinning rate decreases, the diffusion of heat energy becomes slower. Therefore, less thermal contrast is generated, and defect detection is not perfect, resulting in negative errors. As a result of a defect such as B1 with a thinning rate of 40%, a negative error occurred because the calculated 1995 pixels in the image were 3509 pixels less than the estimated 5504 pixels in the calculation. The C1 defect with a thinning rate of 70% was calculated to be 5589 pixels in the image, differing only by 89 pixels from the theoretical calculation of 5504 pixels, and the actual defect size and ratio were similar. On the contrary, in the case of C3 defects with a thinning rate of 90%, the 6427 pixels calculated from the image were 923 pixels more than the 5504 pixels in the estimated value, so they appeared larger than the actual thinning and a positive error occurred.

5. Conclusions

This study presented a lock-in thermography evaluation process to quantitatively investigate the effect of thinning depth on specimens simulating nuclear power CLPs with various thinning rates. The results were analyzed by combining heat wave signals and image processing and showed that LIT can be applied for fast and accurate assessment of CLP thinning detection and depth assessment in nuclear power plants. The possibility of detecting defects was compared through Otsu binarization processing, and the estimation of defect depth according to the thinning rate was evaluated. In particular, it was found that the phase angle according to the temperature difference in lock-in thermography plays an important role in evaluating thickness thinning.

In future research, we plan to improve reliability of actual defect shapes and ratios by reducing transient heat transfer effects through research on advanced noise removal algorithms based on thermal characteristics. Additionally, research will be conducted to examine complex structures such as actual nuclear power plant CLPs in an occlusive environment and practical complementary detection technologies.