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Abstract
Quantitative detection of the defect size by infrared thermography is difficult. In this paper, a novel temperature integral method (TIM) is introduced for the quantitative detection of the defect size. The TIM integrates the temperature values of each pixel across the defect area to obtain the defect sizes quantitatively and conveniently. The performance of the TIM on the defect size detection is evaluated thoroughly with both experiments and simulations. Furthermore, the TIM method was compared with existing methods for quantitative detection of defect size. The results indicate robustness and accuracy of TIM.
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1. Introduction
Infrared temperature measurement has the advantages of non-contact, visualization, high detection efficiency and wide measurement range, and infrared non-destructive testing technology was improved as an effective nondestructive inspection method for special equipments. Extensive research works have been reported based on active thermography, include pulse, pulse phase, lock-in, eddy current pulsed and vibrothermography [1–7]. The characterization of defects is the objective of non-destructive testing, where the defect size is one of the parameters for defect characterization. In recent years, there have been many researches on the quantitative detection of defect sizes. The quantitative detection methods for defect size are divided into two main categories.
The first type of method performs threshold segmentation and edge extraction techniques to obtain the pixel values of the defective area [8–11]. Due to the lateral temperature diffusion, the edge information of the defect area is blurred. The frame that best represents the material defect information from hundreds of thermal sequences needs to be selected and this is highly subjective. Kabouri et al. [12] selected the frames that depicted the largest average surface temperature of the specimen as the candidate image frame data. However, this method has poor robustness and low accuracy. Due to the presence of noise, the raw images are usually not suitable for accurate material assessment [13]. Hansen [14] pointed out that the median filter had better edge detection characteristics on the basis of noise removal capability when the selected image contains the edge feature of the defects. Sreeshan [15] adopted the watershed technique and Gabor filtering to detect defects, which can effectively extract the edge information of defect. However, this method is weak in adaptability and cannot detect fuzzy defects in thermal images. These methods also cannot realize extraction of defect feature automatically. On the basis of those researches of predecessors, Yuan et al. [16] proposed the maximum of standard deviation of sensitive region method (MSDSRM) to decide the best frame to calculate defect boundaries. The whole process is automatic and does not require human intervention.
Another type of method is temperature profile line approach [17–20]. Temperature profile line approach is the most widely used method for defect size measurement, and the temperature profile line of the defective area exhibits Gaussian distribution. The defect size can be detected by the full width at half maximum (FWHM) on the temperature profile line. However, non-uniform heat and surface reflectivity lead to high noise in the thermal image, which embarrasses the evaluation of the defect size. General noise reduction methods only consider the elimination of noise points and the reconstruction of the thermal signal in the depth direction [21–23], while there is no effective means for noise reduction in the lateral direction of the temperature. Therefore, the existing methods are unable to obtain the exact defect size. Vitalij et al. [24–27] performed a discrete Fourier transform (DFT) on the thermal sequence images and proposed four different methods to detect the size of defects. However, it also failed to solve the phase oscillation problem.
Furthermore, Marco et al. [28] proposed an automated detection algorithm to segment the contours of the damages. This approach can identify subsurface defects and quantify their dimensions within 5% error compared to the actual size of the damages. Nevertheless, this method is more complex and mainly used for quantitative size detection of defects with large areas. Liu et al. [29] proposed a characterization method for surface defects based on reflective laser thermography. Although this method is applied to the detection of small defects in metallic materials, the accuracy of this method is low. The maximum error of the detection results of the defect size is 25%. Qiu et al. [30] developed a method for remote measurement and shape reconstruction of fatigue cracks by using laser-line thermography (LLT) technique. Based on this method, both the size and inner profile of the cracks in different shapes can be evaluated quantitatively from the LLT signals. However, this method can only detect the surface cracks.
In this paper, we propose a novel defect size detection method, the Temperature Integral Method (TIM), in which the relevant temperature information is integrated in a pixel-wise manner on the temperature profile line to derive the defect size. This offers particular advantages in terms of (i) higher robustness, (ii) higher detection efficiency, and (iii) higher accuracy. The structure of the remainder of this paper is as follows: Section 2 describes the theory of the TIM and other detection methods. Section 3 provides the details of the simulation setup and the experimental procedures. In section 4, the performance of TIM for quantitative defect size detection is evaluated and compared with other methods. Finally, section 5 gives the concluding remarks.
2. Theory of quantification of defect sizes
2.1 Temperature integral method (TIM)
The quantitative assessment of the defect size has become a hot topic. Many works have been focused on extracting the edge information of the defective area and measuring the full width at half maximum of the temperature profile line. These methods have poor robustness and high subjectivity. In order to solve the problem of quantitative testing of the defect size, we propose a novel method that depends only on the temperature of the defective area and non-defective area.
Moradi et al. [31] proposed the thermal signal area (TSA) method, and he verified that extracting the defect size based on the area ratio is of higher accuracy than that based on the temperature ratio. This brought us new ideas to study the infrared thermography. The heat conduction model of the sample containing defects is shown in Fig. 1. When the heat propagates only in the depth direction, we can directly calculate the size of the defect without considering the lateral heat diffusion, as shown in Fig. 1(a). First, we select one frame from the thermal images. Then, we select a part of the temperature profile line that contains the defective area. The sum of all temperature values on the temperature profile line is:
Fig. 1. The model of the heat conduction: (a) one-dimensional heat conduction model; (b) comparison of the one-dimensional (1D) heat conduction model and the three-dimensional (3D) heat conduction model.
However, the lateral diffusion of the temperature is not negligible, especially for materials with higher thermal conductivity. When the temperature diffuses laterally, the temperature of the defective area is normally distributed [32], as shown in Fig. 1(b). The concentrated heat originally belonging to the defective area will spread to the surrounding non-defective area, resulting in a decrease in the temperature of defective area and an increase in the temperature of the surrounding non-defective area. Therefore, it should be noted that Eq. (3) is calculated based on the parameters in the red rectangular box, as shown in Fig. 1(b).
If the green and yellow areas are approximately equal, Eq. (3) can still be used to calculate the actual defect size, as shown in Fig. 1(b). The yellow and green areas vary with time. Therefore, we need to find the moment when the yellow and green areas are equal in area. First, we define the moments where the yellow and green areas are equal as the characteristic time tc. When the yellow and green areas are equal, the defect size D can be written as Eq. (4):
where σc is the standard deviation of the Gaussian distribution at the characteristic time tc, μ is the coordinate of the center of the peak. Equation (4) can be solved as:Then, we need to find the relationship between defect size and the time. In infrared thermography, the relationship [17,18,33] between the defect size and the time is:
where FWHM is the full width at the half maximum of the Gaussian function, α is the thermal conductivity of materials. The FWHM method has been successfully applied to a number of materials, such as metals, composites and so on [17,18,32,33]. As we all know, the relationship between the FWHM of the Gaussian function and σ is: where σ is the standard deviation of the Gaussian distribution.Finally, we can calculate the characteristic time when the yellow and green areas are equal, i.e., when σ is equal to σc. It can be written as Eq. (8):
Equation (8) can be solved as:
where D can be solved in Eq. (3). We can find the defect size corresponding to the characteristic time tc. Therefore, as long as the defect size calculated at a certain moment and the time at that moment satisfy Eq. (9), the defect size at that moment is the true defect size. Its condition is determined by Eq. (3) and Eq. (9):2.2 Maximum of standard deviation of sensitive region method (MSDSRM)
There is a common method to detect the defect size by combining the threshold method and edge extraction method. However, the diffusion of temperature leads to the blurring of defect edges and hinders the extraction of accurate edge information. In this case, it is critical to choose the optimal number of frames to extract the defect size. Yuan et al. [16] proposed a maximum standard deviation of the sensitive region method, which can identify a reasonable image frame automatically from an infrared image sequence.
The small local area surrounding the selected edge segment is called the sensitive region and it is depicted as C in Fig. 3(a). Assume that the size of the sensitive region in this example varies from 10 × 10 pixels to 15 × 15 pixels such that it contains enough pixels that is neither too large nor too small to define the defect boundary. The curve of Fig. 3(b) shows the standard deviation of the sensitive area as a function of the time, and the frame number represents time. The peak of the standard deviation-time curve at Fmax depicts the maximum temperature differences between the defect and non-defect pixels. Therefore, the appropriate image frame can be extracted for further image processing.
Fig. 3. (a) Schematic diagram to illustrate the sensitive area (C) of defects in sample; (b) the history of standard deviation of the sensitive area with time.
2.3 FWHM and pulsed phase thermography (PPT) processing
From Eq. (7), a plot can be made between FWHM and square root of time t, which exhibits linear fit and the intercept is related with the defect size. Based on this, Vitalij et al. [24] performed DFT on the temperature profile:
where n is the index in the image sequence in time domain, N is the total number of thermal sequences, Re(f) and Im(f) are the real and imaginary components of the F(f) in frequency domain. The phase can be computed using:The processing method is pulsed phase thermography (PPT), which can effectively reduce the noise of the image. After PPT processing, there are four methods to detect the size of defects, as shown in Fig. 4. Figure 4(a) is to measure the distance between the intersections of the tangents at the position of half contrast with the baseline (method A). Figure 4(b) is to measure distance of the intersections of the tangents with maximum slope with baseline (method B). Figure 4(c) is to measure the distance of the positions of the half maximum contrast (method C) while Fig. 4(d) is the distance of the positions with the largest change of phase value dϕ/dx (method D).
Fig. 4. Four different methods for determination of defect size: (a) distance of intersection between tangents at half of the maximum contrast with baseline, (b) distance of the positions of the half maximum contrast, (c) distance of intersection between tangents at maximum slope (dϕ/dx) with baseline and (d) distance between positions of maximum slope (dϕ/dx).
3. Data acquisition
3.1 Numerical simulations
Finite element method (FEM) is a common and effective calculation technique. It discretizes a non-individual object into several finite element sets in order to solve the problems of continuum systems [34]. Several commercially-available software programs based on FEM such as COMSOL, ANSYS, ABAQUS and LS-DYNA, are currently available to analyze heat conduction in a solid. In this study, the heat transfer module of ANSYS 19.0 is used to simulate infrared thermography under three different heating methods. We apply three heat flux loads on the sample surface. The first heat flux load is 4 × 106 W m-2 and lasts for 0.01 s to simulate the flash thermography (FT). The second heat flux load is 20000 W m-2 and lasts for 10 s to simulate the long pulse thermography (LPT). The third heat flux load is a periodic square wave with a value of 10000 W m-2 and lasts for 20 s to simulate the lock-in thermography (LIT). The duty cycle is 50% and the heating time in a single cycle is 2 s.
The sample is a stainless-steel plate (dimension 100 × 100 × 6 mm). There are five different defects on the sample 1, as shown in Fig. 5. The distance from the inspected surface to the bottom of each defect was 1.0 mm. The overall parameters and the thermal characteristics of the material are listed in Table 1.
Table 1. General Parameters of Materials
3.2 Experiments
This experiment was carried out two phases: long pulse thermography and lock-in thermography. In long pulse thermography, the sample was optically excited with two halogen lamps, the power of the halogen lamps is 1 kW, and the heating duration is 10 s. In lock-in thermography, a time relay was added to the experimental setup, the sample was excited with periodic square wave. The temperature evolution of the simulated surface was recorded using an infrared camera (FAST M100k, 3-4.9 µm) using a 640 × 512 pixels array. In addition, the acquiring rate of the infrared camera was set to 50 Hz.
The samples are a stainless-steel plate (sample 2: dimension 100 × 100 × 6 mm) and a carbon fiber reinforced polymer (CFRP) laminate (sample 3: dimension 200 × 150 × 5 mm), as shown in Fig. 6. There are six flat bottom holes (FBHs) on the sample 2, as shown in Fig. 6(a). The diameters of the defects are 12, 8 and 3 mm. The distance from the inspected surface to the bottom of the three holes above is 1.5 mm. The distance from the inspected surface to the bottom of the three holes below is 0.5 mm. There are two defects on the sample 3, as shown in Fig. 6(b). The distance from the inspected surface to the bottom of each defect was 1.0 mm. In order to improve heating efficiency and reduce spurious reflection, the inspected surface was coated with a high emissivity black paint. The experimental setup is shown in Fig. 7.
Fig. 6. The photos of samples: (a) is sample 2 (stainless-steel plate); (b) is sample 3 (CFRP laminate).
4. Result and discussion
4.1 Simulation results
In the simulation, the temperature of the front surface of the sample 1 was extracted. The thermal images of sample under different heating techniques are shown in Fig. 8. Compared with LPT and LIT, the edge characteristic of the defects is the more obvious in FT. The temperature values are different for different defective areas, because the temperature of the sample surface is affected not only by the defect depth, but also by the defect size.
Fig. 8. The thermal sequence images of sample 1 under different heating means: (a) the thermal image at t = 0.10 s in FT; (b) the thermal image at t = 10.00 s in LPT; (c) the thermal image at t = 11.00 s in LIT.
To quantify the lateral dimensions of each defect in the obtained thermal image, five temperature profile lines were extracted for the width or height of the defects, as shown in Fig. 9. Although the shapes of the defects are irregular, the simulation results show that the temperature profile lines of the defects are close to Gaussian distribution. The deviation of the temperature at the highest point is due to the fact that the grid size is only set to 1 mm. The dimensional information of the five different defects is detected by the TIM. According to Eq. (10), we calculated the defect size of sample 1 corresponding to different characteristic times, as shown in Table 2. The results in Table 2 are all derived from measurements of defect sizes on the temperature profile lines of Fig. 9. The maximum relative error by the three methods is 5.37% and the minimum relative error is 0.23%. Kalyanavalli [32] used FWHM method to detect the basalt fiber reinforced epoxy laminate containing four different size defects, and the maximum error of the simulation was 15%. Compared with the FWHM method, the TIM method has higher accuracy and robustness in simulation results.
Table 2. Defect Size Estimation of Sample 1: Comparison Between the Actual Size and the Size Obtained by the TIM from Simulationsa
4.2 Experimental results
In long pulse thermography, the surface temperature of the stainless-steel plate is shown in Fig. 10. We observe the change in temperature before and after heating on the selected red temperature profile line. At t = 3 s, the five different FBHs are fully visible, and the outline of the 3 mm defect is obvious. The outlines of the 13 mm and 8 mm defects are more obvious. At t = 13 s, the four different FBHs are visible, but the 3 mm defect disappears. Therefore, it is difficult to obtain defect sizes for small defects, let alone cracked defects, by relying on visual image information. Both the FWHM method and MSDSRM method rely on visual image information to extract the defect size. The TIM method can extract defect sizes, which relies on the temperature information along the temperature profile line.
Fig. 10. The thermal image and temperature profile line in long pulse thermography: (a) t = 3 s; (b) t = 13 s.
Furthermore, the FWHM method requires that the temperature values on both sides of the defect are close to the same level. In practice, uneven heating is difficult to avoid, as shown in Fig. 10. It is difficult to find full width at half maximum for small-size defects whose outlines are not obvious. These cause significant difficulty for the quantitative detection of the defect sizes.
There are some disadvantages of using the PPT processing to detect the size of defects. The PPT processing effectively reduces the lateral noise, as shown in Fig. 11(a) and 11(b). This helps us to detect the size of the defects using methods A - C. However, the outline of the 3 mm defect completely disappeared. When we derive the phase, Only the size of the 12 mm defect can be extracted, as shown in Fig. 11(c).
Fig. 11. The profiles of representative phase images: (a) the thermal sequence image after PPT processing in long pulse thermography; (b) the profile line of the phase (ϕ) in lock-in thermography; (c) the profile line of the phase gradient (dϕ/dx) after PPT processing in long pulse thermography.
The TIM method was applied to detect the defect sizes from 15 groups of experimental data. The detection results of the defect size using TIM method are presented in Fig. 12. The data and its distribution and box plot are mapped. The actual defect sizes on the temperature contour lines are 3 mm, 8 mm and 13 mm. Detection of defect sizes using LPT (mean size and standard deviation are 2.9315${\pm} $ 0.3257, 8.0665${\pm} $ 0.582, 12.8562${\pm} $ 0.2399) is more accurate than LIT (mean size and standard deviation are 2.8567${\pm} $ 0.5157, 8.3661${\pm} $ 0.4471, 12. 8995${\pm} $ 0.5926).
Fig. 12. The detection results of the defect size using TIM method under different heating techniques.
The MSDSRM method is also applied in this paper. The optimal number of frames can be found based on the maximum value of the standard deviation of the image in the sensitive region. Then, the image is segmented by Ostu’ s method [35] and the results are shown in Fig. 13. The threshold values are 0.4941, 0.4447, 0.5147, 0.4988, 0.4489 and 0.4988 for Fig. 13(a)-(f), respectively. In practical inspection, noise in thermal images is unavoidable, as shown in Fig. 13(a), 13(b), 13(d) and 13(e). In this paper, we knew beforehand the shape of the defect in order to extract the defect edge information approximately. However, it is difficult for the MSRSRM method to detect the defect size with unknown shape in the actual inspection. The optimal frame rate for all three different diameter defects is 204 fps in LPT. The optimal frame rates for three different diameter defects are 202, 498, 570 fps in LIT. Each pixel corresponds to a size of 0.2901 mm. The defect sizes can be calculated as shown in Table 3. The maximum relative error of the MSDSRM method is 50.78%, and the minimum relative error of the MSDSRM method is 6.50%.
Fig. 13. The image processed by threshold segmentation: (a) 8 mm defect in LPT; (b) 3 mm defect in LPT; (c) 13 mm defect in LPT; (d) 8 mm defect in LIT; (e) 3 mm defect in LIT; (f) 13 mm defect in LIT.
Table 3. Defect Size Estimation: Comparison of Actual Size, Size Detected by MSDSRM, Size Detected by Method A, B and Ca
The detection results using method A – C are shown in Table 3. The maximum relative error of method A is 31.02%, and the minimum relative error of method A is 5.19%. The maximum relative error of method B is 27.72%, and the minimum relative error of method B is 3.55%. Both method A and B show poor robustness. The maximum relative error of method C is 23.06%, and the minimum relative error of method C is 11.10%. Method C has a large relative error in the experiment results. Compared to the methods A – C and the MSDSRM method, TIM provides an accurate estimate of defect size. Furthermore, in the experiments of Kalyanavalli, the maximum relative error using the FWHM method is 40%, indicating a lower accuracy than that of the TIM.
The TIM method has shown high accuracy and robustness in metallic materials. Next, we applied the TIM method to composite materials for defect size detection. The thermal sequence of CFRP laminate is shown in Fig. 14. At the heating stage, there is a large noise due to the uneven emissivity of the surface of the CFRP laminate. At the cooling stage, the noise is greatly reduced and the defect profile is more obvious.
Fig. 14. The thermal image and temperature profile line in long pulse thermography: (a) t = 3s; (b) t = 13 s.
The size estimation results of CFRP laminate are shown in Fig. 15. The data and its distribution and box plot are mapped. The actual defect sizes on the temperature contour lines are 5 mm and 10 mm, respectively. Detection of defect sizes using LIT (mean size and standard deviation are 9.5289${\pm} $ 0.3345, 5.0899${\pm} $ 0.1844) is more accurate than LPT (mean size and standard deviation are 10.0572${\pm} $ 1.0127, 5.7671${\pm} $ 0.1441). Finally, we use TIM method to sweep the whole selected defective area, and the result is shown in Fig. 16. This is done by calculating the defect size for all pixel points along the x-direction from “start” to “end” in Fig. 16(a). The calculated results deviate less from the real defect sizes and allow a better reconstruction of the information of the defect sizes, as shown in Fig. 16(b).
Fig. 15. The detection results of the defect size using TIM method under different heating techniques.
Fig. 16. The detection of defect sizes along the sweeping direction: (a) the schematic of TIM; (b) the results of the detection.
5. Conclusion
In this paper, a novel defect size detection technique for LPT, FT and LIT is introduced. In this technique, the temperature is integrated over the relevant temperature profile line range in a pixel-wise manner. The TIM method does not require processing of the entire thermal sequence image, nor does it require measuring the distance of the FWHM on the temperature profile line. In addition, the TIM does not rely on the visual image (finding defect edges by pixels), and the reconstruction of defect sizes can be achieved with a few parameters on the profile line. The performance of TIM has been demonstrated on a metallic sample and a CFRP laminate. The results show that the TIM significantly improves the detection accuracy of the defect size without considering material properties. In addition, the finite element analysis shows that TIM can be used for accurate defect sizing. The performance of TIM has been extensively compared with other methods, and it was found to provide an improved metric for quantitative defect size assessment. However, the results of the TIM sometimes fluctuate because of noise in the raw temperature data on the surface of the sample.
Further effort will be focused on extracting the sizes of complex defects and resolving fluctuations in inspection results. For example, it may be possible to combine the TIM with the thermal signal reconstruction (TSR) method. In addition, the TIM will be applied to more materials (glass fiber reinforced polymer, thermal barrier coatings, etc.), smaller defects (cracks) as well as unknown defects.
In conclusion, TIM is a simple yet effective defect size detection method which can handle demanding inspection conditions (the influence of defect depths, noise).
Funding
National Natural Science Foundation of China (11702151); Natural Science Foundation of Ningbo (2018A610143); K. C. Wong Magna Fund in Ningbo University.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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