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Abstract
In this paper, an improved long-pulse excitation infrared nondestructive testing method is proposed, and a homogeneous pulse thermography (HPT) system is built. Based on the proposed new pulse excitation system, the problem of uneven heating in pulsed infrared non-destructive testing (NDT) has been effectively improved, and the signal-to-noise ratio of thermal images has been improved. Finally, the results of the experimental analysis and discussion show that the improved pulsed infrared NDT system greatly improves the defect detection rate and the reliability of the quantitative analysis of defect depth compared with the traditional pulsed detection system.
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1. Introduction
In recent decades, NDT has been used in various industries and has been one of the best choices for material quality assessment due to its non-destructive nature [1]. Various NDT techniques have been studied and employed, including ultrasonic inspection, x-ray inspection, eddy current thermography, and infrared thermography (IRT) [2–8]. IRT is an effective and convenient NDT method, which has the advantages of large individual inspection area, high inspection efficiency, safety, and non-contact compared to other inspection techniques. Among the thermal imaging techniques, pulsed thermography (PT) is the most 10commonly used, and it is widely used to detect metals [9], concrete [10], ceramics [11], composite materials [12], etc. In PT, the surface of the object under test is instantaneously heated by a flash lamp, and the heated surface temperature is monitored by an infrared camera. Due to the interference of defects to the heat flow, subsurface defects are manifested as localized hot or cold areas on the surface, which are thus visually reflected in the thermal image. According to the basic method of PT inspection, the thermal image is the most important basis for evaluating the defect detection. However, the inspection process is often accompanied by noise, and the factors affecting the noise level are broadly summarized as the influence of the infrared camera, the experimental conditions, the heating method, and the data acquisition and processing [13–16]. The increase of noise will weaken defect information in thermal images, reduce the ability of defect identification, and affect the accuracy of quantitative detection, so the noise reduction is crucial.
PT is broadly divided into two types of thermal imaging, short pulse and long pulse. Long pulses have more adequate heat transfer compared to short pulses, which is beneficial for deeper defect detection. Proper heating time helps to detect deeper defects, as Masashi et al. [17] showed in their study on the effect of heating time on the nondestructive inspection of pulsed phase thermography. However, long pulse thermography has an increasing effect on heating inhomogeneity as the heating time increases. The change in heating mode brings about a change in noise. Many efforts have been made in the experimental setup and thermal image processing to eliminate the effect of noise in long-pulse thermography. Almond et al. [18] proposed a long-pulse excitation thermography technique using a halogen lamp instead of a high-energy flash lamp as the heating source, which reduces the cost of use and avoids the further amplification of uneven heating noise and secondary damage to the specimen. A thin layer of matte black paint is often sprayed on the specimen in IR inspection to increase the reflectivity [19] and improve the thermal image contrast. While Unnikrishnakurup et al. [20] placed polymethylmethacrylate (PMMA) plates in front of the excitation source to improve the thermal image quality by reducing the influence of the excitation source on the thermal imaging camera.
The current mainstream methods in thermal image post-processing are using principal component thermography (PCT) [10], pulse-phase thermography (PPT) [21], thermal signal reconstruction (TSR) [22] and neural networks [23]. For example, Ibarra-Castanedo et al. [15] mentioned PCT, PPT, TSR and other post-processing methods among the methods commonly used for infrared image processing. Cheng et al. [24] used adversarial neural networks successfully for infrared thermal imaging defect detection of composite materials. All these methods improve the signal-to-noise ratio of images in long pulse detection. The improvement of signal-to-noise ratio is beneficial to the qualitative detection of defects and the quantitative detection of defect size. But in terms of pulse depth quantitative detection, the current depth quantitative methods mostly use the temperature contrast method, the first-order derivative of temperature contrast method and the second-order derivative of temperature contrast method, etc. For example, Benitez et al. [25] used differential absolute contrast for defect depth quantification. Kalyanavalli et al. [26] used the first order derivative of temperature contrast method to predict the defect depth of composite materials in long pulse thermography. Zhu et al. [27] studied the relationship between the peak time of temperature contrast second order derivative method and the defect depth and thus reflect the depth information. However, these methods are based on the one-dimensional heat transfer theory and the assumption of uniform heating of the specimen surface. Thus, improving the problem of inhomogeneous heating will undoubtedly contribute to the accuracy of long-pulse infrared thermography in depth quantification.
In this paper, a homogeneous pulse thermography (HPT) is established based on active long-pulse infrared thermal image inspection using lens shaping to make the energy approximately homogeneous. Firstly, we calculate the surface temperature variation of specimens under HPT by analytical analysis based on the one-dimensional heat transfer long-pulse theory. Secondly, based on HPT, the surface temperature of stainless steel specimens and Carbon Fiber Reinforced Plastics (CFRP) were analyzed in experiments for amplitude and uniformity of distribution, as well as post-processing and discussion of thermal images. Finally, we performed quantitative and reliable evaluation of defect depth for stainless steel and CFRP, and comprehensively analyzed the feasibility and applicability of this method.
2. Theoretical basis
2.1 Theoretical analysis of HPT
The basis of the IRT measurement method is the measurement of thermal radiation. The excitation source produces thermal radiation. Then the radiation is transmitted to the target surface and absorbed and reflected. The target surface absorbs energy and the energy radiates outward according to Stephen-Boltzmann and Wayne's law, and finally, the thermal radiation information of the target surface is collected by the infrared thermographic equipment. The amount of energy absorbed by the target surface is mainly related to the intensity of thermal radiation generated by the excitation source, the characteristics of the transmission path and transmission medium, and the characteristics of the target surface. According to Kirchhoff's law, the sum of the energy absorbed on the target surface ${E_\alpha }$, the reflected energyand the transmitted energy ${E_\tau }$ equal the incident radiation energy ${E_\varphi }$.
When the divergent light becomes parallel light, the radiant energy will change during the transmission process. The lens will absorb and reflect a part of the energy, and the energy absorbed and radiated by the target surface will also change. Assuming that the energy absorbed and reflected by the lens is $E_\alpha ^L$ and $E_\rho ^L$, respectively, the radiation energy of the incident target surface is ${E_\varphi } - E_\alpha ^L - E_\rho ^L$. The loss of radiation energy after passing through the lens is related to the lens material properties k and reflectivity a, defining f as the correlation coefficient of (k, a). In Fig. 1, when the excitation source is close to the target surface, ignoring the energy loss on the transmission path, the radiation energy incident on the target surface is:
Although part of the energy is reflected and absorbed by the lens, this process only affects the total energy that the sample can obtain and the energy distribution on the surface of the sample. The study of the heat transfer law inside the specimen is still based on the one-dimensional heat transfer hypothesis. According to the famous Green’s function and assuming that the initial temperature is zero, the long pulse temperature solution is obtained as follows:
T is the temperature of the sample at different depths after the excitation starts, k is the thermal conductivity of the material, $\alpha = k/\rho c$ is the thermal diffusion coefficient of the material, $\rho $ is the density, c is the specific heat capacity, tm is the heating termination time and $\delta (\tau )$ is the Dirac function representing the external heat flow acting on the target surface (z = 0), which is equivalent to ${E_\sigma }$.
If the instantaneous energy pulse ${\delta _0}$ is uniform, it is known that the temperature by short pulse excitation on the surface is solved as:
R = (e1-e2)/(e1 + e2) is the thermal reflection coefficient, $e = \sqrt {\rho ck} $ is the thermal effusivity, e1 is the non-defective region above the defect and e2 is the defect.
If the Eq. (4) uniform energy pulse ${\delta _0}$ is replaced with a long pulse excitation, according to Eq. (3), the theoretical formula for the surface temperature response is:
2.2 Post-processing methods
The principle component thermography (PCT)
The temperature sequences collected by the thermal imaging camera can be seen as a three-dimensional matrix, containing thermal images collected at different sampling time, as shown in Fig. 2. The thermal images acquired in the experiment have a total of n frames, and each image is composed of x × y pixels. The principal component analysis (PCA) enables feature extraction, data compression, and noise reduction of temperature data. When using PCA for data processing, it is necessary to expand the three-dimensional data matrix into a two-dimensional data matrix. Then, the singular value decomposition method is used to reduce the order of the standardized matrix.
X is a two-dimensional matrix. Each column of matrix U represents a set of orthogonal statistical modalities called empirical orthogonal functions (EOFs). The matrix Γ is a diagonal matrix with singular values on the diagonal. The singular value of the matrix Γ is the eigenvalue of the corresponding eigenvector in V. The list of matrix V shows the eigenvectors or principal components of the dataset.
Pulse phase thermography (PPT)
A sequence of thermograms is considered. The time interval between the thermograms corresponds to the image update rate (frames per second) of the infrared camera. The extraction of various frequency components in this sequence is performed via the application of the discrete 1D Fourier transform on each pixel (x, y) of the thermogram sequence, which comprises N images. Let T(n) be the temperature at a particular location (x, y) of the nth thermogram in the image sequence. The discrete Fourier transform F(n) in the frequency domain is computed from T(n) according to the following well-known formula:
where n denotes the frequency number, i.e., fv = v$\Delta f$, v = 0,1,2 … ($\Delta f$ being the frequency increment), while R(v) and I(v) are the real and imaginary parts of F(v), respectively. The amplitude, A(v), and phase, $\varphi (v )$, are computed for each of the transformed terms through the following:The amplitude and phase images are formed by repeating this process for all pixels in the frame. If tw is the time window, i.e., the time interval over which the Fourier transform is performed, and m is the frame rate, then N = m tw.
Defect depth quantification (contrast derivative method)
In long-pulse thermography, for a given heat flux density W the series of impulse responses over the pulse duration ${t_p}$ can be obtained. The temperature contrast relative to the long pulse is:
For long pulse analysis, the dimensionless time ${\omega _d}$ for defect depth d can be represented as:
where tp and td are heating time duration and slope peak time, respectively. For experimental analysis, only the cooling period is considered. Hence tp = 0 and the ${\omega _d}$ is:To determine the proportionality factor ${\omega _d}$, the temperature response of the material surface with different y (d/L) depth ratios are obtained by simulation. The thermophysical characteristics of carbon fiber composites are shown in Table 1. Figure 3 shows the temperature comparison under the simulation results and the temperature contrast derivative vs. the y-value, and the scaling factor ${\omega _d}$ is determined by the constant y value, so the slope-peak time td:
Fig. 3. (a) Temperature contrast at different y values; (b) Temperature contrast first derivative at different y values.
Table 1. Thermophysical Properties of CFRP Materials
The ${\omega _d}$ value can be obtained from Fig. 4:
3. Experimental setup
As shown in Fig. 5, sample A, B, and C are stainless steel plates and two CFRPs, and their surfaces are sprayed with a thin layer of black matt paint. A is a 304 stainless steel material, the size is $110 \times 110 \times 5$mm3 and the defects are flat bottom hole defects. The distance from the surface to the bottom of the holes in sample A are 0.5 mm, 1 mm, 1.5 mm, and the defect diameter is 14 mm, 12 mm, 8 mm. B is CFRP. The size of it is $120 \times 120 \times 6$mm3 and the defects are artificial delamination. The preparation of the delamination defect is realized by embedding a 0.1 mm thick Poly tetra fluoroethylene (PTFE) film in the specimen by a special method. The distance from the inspected surface to the delamination defect of sample B is 0.5 mm, 1.5 mm, 2.5 mm, 3.5 mm, 4.5 mm, and the defect diameter is 11 mm, 9 mm, 7 mm, 5 mm, 3 mm. The sample C is CFRP, the size is $180 \times 180 \times 5$mm3 and the defects are artificial delamination. The distance from the surface to the delamination defect of sample C is 1 mm, 1.2 mm, 1.4 mm, 1.6 mm, 1.8 mm, 2 mm, 2.4 mm, 2.7 mm, 3 mm, and the defect diameter is 10 mm, 7 mm, 5 mm.
Fig. 5. A is 304 stainless steel with flat bottom holes, B and C are CFRP specimens with embedded simulated delamination defect.
An improved pulsed thermal imaging system with energy homogenization is shown in Fig. 6, which consists of two halogen lamps with power 1 KW, two lenses of size $300 \times 300$mm2 PMMA material, and an infrared camera. During the experiment, the lens is closely attached to the halogen lamp to reduce the heat loss. The simulated temperature surface temperature change is recorded by the infrared camera (telops FAST M100K, 3-4.9 µm), and the camera acquisition frequency is set to 40 Hz.
4. Result and discussion
4.1 Experimental results of the 304 stainless steel (sample A)
The temperature sequence diagram of stainless-steel sample A under two test conditions are shown in Fig. 7. It is obvious that the thermal image is more uniform at the moment of heating start in Fig. 7(b). Figure 8 and Table 3 show the thermal image with highest signal-to-noise ratio (SNR) under the two kinds of excitation means. It can be clearly seen that the thermal image noise under the HPT has been greatly weakened, so that the original inconspicuous defects become clearly visible, greatly improving the visibility of the defect. Comparing the SNR calculated by Eq. (14) by the two excitation means, we found that the SNR is increased by 15 times. The post-processing analysis of the thermal images under both detections (PCT and PPT) was performed and the results are shown in Fig. 9. It can be visualized that the image noise under HPT is much less and its defect contours are much clearer. The SNR of the post-processed images is compared in Table 3. The SNR of the post-processed images under the HPT-based is improved by at least 4 times. The detection of stainless steel samples based on HPT achieves good results.
Fig. 7. 304 stainless steel Partial temperature sequence diagram under two different tests: (a) PT; (b) HPT.
Fig. 8. Thermal image of defects of 304 stainless steel plate specimen under different tests: (a) traditional PT without lens at 21.5s; (b) HPT at 22s.
Fig. 9. Thermal image of 304 stainless steel plate material processed by PCT and PPT: (a) PCT post-processed image for sample based on traditional PT; (b) PCT post-processed image for sample based on HPT; (c) PPT post-processed image for sample based on traditional PT; (d) PPT post-processed image for sample based on HPT.
4.2 Experimental results of CFRP (sample C)
The experimental results of sample C are shown in Fig. 10. In Table 3, the SNR by HPT is larger than that by PT. Although the detection effect is similar in PT and HPT, comparing Fig. 10(a) and (b) it can be found that the detecting effect of defects of depth below 3 mm is different. Through further analysis of the original data, we find that the energy distribution based on HPT at the moment of heating start is more uniform as shown in Fig. 11. To further evaluate its uniformity, we quote the following Eq. (15) to evaluate the homogenization effect quantitatively.
Fig. 10. Thermal image of defects of CFRP (sample C) under different tests: (a) traditional PT without lens at 20 s; (b) HPT at 21 s.
Fig. 11. Three-dimensional map of the temperature distribution of the sample surface at the moment of heating onset: (a) traditional PT; (b) HPT.
The parameter SD is the standard deviation of the temperature distribution, which can reflect the degree of dispersion of the data set. Ti is the temperature value of a certain point, $\bar{T}$ is the average of all points in the thermal image. The smaller the SD, the more uniform the temperature distribution.
As shown in Table 2, it can be found that the sample’s surface energy by HPT at the heating start is much more uniform than that by PT. However, the average temperature of the specimen surface was reduced. But this excitation means (HPT) is closer to the uniform heating condition assumed by the one-dimensional heat conduction theory. HPT will be conducive to the quantitative analysis of defect depth, which based on one-dimensional heat conduction theory.
Table 2. Comparison of The Quantitative Evaluation of The Temperature Distribution
4.3 Post-processing analysis to the experimental results of sample B and C
To explore the influence of HPT on the detection effect, the detection results of CFRP materials were post-processed by PCT and PPT methods.
In Fig. 12, samples B and C are processed by PCT respectively. Overall, the noise under both detection methods is well attenuated. But the noise of Fig. 12(b) of sample C ($180 \times 180 \times 5\; m{m^3}$) by HPT is significantly lower than that of the traditional PT (Fig. 12(a)) and the delamination defect at a depth of 3 mm is clearer. Sample B size ($120 \times 120 \times 6\; m{m^3}$), is much smaller than sample C size. From Fig. 12(c), (d), the treatment of noise is not very different. But In Table 3, the SNR by HPT is larger than that by PT. For small specimen the position of the halogen lamp can be adjusted to improve the heating unevenness. But in terms of delamination defect detection, the detection effect of defects at depth of 2.5 mm by HPT is still better than that by traditional PT.
Table 3. Comparison of SNR of Different Post-processing Methods Based on PT\HPT Stainless Steel Materials and CFRP
Fig. 12. Thermal image of CFRP processed by PCT: (a) PCT post-processed image for sample C based on traditional PT; (b) PCT post-processed image for sample C based on HPT; (c) PCT post-processed image for sample B based on traditional PT; (d) PCT post-processed image for sample B based on HPT.
Figure 13 shows the post-processed results of the PPT method. The detection effect of sample C is shown in Fig. 13(a), (b). The processed result of the Fig. 13(b) is better than that shown in Fig. 13(a). For smaller size sample B, the effect is still better for HPT, as shown in Fig. 13(c), (d). In Table 3, the SNR by HPT is much higher than that by PT, especially for large size sample C.
Fig. 13. Thermal image of CFRP material processed by PPT: (a) PPT post-processed image for sample C based on traditional PT; (b) PPT post-processed image for sample C based on HPT; (c) PPT post-processed image for sample B based on traditional PT; (d) PPT post-processed image for sample B based on HPT.
From the above processing results, we can conclude that the HPT is helpful to the thermal image post-processing and further improve its image SNR.
4.4 Defect depth quantitative analysis
Many methods have been proposed for predicting defects depth by utilizing specific characteristics after heat pulses acting on the surface of the sample. We determine the defect depth by finding the peak time of the temperature contrast derivative by the contrasting derivative method established in the theory of the previous section. In this paper, all defect depth of sample A were analyzed, and the 10 mm delamination defects of sample C were analyzed at depths of 1, 2, 2.3, 2.6, and 3 mm.
The original temperature data were fitted in two stages (heating stage and cooling stage), and then the defect temperature contrast derivative curve was obtained to observe its peak information.
Figure 14 shows the defect locations of sample A, marking the defects as 1, 2, 3, 4, 5, 6, 7, 8, 9, dividing the defects into three regions, the left region L, the middle region M, and the right region R. Figure 15(a) is the peak contrast derivative curve of each defect of sample A under PT, its peak information is inconspicuous. In Table 4, the slope-peak time from defects at the L region to the defects at the R region gradually increases, but the defects’ depths are the same. It is necessary to consider the uneven heating. Because based on the one-dimensional heat conduction theory, as Eq. (13), the peak time of the temperature contrast derivative for the same depth should be consistent. However, the experimental results are inconsistent with the theory. Figure 15(b) is the temperature contrast derivative curve of each defect of sample A by HPT. In Fig. 15(b) we can clearly see the difference with Fig. 15(a). On the one hand the peak information is very prominent, on the other hand the peak time of the defects at the same depth is almost the same. These differences also can be seen directly in Table 4. The peak information by HPT is consistent with the theory. The comparison by the two excitation means strongly illustrates the reliability of HPT depth quantification, and it is also proved by the results shown in Fig. 16. In Fig. 16, due to the influence of lateral diffusion of heat waves, the intercept of the PT and HPT curves are non-zero, but the intercept of the curves under the PT gradually increase from the L region to the R region and the intercept of the curves obtained by HPT is almost the same. These results show that HPT effectively suppresses the influence of multiple heat wave reflections between the bottom of the defects and the sample surface due to uneven heating, and the effect of heat wave reflection between defects. Based on this, we next carry out in-depth quantitative analysis of CFRP delamination defects.
Fig. 16. The slope peak time of sample A changes with the square of the defects depth by PT (the defects are divided into three parts, L, M, and R, as shown in Fig. 16) and HPT (these three parts are labeled L1, M1, and R1 by HPT).
Table 4. The Slope Peak Time of Defects in Three Regions L, M, R of sample A under PT and HPT
Figure 17 shows the first derivative of temperature comparison of sample C 10 mm delamination defects at different depths under HPT and PT. In Fig. 17(a), it can be observed that the peak value of the first derivative of temperature contrast based on HPT is still relatively obvious. In Fig. 17(b), the peak time of appearance is proportional to the square of the defect depth, and the linear fits of the R2 values 0.84 and 0.90 for HPT and PT are obtained respectively. The slopes of these two fitting curves are 0.164 and 0.162. Predicting the depth of defects using Eq. (18), the results are shown in Table 5. The scale factor ${\omega _d}$ is selected according to the value of Fig. 4. Due to the complex experimental environment, the thermal characteristics of the CFRP itself and the error induced by the simplification of simulation model, the scale factor is hard to predict accurately. Thus, there is a certain error between the prediction results by PT and HPT and the actual depth. Except for the defects of y = 0.46 and y = 0.52, HPT is more accurate and stable than PT predictions. In the experiment by HPT, the peak information of the 2.6 mm depth defect was not displayed, and the error of the predicted result for 2.3 mm depth defect is large. However, the error of the 2.3 mm and 2.6 mm depth defects by the PT experiment is also large. It was thought that due to 0.1 mm thick PTFE film embedded in the delamination defect, which was not easy to detect. In addition the defect is far away from the surface and is greatly affected by the lateral diffusion of surrounding defects and heat waves, resulting in the concealment of defect information.
Fig. 17. (a) Temperature contrast derivative curve of sample C by PT and HPT; (b) The slope peak time of sample C changes with the square of the defects depth by PT and HPT.
Table 5. PT, HPT Comparison Between Experimental and Modeling Results for Defect Depths Predicted Using Contrasting Derivative Method
5. Conclusion
Based on a new pulse excitation detection system, 304 stainless steel plate sample with flat bottom hole defect and CFRP delamination defect samples were detected respectively. In the detection and post-processing results, because stainless steel has a higher thermal conductivity than CFRP, it can respond faster to the thermal radiation, uneven heating has a greater impact on it. The uneven heating of stainless-steel plate has been well improved through the new pulse excitation detection system (HPT), so a good experimental result has been achieved. Depth quantification directly shows that HPT has obvious advantages in depth quantification and has great application prospects in the detection of steel defects. On this basis, we performed thermal image post-processing and in-depth quantitative analysis on CFRP samples with delamination defects, which are more difficult to detect. Through the results of post-processing (PCT, PPT), we find that the PCT method is more suitable for post-processing analysis of CFRP IRT. From the experimental results, HPT is more suitable for the delamination defect detection of CFRP with larger size. From post-processing analysis results, HPT greatly improves the SNR of the image compared with the traditional PT method. HPT is conducive to the detection of small defects. The predicted depth of the delamination defects by HPT has a smaller error compared with that by PT by temperature contrast derivative method. It is verified that HPT energy homogenization can improve the accuracy of defect depth predicted by the one-dimensional heat transfer theory. By the experiment results, whether in stainless steel materials or low thermal conductivity composites, the HPT is promising for infrared nondestructive testing.
Funding
National Natural Science Foundation of China (11702151); Science and Technology Innovation 2025 Major Project of Ningbo City (2022Z209); 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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