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Abstract
Rolling contact fatigue (RCF) produced by wheel-rail interaction is now considered to be a critical factor that causes failure. Throughout this work, induced scanning thermography (IST) for detecting RCF defects at different depths is investigated. The original thermal sequences could not utilize the features at the heat dissipation stage; thus, a data reconstruction method, including principal component analysis (PCA) and Tucker factorization, was employed to extract the spatial and time patterns. In addition, detectability was evaluated across a range of speed studies. The Tucker-PCA combination algorithms obtained defects with improved quality, showing a clear boundary over the velocity range of 1-4km/h, which dramatically suppressed background noise. A unique gradient response characteristic in the cooling phase was summarized and utilized through experimental verification in order to recognize defect width.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A long-term wheel/rail rolling contact process causes rolling contact fatigue (RCF) cracks, which seriously affect the stability of railways [1]. In most cases, RCF failure can be considered as a sequence of three successive events: crack initiation; crack growth/propagation; and fracture [2]. Environmental factors such as rain, snow, and air humidity can accelerate oxide formation near the crack area and then fill the crack space (closed form) [3,4]. This further increases the difficulty of defect recognition. Therefore, detecting RCF cracks at early stages is critical. Over an extended period, nondestructive testing (NDT) methods have been used in various studies to detect defects in rails, including ultrasonics, radiography, and visual inspection [5–8]. Nevertheless, the methods mentioned above still have various limitations. Ultrasonic testing is not applicable to surface crack detection due to the blind area effect; radiographic testing represents a potential health hazard and is environmentally unfriendly due to the radiation exposure; and analyzing cracks by visual inspection can be influenced by the subjective judgment of the inspector. One promising direction to overcome these limitations is the integration of different NDT approaches with their advantages. Recently, eddy current thermography (ECT), which involves the characteristics of non-contact, high sensitivity, good robustness, and visualization, has been proposed as a competitive candidate for guiding further surface crack detection [9,10]. In this approach, perturbation of eddy current density near the crack can generate substantial local joule heat, resulting in a temperature distribution change.
Considering complex geometry is, in fact, detrimental to the detection of the defect. The RCF cracks can be simplified as angular ones since they have a similar structure. In the early days of angular crack detection using ECT, some researchers characterized the angle and depth information using thermal amplitudes and gradients [11,12]. In [13], a quantitative evaluation framework was reported to describe angular defects using POD curves. In [14], skewness- and kurtosis-based information was utilized for quantitative analysis of inclination angles. In addition, several studies involving ECT have demonstrated that this method could characterize RCF crack information. Peng et al. [15] used Helmholtz-coil to generate a local uniform inductive electric field for inspecting RCF defects. However, shallow faults presented as non-significant due to the insufficient strength of the induced eddy current. Furthermore, it is also possible to use area-based features that offer robustness in the boundary information of RCF cracks [16]. However, these studies have only focused on the static pattern of ECT, rendering the method impractical for an extensive detection range. To overcome this issue, researchers have developed induced scanning thermography (IST) [17]. He et al. [18] automatically detected a notch with different depths in steel at 3 mm/s. The line scanning method (LSM) obtained the defect information from a reconstructed thermal panorama image of a non-homogeneously heated moment. Tuschl et al. [19] detected RCF cracks in rail, reducing the adverse effects of inhomogeneous surface properties and producing good image quality at 100mm/s. Zhang et al. [20] successfully detected holes with a radius of 0.5 mm by scanning ECT and analyzed the equivalent heating model at 100mm/s. Xia et al. [21] discussed the influence of different speeds on defect visualization capability. The notch (25 mm in length, 1 mm in width, and 6mm in depth) can be visualized after the deblurring process reaches 600 mm/s. In summary, as scanning speed becomes faster, motion blurring artifacts will impact the experimental results more significantly.
In order to solve this problem, data processing has been applied to enhance defect characteristics over the past decade. These include the gradient method, principal component analysis (PCA) [22], and Tucker factorization [23]. In [24], the theory behind blind source separation (BSS) algorithms was detailed and compared with the classical algorithms in dynamic thermal imaging. However, as a dimension reduction tool for feature extraction, PCA is not the most efficient way to retain the multi-factor information of the sequence data. Meanwhile, Tucker factorization is an effective method for dynamic background subtraction, but the amplitude of the defect is weakened in a single frame. Therefore, in this case, Tensor-PCA combination algorithms provide the best feature enhancement method, with time patterns and high contrast. Although there are few applications for Tensor-PCA, it has demonstrated precise results in recovering the tensor subspace and detecting outliers [25].
In this paper, an IST method for rail closed crack detection is proposed. The line scanning method (LSM) is used to solve the problem where the coil blocks the field of view (FOV). Through the transient thermal response of each crack in the same location, the transformed and re-ordered thermal sequence shows a diffusive heating process similar to a static measurement. The regime temperature profile is then calculated. For designed rail closed cracks with different depths, the combined algorithm is carried out to strengthen the defect information. Comparative tests are then conducted at four velocities ranging from 1km/h to 4km/h in order to verify the feasibility of the proposed method. The results of the reconstructed image quality are evaluated using the PSNR and SSIM metrics. This paper is organized as follows: In section 2, we introduce the thermal response characteristics obtained by the IST method. In section 3 we discuss in detail the Tucker-PCA combination algorithms and explain how they were implemented in motion thermal sequences. The validation tests, results, and discussion are provided in section 4. Finally, the conclusions are outlined in section 5.
2. Thermal response characteristics obtained by ECT scanning
In this work, we use the IST detection platform to detect closed cracks on the rail surface (Fig. 1). The physical process of static and dynamic detection is almost identical, so there is no particular distinction here. When the tested material is ferromagnetic metal, the small skin depth allows magnetic flux flows on the surface. The skin depth can be depicted as:
In this case, f is the frequency of the excitation current $({Hz} ),\,\mu $ denotes the permeability $({{H / m}} )$, and $\sigma$ is the electrical conductivity $({{S / m}} )$. When the test block contains defects or is discontinuous, heating power generated by Joule heat can be expressed by the equation:
The sample of the field of view can be split into three different regions: region I (heat conduction area), region II (induction heating area), and region III (heat dissipation area). The temperature in region I rises due to the sample being partly located in the effective heating area. The temperature in region II rises dramatically because of the direct heating from the eddy current. The temperature in region III is due to its further distance from the coil in spite of it having been heated before.
Two types of ECT configurations (line-coil and encircling-coil) were modeled by the COMSOL Multiphysics platform to compare the heating efficiency. The generation of heat was simulated using AC/DC module while the temperature distribution was simulated using heat transfer module. The couplings between the above two modules were done using electromagnetic heat module. The schematic diagrams of the simulation model are shown in Fig. 2(a). Two coils are made of copper with a diameter of 7 mm, which is in high electric conductivity. The duration of the heating was 0.2s with a current of 200A/250kHz supplied to exterior boundaries of the coil. The surrounding medium is air, and the infinite domain is used on the edge of the rectangular air domain. The impedance boundary condition is used on the detection sample to improve the convergence of the numerical model. The dimension of the sample model is 150 mm${\times} $90 mm${\times} $10 mm. The coils were placed at the height of 3 mm above the sample. The initial ambient temperature is 19.85°C for two cases of the simulation. The detailed thermal and physical parameters of the materials used in this simulation are shown in Table 1. All material properties in the simulation are matched to the properties of the materials used in the experimental session. Triangular elements between the 0.7 mm and 10 mm sizes are used to mesh the model, as shown in Fig. 2(b). Simulations are gently performed using a backward differentiation formula (BDF) solver. All computations were run on a desktop computer with a 3.6 GHz Intel Core i7-4790 and 16 GB RAM. The calculated times were 11 and 14 min for the line-coil and the encircling-coil model, respectively.
Fig. 2. Simulation results: (a) Schematic illustration of the induction heating apparatus. (b) Meshed model. (c) The eddy current density distribution on Line A. (d) The temperature curve on Line A.
Table 1. Material parameters used in the numerical models
From Fig. 2(c)-(d), distinct response characteristics on the sample surface can be summarized along Line A in Fig. 2(a). First, the eddy current and temperature in the heated area demonstrated uniform heating in the encircling-coil case, while it was uneven for line-coil. Second, the temperature within the heating areas in the encircling-coil case was slightly higher than that for line-coil (about a 1.0°C temperature difference), which means the heating efficiency increased by 32%. Moreover, the structure of the encircling-coil effectively improved FOV, which was blocked by the line-coil. The above analyses suggest that encircling-coil as a potential configuration to substitute for line-coil is feasible in scanning thermography.
3. Post-processing algorithms for thermal images in the IST method
The defect becomes blurred because of the combination of transverse thermal diffusion and speed effect. We adopted a feature-enhanced combination scheme in order to improve the defect characterization more thoroughly. As shown in Fig. 3, data acquisition was performed in the first block. The data were acquired in a specific scan area indicated by an exciting coil along the scanning direction, corresponding to the imaging defect depth range of 0.35-5 mm. Each frame of the thermal image sequence at the 1km/h velocity, 640 × 240 pixels in size, was processed through the following image processing steps (second block) using Matlab (Mathworks, Natick MA). (1) The primitive sequence diagram was stitched in the range of detection of the coils in order to reconstruct the thermal sequence without occlusion. Since the relative position of the cracks in the camera view field during scanning constantly changes, the thermal image sequence needs to be spatially aligned to match these locations and obtain a transient thermal response curve in static mode. (2) To align the sequence scales with different test speeds, the updated splice sequence graph was then interpolated using a spline function. (3) Using the Tucker model, most of the defect information was separated from the third-order tensor as a sparse matrix. Contrast enhancement was applied to the thermal sequence of cracks. (4) A dimension reduction via principal component analysis (PCA) was carried out. The first four principal components were retained, and defect information was superimposed onto the lower-order principal element. (5) A gradient algorithm was employed to reduce the interference caused by background changing; this mean that the defect region where amplitude changes intensely could be observed. Finally, temporal-spatial features analysis was performed on selected regions of interest (ROI) – a defect area (internal ROI) and an area surrounding the defect (external ROI).
3.1 Denoising with tensor decomposition method
A third-order tensor $X \in {{\boldsymbol R}^{{I_1} \times {I_2} \times {I_3}}}$ is used to characterize infrared sequences captured by an IR camera. Each mode is decomposed into a core tensor multiplied by a matrix. The discretized three-way tensor $X \in {{\boldsymbol R}^{{I_1} \times {I_2} \times {I_3}}}$ can be calculated by Tucker decomposition [26] as:
3.2 Principal component analysis (PCA) methods of thermal data
The PCA technique is a competent feature extraction tool that identifies correlations in thermal data sets. By projecting the original data onto a set of orthogonal components, it reduces the dimensionality of collected thermal information. The primitive sequence diagram, A, consists of P image frames with $M \times N$ pixels per frame, which is defined as follows:
4. Validation tests and discussion of the results
4.1 Specimens and the IST system
The materials used in the experiment were U75V rail; representative compositions are shown in Table 2. In this case, 8 artificial cracks with various depths were manufactured on the rail specimen using Wire-cut Electrical Discharge Machining (WEDM) technology. After processing, the width of the cracks was kept constant at 0.2mm, as was the crack angle at 30°; the crack depth ranged from 0.35 to 5.00mm with a 100mm lateral separation among cracks, as seen in Fig. 5(a-h). The crack depth of each defect is shown in Table 3. For further processing, the rail was rolled by a train in a natural environment intended to bring the machining crack-state realistically closer to the RCF crack. After 10 months, the surface of the defect presented with various degrees of wear, and rust was generated, as depicted in Fig. 5(i).
Fig. 5. Cracks on rail surface. (a-h) from Def 1 to Def 8. (i) Def 8 (depth of 5 mm) after vehicle rolling.
Table 2. Chemical composition (%) of U75V rail
Table 3. Depths of the cracks
To investigate the thermal characteristics of defects on the rail surface, we performed a motion experiment with test speeds of 1km/h, 2km/h, 3km/h, and 4km/h, respectively. The experimental setup is shown in Fig. 6. In this experiment, an encircling-coil excitation configuration was motivated by an induction heater. The test process maintained the rail surfaces at a 6 mm distance from the encircling-coil. During the movements, the rail surface was heated, and an IR camera recorded the thermal radiation; the field of view was restricted to the coil center and its periphery site. Meanwhile, the frame rate parameter was set to 100Hz, exactly 10 ms per frame in this experiment.
4.2 Experimental results and discussion
The accuracy and effectiveness of combining algorithms were validated, excluding testing speed. Based on the thermal response characteristic, the data obtained under the excitation of the alternating electric field, including the region of interest and the noise-suppressed images, are shown in Table 4(running speed at 1 km/h). As stated, all of the crack clips were fragmented into a single ROI image. The result contains an interpolation image (II), Tucker decomposition image (TI), Tucker-PCA image (TPCAI), and gradient-based Tucker-PCA image (GTPCAI). The results indicate that the noise suppression method is very effective at detecting rolling contact fatigue cracks in rail; all defects were detected at 1km/h scan speed, although Def 1 was indistinguishable from the background with low contrast. This is because of the induced eddy current perturbation effects, with the EC flow along the most downward depletion path. When the depth is shallow, the induced eddy current is forced to flow under the crack rather than around the edge of the defect, resulting in little change in temperature at the rail surface. The first two rows in Table 4 list the single image processing results, while the final two rows present the sequence graphs processing results; hence, the reconstructed defect has a lower intensity in the latter.
Table 4. The comparison between reconstructed images using different algorithms
Quantitative evaluation was performed using two metrics: the peak signal-to-noise ratio (PSNR) [28] and the structural similarity index (SSIM) [29]. Table 5 shows the PSNR and SSIM values of each defect. The GI method outperforms the PCAI and TDI methods at the same scanning speed. High PSNR and SSIM indicate that the recovered image has higher image fidelity. These results demonstrate that it is possible to use the algorithm presented in this work as a crack metric identifier. Notably, the PSNR index for TDI was better than that of PCAI in the cases of Def1, Def4, and Def8. The SSIM values for Def4 and Def7 show the same regularity. This is somewhat unusual, as subjective evaluation of PCAI images presented better results by overlaying defect information for the heat mitigation stage. One possible reason is that PCAI compresses the multi-frame sequences, which increases the unevenness of the background part and leads to a decrease in the index.
Table 5. Performance comparison of each defect in Table 4
Figure 7 shows how the PSNR and SSIM vary for different depths of defects. In general, both the PSNR and SSIM values increase with deeper crack depths. In the case of 3mm crack depth or above, the impact of different crack depths on the recovery performance is relatively small.
Variations in the temperature during a typical heat dissipation process with the temporal sequence for various defect depths are plotted in Fig. 8. As shown, the temperature profile decreased gradually with time. In the first 50 ms, the temperature of the defect sites decreased rapidly; after that, the temperature decreased slowly. Increasing defect depth increases temperature when the other parameters are constant. This behavior corresponds to heat transfer; with external heating, the temperature at the lower end of the shallow defect is more manageable when conducted to the material surface, resulting in higher cumulative heat.
The corresponding fitting results are plotted in Fig. 9(a)–8(h). The solid line is the fitting result, and the R-square represents the fitness of the correlation coefficient. The coefficients of the goodness of fit were primarily around or >0.75. As expected, the R-square distribution reflected the tendency toward defect depth. A shallower defect indicates a stronger R-square value in the trend than a deeper defect. A possible explanation for this might be that the internal structure of the deeper defects is more complex than that of the shallower defects, producing more significant uncertainty in surface temperature distribution.
Fig. 9. Surface temperature profiles with various defects in time. (a)-(h) correspond to Def 1 – Def 8, respectively.
4.3 Experimental contrast analysis under different speed
In order to verify that the above combined algorithm performed very robustly, experiments at different speeds with all other parameters fixed were carried out systematically. Because the current testing device constituted a constraint, the speed range varied from 1 to 4 km/h with an increasing velocity interval of 1km/h. The thermal-based characteristics of all pixels on Line B (Fig. 3) in the reconstructed image were extracted; the experimental results are detailed in Fig. 10. It can be seen that the temperature distribution for different speeds has similar rules, including the profile of original data, Tensor-PCA, and gradient-based characteristics. Increasing speed intensifies the uncertainty regarding transversal heat diffusion, and the boundaries of the defect region become increasingly blurred until they are indistinguishable from the baseline (defect-free region). This is particularly evident in shallow defect areas. After image processing, the missed detection problem caused by the speed effect is appropriately reduced. Moreover, Tensor-PCA, coupled with gradient, has high sensitivity and accuracy in terms of crack width. This will be useful for guiding future closed crack detection. Table 6 shows the detection performance of various processing methods. “√ “ indicates the excellent performance in crack detection, “— “ indicates that the defect is reaching a detectable level, and “× “ suggests that the defect is almost undetectable. As a result, shallow defects had a lower detection rate, while deep flaws had a higher detection rate.
Fig. 10. Temperature-based feature profiles in different speeds. (a) 1 km/h; (b) 2 km/h; (c) 3 km/h; (d) 4 km/h.
Table 6. Qualitative comparison of various signal processing methods with different velocitya
5. Conclusions
Focusing on the NDT of closed defects in rail, the inductive scanning thermography (IST) method was used in this study in combination with gradient-based Tensor-PCA post-processing algorithms. The following main conclusions were drawn:
- (1) The sensing structural alterations were accompanied by temperature distribution change. Based on the structure of the line-coil, an encircling-coil is designed for defecting closed cracks. This allows homogeneous heating of the sample’s surface, and the decline in thermal gradients changes. The simulation result shows that higher heating efficiency (32%) was observed for encircling-coil compared to line-coil.
- (2) Based on the different depths of the defects, the relationship between temperature and time-equivalent characteristics during heat dissipation for dynamic detecting could be described by a 3-order polynomial fitting function in order to achieve the best global fit. A strong correlation is seen with shallow defects (${\textrm{r}^2} > 0.90$ at Def 1, Def 3, and Def 4).
- (3) In contrast to a transient thermal response that only uses line scanning to analyze a single frame, the presented combined algorithm utilizes the advanced technologies of tensor decomposition, PCA, and gradient-extracted defect features from reconstructed multiple sequential images during the heat dissipation stage. Moreover, the scanning speed does not affect the accuracy of crack width quantification using gradient information.
Funding
National Natural Science Foundation of China (61771409).
Acknowledgments
The authors are grateful to all people involved in this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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