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Quantitative Pulsed Phase Thermography Applied to Steel Plates C. Ibarra-Castanedo1, N. P. Avdelidis2 and X. Maldague1* 1
Computer Vision and Systems Laboratory, Dept. of Electrical and Computer Engineering Université Laval, Quebec City, Canada, G1K 7P4. 2 Technical Chamber of Greece, NDT Representative of HSNT Board, Athens, Greece. ABSTRACT
Pulsed Phase Thermography (PPT) [1] has been proven effective on depth retrieval of flat-bottomed holes in different materials such as plastics and aluminum [2]. In PPT, amplitude and phase delay signatures are available following data acquisition (carried out in a similar way as in classical Pulsed Thermography [3]), by applying a transformation algorithm such as the Fourier Transform (FT) on thermal profiles. The authors have recently presented an extended review on PPT theory [4], including a new inversion technique for depth retrieval by correlating the depth with the blind frequency fb (frequency at which a defect produce enough phase contrast to be detected). An automatic defect depth retrieval algorithm had also been proposed [5], evidencing PPT capabilities as a practical inversion technique. In addition, the use of normalized parameters to account for defect size variation [6] as well as depth retrieval from complex shape composites (GFRP and CFRP) [7] are currently under investigation. In this paper, steel plates containing flat-bottomed holes at different depths (from 1 to 4.5 mm) are tested by quantitative PPT. Least squares regression results show excellent agreement between depth and the inverse square root blind frequency, which can be used for depth inversion. Experimental results on steel plates with simulated corrosion are presented as well. It is worth noting that results are improved by performing PPT on reconstructed (synthetic) rather than on raw thermal data. Keywords: Pulsed Phase Thermography, Phase Contrast, Blind Frequency, Steel, Corrosion.
INTRODUCTION In recent years, several works have been dedicated to the investigation of PPT as a quantitative tool in Nondestructive Testing and Evaluation (NDT&E) of materials [2, 4-7]. The theoretical aspects of PPT were established and supported with experimental results. As was established in [4], experimental uncertainty plays a critical role in quantitative PPT. Errors related to data acquisition should be minimized. Given the time-frequency duality of the Fourier Transform, sampling and truncation parameters should be handled carefully. In this sense, an interactive methodology may be used [8]. In addition, IR data is weak noisy. It has been demonstrated that significant de-noising can be achieved if reconstructed (rather than raw) thermal data is used as input on PPT [9]. In this paper, we explore the capabilities of PPT to quantitatively assess corrosion on steel. Steel is usually the material of choice for applications requiring strength, ease of fabrication, durability and cost (steel is the most recycled material in the world) Applications range from traditional uses (automobiles, buildings, transportation and infrastructure, bridges and road construction) to new ones (roofing, cladding and framing of houses, in distribution towers and in wind-turbine towers), guarantees steel survival as one of the most used material in the world. First, a plate with simulated corrosion is tested. Qualitative results are discussed. In addition, a quantitative analysis is carried out on two academic samples with square flat-bottom holes at different depths. Reconstructed data is used whenever is needed to smooth the temperature profiles prior to the application of the PPT. The coefficients of the polynomial resulting from this reconstruction can be straightforwardly used on the determination of first and second time derivatives, which has proven to give very useful in the past [10]. We begin our discussion with a short recall of the fundamentals of PPT, after what, some experimental results are presented.
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1. THEORY 1.1. Data acquisition and processing by PPT The procedure to perform a PPT experience is depicted on Figure 1. A thermal pulse (e.g. photographic flashes), stimulates the sample . A thermal mapping of the surface or thermogram is then recorded through time using an infrared camera . An N-element 3D matrix (with x and y coordinates being the horizontal and vertical pixel positions respectively, and the z-coordinate corresponding to the time evolution) can now be reconstructed and processed with the Fourier Transform . Amplitude and phase 3D matrixes are available as described in [4] and illustrated in Figure 1. Phase possesses interesting properties that are very useful in NDT&E: phase is less affected by reflections from the environment, to surface emissivity variations, to non-uniform heating and to surface geometry [13].
Figure 1. Data acquisition and processing by PPT. Moreover, depth probing using phase data is around 2µ, where µ is the thermal diffusion length equation given by [4]: µ=(α/πf)1/2, i.e. twice the maximum depth using amplitude data. 1.2. Depth Inversion using phase information Given the phase characteristics described above, contrast changes at the defects can be more clearly observed using phasegrams compared with conventional thermograms [11]. The absolute phase contrast ∆φ, is defined as: ∆φ= φd- φSa, with φd being the phase of a defective area, and φSa the phase of a non-defective sound area, Sa. There is a limiting frequency at which the defect presents enough phase contrast to be detected on the frequency spectra, which has been conveniently referred as the blind frequency fb [12]. It is possible to estimate fb using the phase contrast definition presented above ∆φ. After performing the PPT on thermal data, and knowing the material thermal characteristics, the inverse problem reduces to the estimation of fb and its corresponding φd. Details can be found in references [4] and [8].
For instance, it has been observed that depth z, and fb, are related through a correlation of the form:
z d = C1φd
αd + C2 = C1 (φd µ d ) + C2 π fb
(1)
where the regression constant C1 is a function of the material thermal properties, and the regression constant C2 gives an indication of the fitting error; φd is the phase at fb, µd=(αd /πfb)1/2 is the diffusion length at fb, and αd is the thermal diffusivity of the defect (since defect is visible at fb). Eq. (1) is valid only when defects are of the same size. This relationship collapses when inspecting defects at the same depth but considerably different sizes. The use normalized depth zn, and diffusion length µn, has been proposed to solve this problem using a procedure by which, size and depth of a defect can be extracted at once by locating fb [6]. 1.3. Thermographic Signal Reconstruction Thermographic Signal Reconstruction (TSR) [10] is an interesting technique that allows increasing spatial and temporal resolution of a sequence, reducing the amount of data to be manipulated at the same time. TSR is based on the assumption that, non-defective pixels temperature profiles should follow the decay curve given by the one-dimensional solution of the Fourier Equation at the surface for a semi-infinite body stimulated by a Dirac delta function, which may be written in the natural logarithm form as:
Q 1 ln(∆T ) = ln − ln(πt ) e 2
(2)
A temperature profile that follows a behavior as predicted be Eq. (2) will correspond to a non-defective area, i.e. it should follow a straight-line decay on a logarithmic scale corresponding to -½ slope. The offset is then given by input energy Q, and the effusivity of the specimen e. From this reasoning, Shepard [10] proposes to use a low order (Nth) polynomial function to fit the experimental data:
ln (∆T ) = a 0 + a1 ln (t ) + a 2 ln 2 (t ) + ... + a N ln N (t )
(3)
There are some advantages of using synthetic data with respect to raw thermal data. First, signal de-noising is accomplished especially high frequency noise. Also, data storage reduction, for instance a typical thermogram sequence can have 500 frames or more on a 320x256 pixels configuration, i.e. a 320x256x500 matrix. Using a 4th degree polynomial, data will be reduced by a factor of 100 since only the coefficients of the polynomial function are needed to reconstruct the thermal profiles for each pixel, i.e. a 320x256x5 matrix. Moreover, time derivatives are easily computed knowing the polynomial coefficients and temperature for a time between actual acquisitions can be calculated. Furthermore, the de-noising capabilities of TSR can be exploited to improve phase (and amplitude) results using synthetic data as input for PPT (instead of raw thermal data) [9].
2. EXPERIMENTAL RESULTS 2.1. Experimental Setup The experimental configuration is depicted in Figure 1. An FPA infrared camera (Santa Barbara Focalplane SBF125, 3 to 5 µm, with a 320x256 pixel array), working at a sampling frequency of 45.1 Hz was used. Two high power photographic flashes (Balcar FX 60), giving 6.4 kJ for 15 ms each, were used as heating sources. Reflection mode was used in all cases. Thermographic data was analyzed with a PC (Pentium 4, 2 GB RAM), and thermal data was processed using MatLab®. 2.2. Qualitative inspection: simulated corrosion A first test was performed on a steel plate with simulated corrosion. To simulate corrosion of different degrees of severity, three slots of equal depth where first machined on the rear part of the plat at approximately 1 mm depth, i.e. 5.5
mm depth from the front side. Then, an acid solution was applied and left for several hours. The process was repeated several times in random areas of the three slots resulting on more realistic irregularly corroded areas. For instance, the right slot present carrying corrosion from 5.5 mm (at the bottom) to 0 mm (at the top), where there is a hole at the top of this slot as can be clearly seen in Figure 2a, b and c. These images correspond all three to t=1.42 s (the best overall contrast of the thermal sequence), but different processing techniques were used as described below. Figure 2a correspond to a raw thermogram, which is affected by Fixed Pattern Noise (FPN), contributing to hide defect information. Corrosion is better seen in Figure 2b, which is obtained by subtracting a pre-flash (cold) image from the thermogram in Figure 2a. This simple arithmetic operation is good enough to reveal almost entirely the artificially corroded areas on the three slots. However, information about the subsurface condition of the plate is still missing. Figure 2c corresponds to the second coefficient image (the one showing the higher contrast of all 6 coefficient images) as obtained by TSR fitting raw thermal data (after cold image subtraction) with a 5th degree polynomial. Figure 2d is the 1st time derivative image at t=1.42 s (calculated from the polynomial coefficients). Besides an increase in thermal contrast and resolution, more internal information becomes available. Although the hole may still be distinguished at this particular time, this image reveals deeper information more clearly.
(a)
(b)
(c)
(d) (e) (f) Figure 2. Simulated corrosion on a steel plate. Thermograms at t=1.42 s obtained (a) from the raw temperature sequence, (b) after subtracting the cold image from the raw sequence, (c) after reconstruction using a 5th degree polynomial, (d) first time derivative calculated from the synthetic sequence. Phasegrams at f=0.55Hz after performing PPT on (e) the raw temperature sequence; and (f) the synthetic thermal sequence. Although the 1st time derivative image show considerable enhanced contrast with respect to the raw thermograms, additional subsurface information can be recovered with the phase. Phasegram in Figure 2e corresponds to f=0.55Hz. At this frequency, it was possible to see some (deeper) internal features due to material imperfections (small clusters at different locations) that were not detected in Figure 2d. These internal features are also seen in Figure 2f with enhanced contrast. Figure 2f is the phasegram at f=0.55Hz obtained after applying the PPT on reconstructed data.
2.3. Quantitative analysis: machined flat-bottom holes The two steel plates, specimens ACIER001 and ACIER002 shown in Figure 3, were tested. Same size (30x30 mm2) but different depths (from 1 to 4.5 mm) flat-bottom holes were machined on the rear size of each plate. Defect’s dimensions and locations are shown on top of Figure 3.
(a) (b) Figure 3. Dimensions (top) and phasegrams (bottom) for specimens (a) ACIER001, and (b) ACIER002. Each plate has with four 30x30 mm2 flat-bottomed holes at different depths. 2.4. Acquisition and truncation parameters Acquisition and truncation parameters used as input on PPT computations have to be addressed individually as a function of the defect’s depth [8]. In all cases, the maximum possible truncation size, i.e. T= 22.2s, was used to increase frequency resolution. On the contrary, time resolution ∆t, was optimized for each specific depth following the methodology proposed in reference [8]. Conditions for specimen ACIER001 were: ∆t=88.7 ms and T=22.2s, giving a total number of images N=250. Figure 4a shows the phase and phase contrast profiles for the four defective zones highlighted on the phasegram in Figure 3a (the area enclosed by the ‘Xs’). As can be seen, data is covered by noise and, even though a relationship between depth and their corresponding fb values may be distinguished, it is difficult to perform accurate fb estimations in these conditions. Thermographic Signal Reconstruction (TSR) as proposed in [10] was applied to raw thermal data using a 7th degree polynomial. Such a relatively high degree polynomial proves effective for signal de-noising without introducing ringing
effects on phase results as seen in Figure 4b. Another possibility is to fit phase or phase contrast profiles directly following a similar procedure as with thermal data. However, ringing effects are far more important in this case. Phase contrast profiles can be used now to retrieve the fb.
(a)
(b) Figure 4. Phase and phase contrast profiles for specimen ACIER001 obtained by performing PPT on (a) raw and (b) reconstructed thermal profiles.
For specimen ACIER002: ∆t=44.3 ms and T=22.2s (with a total number of images N=500) for the three deeper defects (1.5, 2.0 and 2.5 mm depth), see Figure 5a. Higher time resolution was needed for the shallowest defect (1.0 mm depth) since in this case since the corresponding fb was too close to the maximum available frequency (fc=11.28 Hz, fb∼10 Hz). As stipulated by the Sampling Theorem [13], the Nyquist limit fc, can be increased the time resolution. Hence, ∆t=22.2 ms and T=22.2s (with a total number of images N=1000, i.e. near the maximum buffer storage capacity of the IR system) were used for the shallowest defect, see Figure 5b.
As seen from Figure 5, no smoothing by TSR was required for specimen ACIER002 since phase and phase contrast profiles obtained from raw thermal data presented low noise levels (when compared with corresponding data for specimen ACIER001). This is due to the fact that defects in ACIER002 were closer to the surface than defects in ACIER001. Hence, more information about the depth is available early in the sequence, which is traduced as less noisy profiles in the frequency domain.
(a)
(b) Figure 5. Phase and phase contrast profiles for specimen ACIER002 obtained by performing PPT on raw thermal data for (a) the three deeper defects (1.5, 2.0 and 2.5 mm depths) and (b)the shalowest defect (1.0 mm depth). 2.5. Depth inversion Phase contrast profiles presented in Figure 4b and in Figure 5, where used to estimate the fb values for each defect. Correlation results by linear least squares regression of depth z on parameter µd=(αd /πfb)1/2, Eq. (1), are shown in Figure 6. A high correlation coefficient (R=0.98624)is obtained. This result confirms the depth dependency on fb1/2, a relationship that was previously observed with plastic and aluminium specimens [2], [4], [5]. However, Eq. (1) works well for a given defect size and will be ineffective in real world applications where there is no way to know the actual size of internal flaws. An alternative relationship can be obtained through the use of normalized parameters to account for size variations, see references [6] (in Thermosense XXVII Proceedings) and [8].
Figure 6. Linear correlation using least squares regression of z on fb. Data from both plates: ACIER001 and ACIER002, are included.
CONCLUSIONS Detection of simulated corrosion and other internal flaws on steel was possible by means of Pulsed Phase Thermography (PPT). Results where further enhanced using Thermographic Signal Reconstruction (TSR) as input of the PPT algorithm. TSR possesses excellent de-noising capabilities that can be conveniently used in combination with PPT, allowing defect detection and characterization of deep defects, where noise content is significant. With respect to other de-noising techniques such as Gaussian filters, TSR applied on raw thermal data prior to PPT show reduced impact on the real shape of phase profiles, and low ringing effects when compare to TSR applied on phase profiles. Phase contrast profiles can be used in the determination of the blind frequency fb, i.e. the frequency at which a defect at a particular depth z, becomes visible. Experimental results on steel plates with same size defects at different depths confirm that z is strongly correlated to fb. This relationship can be determined experimentally with an expression of the form of Eq. (1), which works well with same size defects. Other forms can be derived to take into account defect size variations, see for instance reference [6] in this Proceedings volume.
ACKNOWLEDGES Authors wish to thank the support from the Natural Sciences and Engineering Research Council of Canada.
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