applied sciences Article
Depth Retrieval Procedures in Pulsed Thermography: Remarks in Time and Frequency Domain Analyses Panagiotis Theodorakeas *
ID
and Maria Koui
NDT Laboratory, Department of Materials Science & Engineering, School of Chemical Engineering, National Technical University of Athens, Iroon Polytechniou No. 9, Zografou Campus, 15780 Athens, Greece;
[email protected] * Correspondence:
[email protected]; Tel.: +30-210-7723233 Received: 15 January 2018; Accepted: 7 March 2018; Published: 9 March 2018
Featured Application: The present study intends to show the potentiality of pulsed thermographic imaging to quantitatively characterise hidden defects in Carbon Fibre Reinforced Polymers. By comparing the performance of different depth retrieval procedures, it was possible to evaluate the produced depth estimation accuracy and to define the impact of different experimental and analysis parameters in quantitative analysis. Abstract: In the present study, a Carbon Fibre Reinforced Polymer (CFRP) sample of trapezoid shape, consisting of internal artificial delaminations of various sizes and depth locations, is investigated by means of optical pulsed thermography for the retrieval of quantitative depth information. The main objectives of this work are to evaluate the produced depth estimation accuracy from two contrast-based depth inversion procedures as well as to correlate the acquired results with characteristics such as the location and size of the detected features and with analysis parameters such as the selection of the sound area. Quantitative analysis is performed in both the temporal and frequency domains, utilising, respectively, the informative parameters of thermal contrast peak slope time and blind frequency. The two depth retrieval procedures are applied for the depth estimation of features ranging in size from 3 mm to 15 mm and in depth from 0.2 mm to 1 mm. The results of the present study showed that the two different analyses provided efficient depth estimations, with frequency domain analysis presenting a greater accuracy. Nevertheless, predicting errors were observed in both cases and the factors responsible for these errors are defined and discussed. Keywords: pulsed thermography; quantitative analysis; depth; peak slope time; blind frequency; CFRP; delaminations
1. Introduction Pulsed Thermography (PT) is a widely used technique for the Non-Destructive Testing and Evaluation (NDT&E) of advanced materials and structures [1–5]. Compared with other NDT&E technologies, this thermographic configuration presents remarkable benefits such as its rapid and simple implementation, its suitability for large-scale inspections and complex surface monitoring, as well as its contactless application requiring no physical contact to the material being inspected. The implementation of a pulsed thermographic inspection is based on the monitoring of the heat transfer occurred during the cooling of the test item after the application, usually to its surface, of an instantaneous and high energy pulse heating procedure [6]. The application of the thermal stimulus is followed by the recording of the resultant surface temperature response through the aid of an IR camera, aiming to detect changes in the surface temperature distribution. These changes are normally owned to the presence of internal defects and/or discontinuities which are altering the heat diffusion rate into the inspected component. Appl. Sci. 2018, 8, 409; doi:10.3390/app8030409
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Nowadays, PT is recognised as a testing procedure that can provide inspectors not only with the ability to detect defects, but also the means to quantify these defects for continuous monitoring and assessment [7]. This is a result of the advances in thermographic imaging technology that have orientated the analysis to the independent spatial and/or temporal treatment of each pixel of the thermal images’ sequence, along with the development and use of advanced signal processing techniques [8,9]. Signal processing techniques have been developed for the interpretation of infrared thermographic data, targeting the defect detectability enhancement and noise reduction on the final imaging output, while the importance of these processing tools is also devoted to the preparation of data for the continuation to the phase of quantitative characterisation [10,11]. Regardless of the domain where the thermal data are processed (the most common are temporal domain processing and frequency domain processing), different techniques have been proposed to quantitatively characterise detected defects. These techniques are based either on analytical methods [12] or inverse methods that are implementing numerical calculations and experimental measurements [13]. In the former case, experimental data can somehow produce results in a straightforward manner, as these are used to solve analytical formulas. On the other hand, by involving inverse techniques, quantitative characterisation requires the establishment of a numerical model taking into account many parameters. Usually, only one parameter is of interest (e.g., depth) which can be estimated by correlating the numerical and the experimental results. Quantitative characterisation by means of pulsed, and more generally speaking of active thermal imaging, includes mainly depth information retrieval [14–18] and the estimation of defect’s lateral dimension [19–21], while several studies have also investigated the determination of the thermal properties either of the material being inspected [22,23] or of the hidden features [24]. Based on the above mentioned, the present study focused to the application of optical Pulsed Thermography for the quantitative characterisation of induced artificial defects in a CFRP component, aiming to highlight the strengths and limitations of this technique in similar quantitative inspections. The quantitative depth estimation procedures applied in this study evaluated the performance of two contrast-based methods, one in the time and one in the frequency domain, respectively, and in particular through the study of the temperature–contrast slope temporal variations and the monitoring of the phase-contrast variations as a frequency function. These analytical methods for depth prediction require the need for a sound area determination and thus a comparison was performed regarding the influence degree of the sound area selection in depth prediction accuracy working with either raw temperature or phase data. The depth results produced from the two quantification procedures were compared in terms of error production, and the divergences observed between the estimated and the pre- known nominal depths were evaluated taking into consideration the specifications of the investigated sample along with the experimental parameters selected to conduct this study. In the following, a brief description of the quantification techniques used in this study is presented. 1.1. Quantitative Depth Estimation in the Time Domain For quantitative depth prediction in the time domain, the most widely used algorithms utilise temporal characteristics of the thermal response received from the tested surface. In particular, these methods are based on the correlation of the defect’s depth with a time point at which the hidden feature appears as a temperature difference on the surface of the inspected sample. The idea behind the determination of these time points is based on the fact that, when studying the heat diffusion into the material bulk after the application of a thermal pulse, the time taken for the thermal wave to be reflected back to the surface is inversely proportional to the thermal diffusivity of the material and directly proportional to the square of its depth [6]. The first proposed and the most commonly used method utilises the time point when the maximum thermal contrast between a defective and a preselected reference point occurs, known as Peak Contrast Time [25–27]. Even though this informative parameter can produce quantitative depth information, one of its major limitations is the fact that the peak contrast appears relatively late, when the 3D heat diffusion around the defect has a great influence on
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the acquired result. Consequently, different methods have also been proposed investigating the use of earlier temporal points, targeting to the produced accuracy enhancement. One of the earliest time points on a temperature–time evolution curve, which is used for defect depth estimations, is the moment when the behaviour of the studied temperature signal above the defect diverges from the behaviour of the reference signal [28]. Usually, as raw thermal data contain noise, the establishment of a threshold level is required to identify this point on the temperature–time curve [29]. Quantitative depth estimations through the aid of this informative parameter have the advantage of early depth prediction, thus possible effects produced from lateral heat diffusion in the defective area are negligible. However, the determination of this value requires a sampling rate high enough to accurately capture the initial time when the temperature in the defective zone diverse from the reference temperature, impeding the providing of accurate results in the case of shallow defects characterisation [30]. A later time interval but early enough to suppress the negative effects of lateral heat diffusion is the moment when the thermal contrast curve presents its peak slope [31,32]. This point can be easily found as it corresponds to the peak of the 1st derivative of the thermal contrast and is commonly referred as Peak Slope Time method. The exact relationship between depth and peak slope time can be determined by solving, for this specific time value, Equation (1) [33]: t peak =
3.64z2 π2 α
(1)
where tpeak is the time at which the peak in the slope contrast occurs, z is the defect depth in a sample of thickness L and α the thermal diffusivity of the tested material. This parameter is essential for defect depth estimation as experimental and numerical studies have shown that results are unaffected from the size of the defect, while the proportionality coefficient equal to 3.64 was found to be valid regardless the type of the material when z/L ≤ 0.5 [33]. 1.2. Quantitative Depth Estimation in the Frequency Domain Frequency domain analysis using quantitative Pulsed Phase Thermography (PPT) and phase data are of prime interest in thermographic imaging, as, in addition to the enhanced detectability that this technique provides, a depth prediction approach similar to the early detection in time domain analysis has been developed and widely used [34,35]. This approach consists of identifying the depth of the defect from the frequency for which the phase contrast between a defective and a sound area crosses the zero-contrast line. This technique relies on the thermal diffusion length, i.e., µ = (α/πf)1/2 as the depth of the defect can be estimated from a relationship of the form [36]: z = C ·µ = C
r
α π fb
(2)
where C is a correlation constant and fb (Hz) is the blind frequency, defined as the limiting frequency at which the feature of interest presents enough phase contrast for its detection in the frequency spectrum. The above described procedure for quantitative analysis requires the determination of the blind frequency and of the correlation coefficient C, when the material’s thermal properties are known. Conventional experimental C values when using the phase in lock-in experiments range from 1.5 to 2 [37] with a value of C = 1.82 typically adapted in experimental studies [38,39]. PPT results agree with this value range either for homogeneous or composite materials [35,36]. Thus, when the value of proportionality coefficient is known, the quantitative PPT requires the measurement of the blind frequency. In any other case, to validate the depth results, the accuracy of the correlation coefficient value used in Equation (2) should be graphically evaluated by the variables z and µ [36].
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2.2.Materials Materialsand andMethods Methods To Toevaluate evaluatethe thepotential potentialofofpulsed pulsedthermography thermography for forquantitative quantitative depth depth characterisation, characterisation, experimental testing was carried out in a trapezoid CFRP laminate, having fabricated experimental testing was carried out in a trapezoid CFRP laminate, having fabricateddefects defectsofof known knowncharacteristics. characteristics.The TheCFRP CFRPsample samplewas wasa alaminate laminate3030cm cm××30 30cm cmtrapezoid trapezoidstructure structureconsisted consisted ofoften orientation ofof 0◦0°/90° /90◦ cross ten(10) (10)plies pliesgiving givinga atotal totalspecimen specimenthickness thicknessofof2 2mm mmand anda laminae a laminae orientation cross TM TM ply through its volume. As illustrated in the schematic of Figure 1, 25 square Teflon insertions ply through its volume. As illustrated in the schematic of Figure 1, 25 square Teflon insertionsofof different differentdimensions dimensionsranging rangingfrom from33mm mmtoto15 15mm mmwere wereplaced placedbetween betweenthe theplies pliessimulating simulatinglocal local detached regions. These insertions were divided into five series (A–E in the schematic), placed detached regions. These insertions were divided into five series (A–E in the schematic), placedatat different differentdepths depthsranging rangingfrom from0.2 0.2mm mmtoto11mm, mm,while whileeach eachseries seriesconsisted consistedofoffive fivesquare squareinsertions insertions ofofdifferent differentlateral lateraldimensions dimensions(No. (No.11totoNo. No.55ininthe theschematic). schematic).As Asstated statedabove, above,the thesample samplewas was inspected by depositing heat energy on its rear surface, the opposite from this presented in Figure inspected by depositing heat energy on its rear surface, the opposite from this presented in Figure1,1, allowing allowingaadepths’ depths’range rangeinvestigation investigationfrom from0.2 0.2mm mmtoto1 1mm. mm.The Theconvenience convenienceofofinspecting inspectingthis this component component(widely (widelyused usedininseveral severalstudies) studies)isisderived derivedfrom fromthe thefact factthat thatits itscharacteristics characteristicsand andthe the presence of similar defects at different depths enable the conduction of relative comparisons. presence of similar defects at different depths enable the conduction of relative comparisons.
Figure 1. Schematic representation of defects characteristics and sample description. Figure 1. Schematic representation of defects characteristics and sample description.
For data acquisition, a flash thermographic system in reflection mode was used and two high For data acquisition, flash thermographic system an in reflection mode(ofwas and two high energy flash lamps were atriggered at t = 0 s to deposit instantaneous a 5used ms pulse duration) energy flash lamps were triggered at t = 0 s to deposit an instantaneous (of a 5 ms pulse duration) heat pulse on the sample’s surface. The temporal and spatial surface temperature variations after the heat pulse onofthe surface. The temporal through and spatial variations after application thesample’s energy pulse were monitored the surface aid of atemperature high-speed infrared camera, the application of the energy pulse images were monitored through thedown aid ofphase. a high-speed infrared camera, capturing a sequence of thermal during the cooling The camera used in this capturing a sequence of thermal images during the cooling down phase. The camera used in this study was a mid-wave (3–5 µm) device, containing a focal plane array of 320 × 256 infrared study was aThe mid-wave (3–5 µm) device, containing a focal the plane array of 320 × 256 infrared detectors. detectors. experimental parameters used to acquire thermographic sequence along with the The experimental parameters used to acquire the thermographic sequence along with the characteristics characteristics of the inspection equipment are summarised in Table 1. of the inspection equipment are summarised in Table 1. Table 1. Experimental equipment and acquisition parameters. Table 1. Experimental equipment and acquisition parameters. Experimental Equipment Acquisition Parameters Thermal Equipment stimulation: Sampling rate, f 157 Hz Experimental Acquisition Parameters Photographic Flashes: Balcar FX 60 Acquisition duration, 6.7 s Thermal stimulation: pulse duration: 5 ms thermal pulse, Time interval, ∆ = 1/ 6.3 ms Sampling rate, fs 157 Hz Photographic Flashes: Balcar FX 60 deposited energy: 3.2 KJ/ flash energy pulse duration: 5 ms (total thermal pulse,deposited 6.4 KJ) deposited energy: 3.2Thermographic KJ/ flash (totalmonitoring: energy deposited 6.4 KJ) Acquisition duration, t acq N 6.71052 s Total number of frames, Thermographic monitoring: Santa Barbara infrared camera, Focal Plane Array, nitrogen cooled, InSb, Time interval, ∆t = 1/ f 6.3 ms s Santa Barbara infrared camera,320 Focal Plane Array, nitrogen cooled, InSb, × 256 pixels 320 × 256 pixels Total number of frames, N 1052
The acquired pulsed thermal dataset measured the two dimensional surface temperature The acquired thermal dataset measured the two dimensional surface temperature distribution T(x,y) pulsed as a function of time t. Because quantification in the frequency domain requires distribution T(x,y) as a function of time t. Because quantification in the frequency domain requires the the application of PPT technique to treat the raw data, which is a pixel-wise transformation application of PPT technique treat the raw data, which is a pixel-wise transformation technique, technique, and to increase thetodata processing speed, it should be noted that before continuing to the data analysis phase, the recorded data were sub-sampled by a factor of 4. As a result, the parameters of the truncated sequence were redefined as N = 263 frames, f = 39.25 Hz, and time interval Δt = 25
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and to increase the data processing speed, it should be noted that before continuing to the data analysis phase, the recorded data were sub-sampled by a factor of 4. As a result, the parameters of the truncated sequence were redefined as N = 263 frames, f = 39.25 Hz, and time interval ∆t = 25 ms. Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 22 The adoption of the above sub-sampling procedure had a dual objective, initially to overcome the long ms. computation times andabove secondly to assessprocedure the impact the sampling The adoption of the sub-sampling haddegree a dual of objective, initially resolution to overcometo the acquisition quantitative depth Intosuch a manner and by capturing the data at the highest the longofcomputation times andresults. secondly assess the impact degree of the sampling resolution to the acquisition of apparatus, quantitative an depth results. resolution In such a manner by capturing the data at the the sampling rate of the inefficient could and be easily re-optimised through highest rate of the apparatus, inefficient resolution could be easilydataset. re-optimised selection of asampling lower sub-sampling factor and an without the need of capturing a new through the selection of a lower sub-sampling factor and without the need of capturing new As stated above, the quantitative depth determination procedures applied in this study,a evaluated dataset. the performance of two contrast-based methods. The correlation expressions used to determine As stated above, the quantitative depth determination procedures applied in this study, the depth z of the inserts were based on the determination of the thermal contrast peak slope time evaluated the performance of two contrast-based methods. The correlation expressions used to (timedetermine domain analysis) theinserts blindwere frequency domain analysis) usingcontrast the Equations the depthand z ofofthe based (frequency on the determination of the thermal peak (1) and (2), respectively. As a result, for known thermal properties of the tested material, the determination slope time (time domain analysis) and of the blind frequency (frequency domain analysis) using the of tpeak and fb can be used for depth quantification purposes. Additionally, factor C Equations (1) and (2), respectively. As a result, for known thermal properties ofthe thecorrelation tested material, used the in this study (frequency domain the value of 1.82, while the thermal diffusivity determination of tpeak and fb cananalysis) be used had for depth quantification purposes. Additionally, the α of correlation factor C used in this study (frequency domain analysis) had the value of 1.82, while the the inspected component according to its manufacturing characteristics was defined by the literature, − 7 2 − 1 thermal diffusivity α of the inspected component according to its manufacturing characteristics was having the value of 4.2 × 10 m s [6]. defined the literature, the value of 4.2 × 10−7 m2 s−1 [6]. Both theby temporal and thehaving frequency domain quantification techniques required the selection of a sound Both the temporal and the frequency domain quantification techniques required the selection of area. An inappropriate sound area selection can be an important factor for error production when depth has a sound area. An inappropriate sound area selection can be an important factor for error production to be estimated, making its selection the most crucial parameter which in combination with a non-uniform when depth has to be estimated, making its selection the most crucial parameter which in stimulation process cana provide largestimulation deviationsprocess from the depth which thefrom detected feature is combination with non-uniform canactual provide largeindeviations the actual located to. Based on the qualitative assessment of the examined sample presented in a previous depth in which the detected feature is located to. Based on the qualitative assessment of study the by the authors [40], which showed that temperature data elaboration suffered from uneven heating, examined sample presented in a previous study by the authors [40], which showed that temperaturedepth data elaboration suffered from uneven heating, depth quantification in next the time domain quantification in the time domain was designed by selecting the sound area to each defect.was In such designed by ensured selecting that the sound area next to each defect. In such the a manner, it was ensured the and a manner, it was the two respective regions received same amount of heatthat energy two respective regions received same heating. amount In of particular, heat energy and consequently minimising consequently minimising errors due tothe uneven according to the lateral dimensions of errors due to uneven heating. In particular, according to the lateral dimensions of the the detected Teflon squares, a sound area occupying exact the same pixels as the defective onedetected was selected Teflon squares, a sound area occupying exact the same pixels as the defective one was selected next next to the insertion as illustrated in Figure 2 and their dimensions were defined in terms of pixels as 4 × 4, to the insertion as illustrated in Figure 2 and their dimensions were defined in terms of pixels as 4 × 6 × 6, 8 × 8, 10 × 10 and 12 × 12 for correspondent defects No. 1, No. 2, No. 3, No. 4 and No. 5. 4, 6 × 6, 8 × 8, 10 × 10 and 12 × 12 for correspondent defects No. 1, No. 2, No. 3, No. 4 and No. 5.
Figure 2. Selection of the sound area for each detected defect in order to calculate the peak slope time
Figure 2. Selection of the soundcontrast area for eachindetected defect in order to calculate the peak slope time from the respective thermal curve the time domain analysis. from the respective thermal contrast curve in the time domain analysis.
However, as the application of PPT produced enhanced background uniformity, only an area from the background was selected for the calculations of the produced phase contrasts. In other
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However, as the application of PPT produced enhanced background uniformity, only an area from the background was selected for the calculations of the produced phase contrasts. In other words, Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 22 contrary to the time domain analysis the same sound area was used in this case for the calculations of all the phasecontrary contrasttocurves and consequently depth measurements words, the time domain analysis for the the same sound area was usedof inthe thisdetected case for features. the Additionally, due to the enhanced background uniformity observed on the frequency domain calculations of all the phase contrast curves and consequently for the depth measurements of analysis, the detected features. Additionally, due to the enhanced background uniformity this depth quantification method was repeated and assessed, considering as wellobserved the fieldon of the view as frequency depth quantification method was repeated and assessed, the sound area.domain For the analysis, clarity ofthis the readers about the above selections, indicative imaging results considering as well the field of view as the sound area. For the clarity of the readers about the above from the two domains are presented in Figure 3, justifying the decisions concerning the selection of the selections, indicative imaging results from the two domains are presented in Figure 3, justifying the sound areas in both the temporal and frequency domain analysis. In particular, the influence of uneven decisions concerning the selection of the sound areas in both the temporal and frequency domain heating can be observed in Figure 3a, contrary to the phase image of Figure 3b, where background analysis. In particular, the influence of uneven heating can be observed in Figure 3a, contrary to the uniformity was observed. phase image of Figure 3b, where background uniformity was observed.
(a)
(b)
Figure 3. (a) Raw thermal image of the inspected surface at t = 1.25 s after the application of the
Figure 3. (a) Raw thermal image of the inspected surface at t = 1.25 s after the application of the heating heating pulse; and (b) phase image of the inspected surface at f = 0.16 Hz. pulse; and (b) phase image of the inspected surface at f = 0.16 Hz.
3. Results and Discussion
3. Results and Discussion
In the following, the results from the two quantification methods are presented and discussed.
Initially, the two quantification procedures along with the informative utilised each In the following, the results from the two quantification methodsparameters are presented andindiscussed. case the are evaluated followed byprocedures the presentation of with the depth results in eachparameters case, while atutilised the end in of each Initially, two quantification along the informative this section a comparison of temporal and frequency domain analysis in term of error production is end case are evaluated followed by the presentation of the depth results in each case, while at the reported. of this section a comparison of temporal and frequency domain analysis in term of error production is reported. 3.1. Depth Retrieval with Thermal-Contrast Peak Slope Time the application of the pulse thermal energy and the recording of the surface temperature 3.1. DepthAfter Retrieval with Thermal-Contrast Peak Slope Time response, the delaminated regions’ detection was produced due to the lower thermal conductivity
After the application the respect pulse thermal energy and The the recording thethermal surface temperature that these features haveofwith to the host material. variation inofthe properties response, the delaminated regions’ detection was produced due to the lower thermal conductivity affected the penetration rate of the heat flux into the composite bulk and therefore the surface that these features have with respecttotothe theappearance host material. in time the thermal temperature distribution, resulting of localThe “hotvariation spots”. The points ofproperties these hot spots appearance were according to the inserts’ location (depth) size. Thus, when affected the penetration ratevaried of the heat flux into the composite bulkand and therefore theraw surface temperature data are handled, the depth at which these inserts are located to, can be determined bythese temperature distribution, resulting to the appearance of local “hot spots”. The time points of subtracting the cooling curve over a reference area from the cooling curve over the damaged one. hot spots appearance were varied according to the inserts’ location (depth) and size. Thus, when raw The resulting temperature difference curve can produce the correlation of the detected feature’s temperature data are handled, the depth at which these inserts are located to, can be determined by depth with two characteristic points, this of peak temperature difference and this of the peak slope subtracting the cooling curve over a reference area from the cooling curve over the damaged one. of this difference, which are further associated with the correspondent times when these phenomena The resulting temperature difference curve can produce the correlation of the detected feature’s depth occur (peak contrast time and peak slope time). with two Before characteristic points, of peak temperature difference and thisofofthese the peak slope of this the actual depththis information retrieval through the correlation specific time difference, further with the times thesecontrast phenomena points which with theare depth of theassociated detected features, thecorrespondent temporal functions of when the thermal and ofoccur (peakthe contrast time peak were slopestudied, time). verifying that the selection of peak slope time for depth slope of thisand contrast calculations is a more working with raw of temperature data. The Before the actual depthappropriate informationmethod, retrievalwhen through the correlation these specific time points experimental results in terms of thermal contrast curves and of the correspondent slope curves as with the depth of the detected features, the temporal functions of the thermal contrast and of theaslope function of time illustrated in Figures specifically, figure indicates the thermal of this contrast wereare studied, verifying that4–8. theMore selection of peakeach slope time for depth calculations contrast evolutions and their respective contrast slope curves for all the detected defects in each is a more appropriate method, when working with raw temperature data. The experimental results
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in terms of thermal contrast curves and of the correspondent slope curves as a function of time are illustrated in Figures 4–8. More specifically, each figure indicates the thermal contrast evolutions and their respective contrast slope curves for all the detected defects in each individual series. To achieve a clearer presentation and a higher resolution-clarity for these peaks determination, the time-dependent Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 22 1D contrast slope profiles were plotted only at the time region where the peaks occurred. Additionally, as theindividual flash energy deposition was not uniform over the the negative of slopes series. To achieve a clearer presentation andsample a highersurface, resolution-clarity for values these peaks measured at the very early time intervals were adjusted to zero, until the time point in which determination, the time-dependent 1D contrast slope profiles were plotted only at the time region the slopewhere of the the thermal departing as thethe zero value [32].deposition In other words, initial over temperature peakscontrast occurred.was Additionally, flash energy was notthe uniform the surface, thescaled negative values of slopes measured at the veryreference early time intervals were rise atsample each defect was to be the same as that of the respective area. The previously adjustedthermal to zero, response until the time point in whichprovided the slope of thermal contrast was departing the mentioned representations thetherequired information for quantitative zero value [32]. In other words, the initial temperature rise at each defect was scaled to be the same analysis, determining the peak thermal contrast and the peak slope of this contrast along with the as that of the respective reference area. The previously mentioned thermal response representations correspondent peak times. provided the required information for quantitative analysis, determining the peak thermal contrast As regards the shallowest defect series on the trapezoid sample (Figure 4), the time of peak thermal and the peak slope of this contrast along with the correspondent peak times. contrast occurrence was measured to be the same for all the detected defects, regardless the size of As regards the shallowest defect series on the trapezoid sample (Figure 4), the time of peak each square insertion. Usually, for having larger lateral it takes regardless more timethe for the thermal contrast occurrence wasfeatures measured to be the same for alldimensions, the detected defects, trapped above them to be diffused throughhaving the sides of lateral the “trap”, and this can be seen on sizeheat of each square insertion. Usually, out for features larger dimensions, it takes more the plot from thetrapped different time points intowhich each temperature difference curve is approaching time for the heat above them be diffused out through the sides of the “trap”, and this can zero. be seen the plot of from thetemperature different time points in curves which each temperature curve isdepth However, theon evolution these difference is indicating that difference when the defect approaching zero. However, the evolution of these temperature difference curves is indicating that thus is approaching zero, the peak thermal contrast time approaches zero as well (t = 0.1019 s) and when the defect depth is approaching zero, the peak thermal contrast time approaches zero as well (t the temporal characteristics of this phenomenon remain unaffected from the 3D conduction problem. = 0.1019 s) and thus the temporal characteristics of this phenomenon remain unaffected from the 3D Similar results were also produced by the study of the temporal function of the thermal contrast slopes, conduction problem. Similar results were also produced by the study of the temporal function of the as these peaks occurred as well at exactly the same time for all five insertions of Series A. However, thermal contrast slopes, as these peaks occurred as well at exactly the same time for all five the peak slope appeared earlier = 0.02447 s) with respect to peak(t thermal On thetoother insertions of Series A.much However, the(tpeak slope appeared much earlier = 0.02447contrast. s) with respect hand,peak the 3D heatcontrast. conduction around defects to affect the peakthe values of seems eitherto the thermal thermal On the other the hand, the 3Dseems heat conduction around defects affect contrast or of values its slope. In particular, in contrast Figure 4, be seen that largerininserts the peak of either the thermal oritofcan its slope. In particular, Figuregenerally 4, it can bepresented seen higher peak contrast and peak contrast slope values with respect to peak these contrast produced by the smaller that larger inserts generally presented higher peak contrast and slope values with ones. respect tothe these produced the smaller ones. contrast For instance, thermal contrast and peak For instance, peak thermalby contrast and peak slopethe forpeak defect A5 (15 mm) were 2.25 and slope while for defect A5 (15 mm) were 2.25 for anddefect 52.95, A1 respectively, while theand correspondent 52.95,contrast respectively, the correspondent values (3 mm) were 0.63 8.19, indicating values for is defect A1 (3 mm) of were andthe 8.19, indicating that as take smaller is the dimension of themore that as smaller the dimension the0.63 defect, heat diffusion can place around this region defect, the heat diffusion can take place around this region more easily, producing as well a reduced easily, producing as well a reduced contrast. Nevertheless, some differentiations detected regarding this contrast. Nevertheless, some differentiations detected regarding this phenomenon (i.e., peak phenomenon (i.e., peak contrast values of defects A5 and A4) can be possibly attributed to the selection contrast values of defects A5 and A4) can be possibly attributed to the selection of different sound of different sound for each peakalong determination along with the of heat areas for each areas individual peakindividual determination with the non-uniformity of non-uniformity heat deposition on deposition on the inspected surface. the inspected surface.
(a)
(b)
Figure 4. Temporal evolution of: (a) the thermal contrast curves; and (b) the correspondent slope of
Figure 4. Temporal evolution of: (a) the thermal contrast curves; and (b) the correspondent slope of the the thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 0.2 thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 0.2 mm (Series A). mm (Series A).
Contrary to the results produced from the shallowest defects, as the depth of the Teflon insertions was increased, the consistency detected regarding the time points of the peak contrast appearance was altered. More specifically, by studying the produced thermal contrasts and their
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Contrary to the results produced from the shallowest defects, as the depth of the Teflon insertions was increased, the consistency detected regarding the time points of the peak contrast appearance was altered. More specifically, by studying the produced thermal contrasts and their evolution to time for Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 22 all the insertions to the depth of 0.4 mm (Figure 5a), it can be generally seen that the smaller defects produced an earlier point of maximum appearance andbevice versa. seen For that instance, evolution to timetime for all the insertions to thethermal depth ofcontrast 0.4 mm (Figure 5a), it can generally the smaller defects produced an earlier time point of occurred maximumfor thermal contrast appearance and was the temporal region where the peak thermal contrasts the five defects of this series vicefrom versa.0.3312 For instance, the temporal region swhere the peakB4 thermal contrasts occurred the five ranging s (for defect B1) to 0.4331 (for defects and B5), indicating thatfor smaller lateral defects of this series was ranging from 0.3312 s (for defect B1) to 0.4331 s (for defects B4 and B5), sizes produced an easier path for heat to be laterally diffused and consequently a reduced contrast on indicating smaller lateral produced easier path heatcontrast to be laterally and for an earlier time that interval. Thus, thesizes above results an verify that thefor peak time isdiffused appropriate consequently a reduced contrast on an earlier time interval. Thus, the above results verify that the relative comparisons but not reliable for quantitative information retrieval on deeper probing, as the 3D peak contrast time is appropriate for relative comparisons but not reliable for quantitative conduction effect has an impact on the acquired information. Some deviations from the above general information retrieval on deeper probing, as the 3D conduction effect has an impact on the acquired observation were Some detected in this case time points defect B3 and B4),inwhich can (i.e., be also a information. deviations from (i.e., the above generalofobservation weredefect detected this case resulttime of the procedure used to produce these temperature difference functions (selection of different points of defect B3 and defect B4), which can be also a result of the procedure used to produce sound areas). On the other hand, the study of contrast slope evolution to time (Figure 5b), revealed these temperature difference functions (selection of different sound areas). On the other hand, the study of contrast slope time (Figure 5b), revealed that themore characteristic of that the characteristic timeevolution points oftothis peak occurrence remained constanttime andpoints less affected this peak occurrence remained more constant and less affected from the negative effects of lateral from the negative effects of lateral heat conduction around the detected features. For instance, the time conduction detectedwas features. For instance, the time range when thethough peak slopes rangeheat when the peakaround slopesthe occurred between 0.2547 s and 0.3057 s and even the peak occurred was between 0.2547 s and 0.3057 s and even though the peak slope times did not have slope times did not have exactly the same value, the shorter time range (approximately half) observed exactly the same value, the shorter time range (approximately half) observed in this case, indicates in this case, indicates the reliability of this quantity for depth prediction. However, similar to the the reliability of this quantity for depth prediction. However, similar to the temperature difference temperature difference evolution study, the 3D conduction is strongly influencing only the peak slope evolution study, the 3D conduction is strongly influencing only the peak slope values, but this values, but this isparameter is not of prime whenis the is the quantitative parameter not of prime interest wheninterest the objective the objective quantitative depth analysis. depth analysis.
(a)
(b)
Figure 5. Temporal evolution of: (a) the thermal contrast curves; and (b) the correspondent slope of
Figure Temporal evolution (a) the thermaloncontrast curves; and located (b) thetocorrespondent the5.thermal contrasts for the of: detected insertions the trapezoid surface the depth of 0.4slope of themm thermal contrasts for the detected insertions on the trapezoid surface located to the depth of (Series B). 0.4 mm (Series B). The thermal behaviour assessment regarding the detected defects on the Series C, D and E provided similar results,assessment as shown in Figures the 6–8.detected As can be seen on from respective plots, the The thermal behaviour regarding defects thethe Series C, D and E provided observations discussed above were further confirmed from the study of the thermal profiles similar results, as shown in Figures 6–8. As can be seen from the respective plots, the observations acquired for the deeper defects. In particular, as the probing became deeper, a high divergence on discussed above were further confirmed from the study of the thermal profiles acquired for the deeper the characteristic peak contrast time range was observed for defects of the same depth but with defects. In particular, as the probing a highAdivergence the characteristic peak contrast different lateral dimensions. For became instance,deeper, while Series defects hadon the same peak contrast time, time range was observed for defects of the same depth but with different lateral dimensions. For instance, Series B and C defects produced a peak time range of approximately 0.1 s, and Series D and E whileproduced Series A defects had range the same peak contrast 0.37 time,s Series B and C defects produced a peak a temporal of approximately and 0.15 s, respectively. Contrarily, thesetime timerange differences were studyingathe correspondent slope variations. For0.15 s, of approximately 0.1 s,remarkably and Seriesreduced D and Eby produced temporal range ofcontrast approximately 0.37 s and instance,Contrarily, Series C defects a peak slope range from 0.40 s toby 0.48 s, while the the correspondent ranges for respectively. theseproduced time differences weretime remarkably reduced studying Series D and E defects For wereinstance, from 0.66Series s to 0.76 and from 0.91 s to a0.99 s, respectively. Additionally, contrast slope variations. C sdefects produced peak slope time range from 0.40 s comparing the plots retrieved from each individual series investigation, it can be seen that the high to 0.48 s, while the ranges for Series D and E defects were from 0.66 s to 0.76 s and from 0.91 s to 0.99 s, noise levels produced for increasing the inspection depth, did not have an impact on the respectively. Additionally, comparing the plots retrieved from each individual series investigation, it can determination of the two characteristic time points. Moreover, for the deeper defects no clear observations can be done regarding the correlation of square size and the 3D conduction
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be seen that the high noise levels produced for increasing the inspection depth, did not have an impact on the determination of the two characteristic time points. Moreover, for the deeper defects no clear observations can8, done regarding Appl. Sci. Sci. 2018, 2018, 8,be FOR PEER REVIEW the correlation of square size and the 3D conduction phenomenon of 22 22 Appl. xx FOR PEER REVIEW 99 of around it. This can be explained by the fact that a reduced contrast was produced mainly for the defects phenomenon around it. it. [40], This indicating can be be explained explained bythermal the fact factwave that aadid reduced contrast was was produced phenomenon around This can by the that reduced contrast produced on Series D and E (Figure 3) that the not penetrate efficiently enough mainly for the defects on Series D and E (Figure 3) [40], indicating that the thermal wave did not mainly for the defects on Series D and E (Figure 3) [40], indicating that the thermal wave did not to these locations and a weak thermal effect was produced from these heat flow barriers. As a result, penetrate efficiently efficiently enough enough to to these locations locations and and aa weak weak thermal effect effect was was produced produced from from these penetrate the reduced amount of heat reachedthese these areas, was not ablethermal to produce sufficient lateral heatthese diffusion heat flow barriers. As a result, the reduced amount of heat reached these areas, was not able to to heat flow barriers. As a result, the reduced amount of heat reached these areas, was not able around these defects. The above observation was mainly detected on defect Series D and E, as for instance produce sufficient lateral heat diffusion around these defects. The above observation was mainly produce sufficient lateral heat diffusion around these defects. The above observation was mainly the smaller detected defects andE, E2aspresented a slightly greater peakdefects contrast value with respect detected on defect defect SeriesD3 D and and for instance instance the smaller smaller detected D3time and E2 E2 presented detected on Series D E, as for the detected defects D3 and presented aa to theslightly time ofgreater the largest defects D5 and E5. peak contrast time value with respect to the time of the largest defects D5 and E5. slightly greater peak contrast time value with respect to the time of the largest defects D5 and E5.
(a) (a)
(b) (b)
Figure 6. 6. Temporal Temporal evolution evolution of: of: (a) (a) the the thermal thermal contrast contrast curves; curves; and and (b) (b) the the correspondent correspondent slope slope of of Figure
Figure Temporal evolution of:detected (a) the thermal curves; and (b) the correspondent slope the6.thermal thermal contrasts for the the insertionscontrast on the the trapezoid trapezoid surface located to the the depth depth of 0.6 0.6of the the contrasts for detected insertions on surface located to of thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 0.6 mm (Series C). mm (Series C). mm (Series C).
(a) (a)
(b) (b)
Figure 7. 7. Temporal Temporal evolution evolution of: of: (a) (a) the the thermal thermal contrast contrast curves; curves; and and (b) (b) the the correspondent correspondent slope slope of of Figure
Figure Temporal evolution of:detected (a) the thermal curves; and (b) the correspondent slope the7.thermal thermal contrasts for the the insertionscontrast on the the trapezoid trapezoid surface located to the the depth depth of 0.8 0.8of the the contrasts for detected insertions on surface located to of thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 0.8 mm (Series D). mm (Series D). mm (Series D).
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(b)
Figure 8. Temporal evolution of: (a) the thermal contrast curves; and (b) the correspondent slope of
Figure 8. Temporal evolution of: (a) the thermal contrast curves; and (b) the correspondent slope of the the thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 1 thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 1 mm (Series E). mm (Series E).
Through the above discussed procedure,the thedepths depths of artificial defects into into the the Through the above discussed procedure, of all allthe thedetected detected artificial defects CFRP specimen were quantitatively estimated, correlating the measured peak slope time with the the CFRP specimen were quantitatively estimated, correlating the measured peak slope time with depth. This method for depth calculations was selected, as the peak contrast time was proven to be depth. This method for depth calculations was selected, as the peak contrast time was proven to be seriously affected by the lateral dimensions of the detected features, whereas peak slope time seriously affected by the lateral dimensions of the detected features, whereas peak slope time appeared appeared to remain more constant regardless these size variations. Table A1 in the Appendix to remain more constant regardless theseofsize variations. summarises the experimental values summarises the experimental values peak slopes andTable peakA1 slope times along with the produced of peak slopes and peak slope times along with the produced depth results for all the detected defects. depth results for all the detected defects. In general, peak slope time provided an efficient estimation In general, slope timehowever, providedinansome efficient estimation of the Teflon depths; however, of the peak Teflon depths; instances, increased errors were produced. From in thesome summary of theerrors depth were results, it can be seen more accurate were produced forseen the that instances, increased produced. Fromthat thethe summary of the results depth results, it can be deeper insertions (despite noise exhibited this case) and the larger errors were observed on the the more accurate results werethe produced for theindeeper insertions (despite the noise exhibited in this defects Series B and C. A possible explanation about these large deviations from the actual depth on case) and the larger errors were observed on the defects Series B and C. A possible explanation about and C defects, can be attributed to the fact that these inserts were more strongly affected these Series large B deviations from the actual depth on Series B and C defects, can be attributed to the fact from the 3D heat conduction, contrary to the shallowest and deepest insertions which seem to be that these inserts were more strongly affected from the 3D heat conduction, contrary to the shallowest unaffected from the above phenomenon for different reasons as discussed above. On the other hand, and deepest insertions which seem to be unaffected from the above phenomenon for different reasons a factor that may produce deviations between the measured and actual depth could be the as discussed above. On thermal the other hand, a which factor might that may produce between the measured uncertainty on the properties contribute to deviations error as well. In particular, the and actual could be the uncertainty on the thermal properties which from might actualdepth value of the thermal diffusivity might differ in anisotropic materials thecontribute value usedtoinerror as well. particular, of the thermal diffusivity might differ in anisotropic materials thisInstudy. Besidesthe thisactual factor,value the selection of the truncation parameters to overcome the processing could in be this a factor of extra error. this For instance, the selection peak slopeof time the defects parameters in Series A to from limitations the value used study. Besides factor, the theoftruncation (0.2 mm) was determined in the lower time truncated producing an error oftime overcome the processing limitations could be interval a factorofofthe extra error. sequence For instance, the peak slope 15%. The appearance of the peak slope time in this very early time point and the correspondent of the defects in Series A (0.2 mm) was determined in the lower time interval of the truncated sequence produced error may be further reduced if new truncated parameters are defined, increasing the producing an error of 15%. The appearance of the peak slope time in this very early time point and temporal resolution of the cooling down phase monitoring. Finally, the slight variability of peak the correspondent produced error may be further reduced if new truncated parameters are defined, slope times detected for defects located to the same depth (except the shallowest ones) can be increasing the temporal resolution of the cooling down phase monitoring. Finally, the slight variability attributed to the variability of the sound area selection in each defect depth measurement, which can of peak slope for defects located to the same depth (except the shallowest ones) can be also be antimes extra detected error production factor. attributed to the variability of the sound area selection in each defect depth measurement, which can 3.2. with Blind Frequency also be anDepth extraRetrieval error production factor. The second depth estimation procedure was performed by means of quantitative pulsed phase thermography, investigating the accuracy produced on depth information retrieval from the analysis of the phase data, theprocedure phase contrast calculations by and the determination of pulsed the blind The second depth estimation was performed means of quantitative phase frequency investigating . As presented above, whenproduced working with temperature data, the selectionfrom of the sound thermography, the accuracy on depth information retrieval the analysis maydata, havethe an impact on the thermal contrastand calculations and this impact canblind be additionally of thearea phase phase contrast calculations the determination of the frequency f b . enhanced in the case of uneven heating. As a result, in the previous case study different sound areas As presented above, when working with temperature data, the selection of the sound area may have were selected for the retrieval of depth information, minimising the risk of plotting inappropriate
3.2. Depth Retrieval with Blind Frequency
an impact on the thermal contrast calculations and this impact can be additionally enhanced in the case of uneven heating. As a result, in the previous case study different sound areas were selected for the retrieval of depth information, minimising the risk of plotting inappropriate temperature–time
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evolution curves. However, from the qualitative interpretation of phase images, it was observed that the frequency domain analysis greatly increased the background uniformity (as presented in Figure 3b). Based on the aforesaid, the first depth estimation method in the frequency domain was performed by measuring the correspondent phase contrasts between the defective areas and a region acting as the sound area pre-selected from the background (top left corner of the CFRP surface). Additionally, this procedure was repeated by calculating the average phase intensity from all the pixels on the surface (as the overall surface occupied by the defects was much smaller than the field of view). In such a manner, the use of the overall surface as a sound area was also assessed, aiming primary to evaluate the possibility of overcoming the need for a sound area/point selection in similar inspections. For the purposes of this study, similar to the temporal analysis, the phase contrasts profiles were plotted as a function of frequency for all the detected inserts, aiming to define the characteristic frequency point when the phase contrast diverged zero. Additionally, a comparison of sound area selection impact is performed through the two above mentioned procedures. Similar to the presentation of results in the time domain, before continue with the actual depth characterisation procedure, the phase contrast profiles obtained from the study of the CFRP sample are discussed, investigating the influence of depth and size on the produced contrast and the blind frequency determination. Figure 9 illustrates the phase contrasts produced from the shallowest insertions (Series A), either selecting a random sound area from the background (left column plot) or by using the entire surface as a sound area (right column plot). Similar to the thermal contrast slope function, phase contrasts were plotted only at the region of interest (frequencies region where the defect was visible), removing the information from the frequency spectrum in which only noise variations were appeared. As can be seen from the 1D phase contrast profiles, similar to the thermal data, in general, larger defects produced a greater phase contrast. A deviation can be seen between the phase contrast intensities measured for defects No. 3 and No. 4 (located at the centre of the panel) and that of defect No. 5 (located at the lower edge of the panel). Nevertheless, for depth calculations the parameter of interest is the blind frequency, which as can be seen from the correspondent plots, it is approximately the same regardless the size of the insertion inspected. The comparison of the two procedures used for the determination of the blind frequency, is revealing that an enhanced similarity was produced regarding the phase contrast evolutions either working with the random sound area or the overall surface, thus its selection has a low impact on the measurement of the blind frequency on Series A defects. However, the interesting point observed by this comparison is the fact that less noise content can be observed in the latter case, which is important when the depth of a shallow defect has to be estimated [36]. Nonetheless, a possible approach for eliminating further the produced noise can be based on repeated measurements, normalising the phase contrast plots. By studying the effects from the detected defects of Series B and as the depth of the detected features was increased, the phase contrast was affected by the detected feature’s size. More specifically, as can be seen in Figure 10, larger detected insertions in Series B produced greater phase contrasts, regardless the selection of the sound area. However, the size of the insertions had an impact only to the produced contrast as all defects at this depth are visible in approximately the same frequency range. The noise reduction observed in the previous inspection through the selection of the whole surface as a sound area can be also seen from the respective plots of Series B defects, as the Figure 10b is much freer of noise with respect to Figure 10b.
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(a)
(b)
(a) profiles of the Series A insertions (0.2 mm) after: (b) Figure 9. Phase contrast (a) selecting the left top
Figure 9. Phase contrast profiles of theasSeries Aarea. insertions (0.2 mm) after: (a) selecting the left top corner; corner; and (b) the whole surface a sound Figure 9. Phase contrast profiles of the Series A insertions (0.2 mm) after: (a) selecting the left top and (b) the whole surface as a sound area. corner; and (b) the whole surface as a sound area.
(a)
(b)
Figure 9. Phase contrast profiles of the Series A insertions (0.2 mm) after: (a) selecting the left top corner; and (b) the whole surface as a sound area.
(a)
(b)
(a) profiles of the Series B insertions (0.4 mm) after: (b)(a) selecting the left top Figure 10. Phase contrast corner; and (b) the whole surface as a sound area. Figure 10. Phase contrast profiles of the Series B insertions (0.4 mm) after: (a) selecting the left top Figure 10. Phase profiles of the insertions (0.4 mm) after: (a) selecting the left top corner; corner; andcontrast (b) the whole surface as aSeries soundBarea.
The above presented results for Series B insertions were further confirmed from the plot results (b) from the correspondent of theThe deeper of this panel, in Figurewere 11. As can be seen abovedefects presented results forillustrated Series B insertions further confirmed from the plot results plots the greater is the depth is the 11. frequency range infrom which 10.defects Phase contrast profiles ofthe the shorter Series insertions (0.4 mm)be after: selecting the defects left top are of theFigure deeper of defect this panel, illustrated inBFigure As can seen(a) thethe correspondent Theobvious. above presented results for Series B insertions were further confirmed from the plot results instance, the insertions of Series Cishave a frequency range of visibility from the and (b)isthe surface as athe sound area. plots corner; the For greater thewhole defect depth shorter the frequency range in which the defects are minimum available frequency (0.149 Hz) to approximately 1 Hz, while for the deepest defects (Series of the deeper of thisthe panel, illustrated in Figure As can be seen the from correspondent obvious.defects For instance, insertions of Series C have 11. a frequency range of from visibility the above results forshorter Series Bisinsertions were further confirmed from the plot results theThe corresponding frequency range 0.149 torange approximately 0.5 However, plots theE) greater is the presented defect depth the the frequency in the which theHz. defects are obvious. minimum available frequency (0.149 Hz)isto between approximately 1Hz Hz, while for deepest defects (Series of the deeper defects of thisranges panel,perform illustrated in Figure 11. As canofbethe seen from the correspondent shorter detection frequency clearer determinations blind frequency, thus less E) thethe corresponding frequency between 0.149 Hz of to visibility approximately However, For instance, insertions of Series Crange have isa frequency range from 0.5 theHz. minimum available plotscontent the greater is the defect depth the shorter is the presented frequencyinrange in11 which theindicate defectsthe are noise is presented in these cases. The plot results Figure further shorter detection frequency ranges perform clearer determinations of the blind frequency, thus less frequency (0.149 Hz) instance, to approximately 1 on Hz, while the deepest defects (Series E) the from corresponding obvious. For insertions ofthe Series for C have a frequency range of visibility the impact of feature’s lateralthe dimensions contrast, as smaller inserts, regardless of their noise content is presented in these cases. Theproduced plot results presented in Figure 11 further indicate the frequency range is between 0.149 Hz to approximately 0.5 Hz. However, shorter detection frequency minimum available frequency (0.149 Hz) to approximately 1 Hz, while for the deepest defects (Series location, produced weaker phase contrast with respect to the larger ones. impact of feature’s lateral dimensions on the produced contrast, as smaller inserts, regardless of their E) the corresponding frequency range is between 0.149 Hz to thus approximately 0.5 Hz. However, ranges perform clearer determinations of the frequency, location, produced weaker phase contrast withblind respect to the larger ones.less noise content is presented shorter detection frequency ranges perform clearer determinations of thethe blind frequency, thus less lateral in these cases. The plot results presented in Figure 11 further indicate impact of feature’s noise content is presented in these cases. The plot results presented in Figure 11 further indicate the dimensions on the produced contrast, as smaller inserts, regardless of their location, produced weaker impact of feature’s lateral dimensions on the produced contrast, as smaller inserts, regardless of their phase contrast with respect to the larger ones. location, produced weaker phase contrast with respect to the larger ones.
and (b) the whole surface as(a) a sound area.
(a)
(b)
(a)
(b)
(a)
(b)
Figure 11. Cont.
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(c)
(d)
(e)
(f)
Figure 11. Phase contrast profiles for: (a,b) the defects of Series C (0.6 mm); (c,d) the defects of Series
Figure 11. contrast profiles for: (a,b) the defects of Series (0.6plots mm);correspond (c,d) the defects of Series D D Phase (0.8 mm); and (e,f) the defects of Series E (1 mm). The leftCside to the phase (0.8 mm);contrasts and (e,f) the defects of Series E (1 mm). The left side plots correspond to the phase contrasts calculated through the aid of the top left sound area and the right plots correspond to the phase contrasts as a sound calculated through theselecting aid ofthe theentire top surface left sound area area. and the right plots correspond to the phase contrasts selecting the entire surface as a sound area.
From the phase contrast measurements and the determination of the blind frequency, the depths of all the detected defects into the CFRP panel were quantitatively estimated. Table A2 in the From the phase contrastthe measurements and the determination of the frequency, theasdepths Appendix summarises experimental values of the blind frequencies and blind the calculated depths productdefects of the diffusion the were correlation factor C = 1.82. In general, frequency domain of all thethe detected into thelength CFRPand panel quantitatively estimated. Table A2 summarises the analysis and phase data manipulation provided an efficient estimation of the inserts depth, experimental values of the blind frequencies and the calculated depths as the product of the diffusion regardless their location and size. Additionally, the similarity of results in terms of error production length and the correlation factor C = 1.82. In general, frequency domain analysis and phase data for inserts having the same depth indicates that the potential non-uniform heat deposition on the manipulation provided an efficient estimation of the inserts depth, regardless their location and size. inspected surface has a negligible impact on the quantitative information retrieval. Moreover, as Additionally, the of information results in terms of and error production inserts having the same regards thesimilarity quantitative retrieval their correlationfor with the investigated depth, it depth indicatescan that the potential non-uniform heat deposition on the inspected surface has a negligible be generally seen that defects nearer to the surface produced a larger divergence from the actual depth to the information deeper ones where the error production was lower. above remark was impact on the contrary quantitative retrieval. Moreover, as regards theThe quantitative information somehow expected as it is attributed to the increase noise levels produced as higher is the frequency retrieval and their correlation with the investigated depth, it can be generally seen that defects nearer range of detection, incommoding the accurate detection of the blind frequency. to the surface produced a larger divergence from the actual depth contrary to the deeper ones where The comparison of the two different procedures used for the depth measurements with the the errorphase, production was lower. The above remark was somehow expected as it is attributed to the referring to the two different sound areas selection, indicates that the selection of the entire increase noise levels produced as higher is the frequency of detection, the accurate surface as a sound area either provided similar resultsrange with these produced incommoding from the random area detectionselection of the blind frequency. or it was reducing the error production as in the cases of the Series A and C defects. Thus, use of the overall as a soundprocedures area primaryused eliminates the depth need formeasurements a sound area/point Thethe comparison of thesurface two different for the with the selection and secondly might reduce the potential uncertainty produced from a random selection phase, referring to the two different sound areas selection, indicates that the selection of the entire from the background. surface as a sound area either provided similar results with these produced from the random area Some deviations were further detected on depth determinations for defects of the same depth. selectionFor or instance, it was reducing the error production in the the Series A and defects. Thus, by calculating the Series E defects as depth, by cases settingof the whole surface as aCreference, the use of the overall surface as a sound area primary eliminates the need for a sound this was measured to be 0.994 mm for E2, E3, E4 and E5 defects and 0.861 mm for defect E1. A area/point more study of might the measured frequencies in this caseproduced is indicating thata the phase selection contrast from selectioncareful and secondly reduceblind the potential uncertainty from random
the background. Some deviations were further detected on depth determinations for defects of the same depth. For instance, by calculating the Series E defects depth, by setting the whole surface as a reference, this was measured to be 0.994 mm for E2, E3, E4 and E5 defects and 0.861 mm for defect E1. A more careful study of the measured blind frequencies in this case is indicating that the phase contrast deviation from zero was detected very nearly for all the defects. In particular, it was detected at
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0.447 Hz in the former case and at 0.596 Hz in the latter one. Taking into consideration that the truncated frequency interval ∆f is 0.149 Hz, this means that the error produced in the second case 16.1% (0.6% in the first case) can be possibly attributed as well to the truncated parameters selected to process the acquired sequences, as the frequency is inversely related to the time interval. As a result, and considering that deeper probing in the frequency domain is less affected by noise, depth estimations for deeper defects seem to be more affected by the truncated parameters due to the lower frequency range in which the defects are visible. Finally, as in the case of temporal analysis, source of extra error could be the deviation from the actual thermal properties of the inspected panels. 3.3. Comparison of Temporal and Frequency Domain Analysis for the Acquisition of Depth Information In the previous subsections, results from the quantitative analysis of the CFRP sample were presented, based on the use of the two depth prediction methods. Figure 12 shows a comparison of the measured depths from each individual method in terms of prediction errors. These 3D plots intend to summarise the above discussed quantitative results in a single imaging result, enabling relative comparisons. For this purpose, the scale of the error axis was fixed to be the same in all the three plots, enabling the qualitative evaluation of the produced errors according to the height of each respective bar. The above can be performed as the plots include all the detected defects and the location of each error bar corresponds to the location of the specific insertion with respect to the defect description figure included on the top right side of the figure. As can be seen from the previously mentioned plots, generally, temporal analysis for depth determination produced larger prediction errors with respect to the correspondent method on the frequency domain. For instance, while peak slope time method provided large divergences on depth prediction of Series B and C defects, this was importantly reduced on the results acquired from the two respective procedures on the frequency domain. Additionally, for some defects mainly in the deeper series which were estimated with a considerable error in the frequency domain, these were not able to be detected and quantified in the temporal domain. Contrarily, the comparison of quantification results acquired by the phase data showed that the selection of the entire surface as sound area either produced similar results with those provided from the random sound area or in some instances this method provided results closer to the actual depth. As regards the error production and its correlation with the depth, it can be seen that larger errors were produced mainly on Series B and C when working with temperature data, while, in phase data manipulation, a considerable error was produced for defects located at depths of 0.2 mm and 0.4 mm, respectively. Contrarily, more efficient results were produced for Series A, D and E in time domain analysis and for the deeper Series C, D and E in the respective frequency domain analysis. As stated above, the increased errors produced for Series B and C on the temporal analysis can be attributed to the 3D conduction problem, which is not presented on the shallower defects series due to the early time detection and on the deepest ones due to weak signal that they produced. One other hand, the deviations from the actual depth observed from frequency analysis can be attributed to the increased noise levels on the phase contrast plots when the defect is visible in a large frequency range.
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(a)
(b)
(c) Figure 12. 3D representation of insertions estimated depth in terms of error production for all the Figure 12. 3D representation of insertions estimated depth in terms of error production for all detected defects in the trapezoid specimen through: (a) peak slope time; (b) blind frequency (random the detected defects in the trapezoid specimen through: (a) peak slope time; (b) blind frequency sound area); and (c) blind frequency (overall surface). (random sound area); and (c) blind frequency (overall surface).
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4. Evaluation of Analysis Parameters for Depth Prediction Through the above quantitative analysis of the CFRP component in both the temporal and frequency domains, the acquisition of depth results was achieved and a discussion concerning the possible parameters for error production was done. In the present section, a thorough analysis for the influence degree of these parameters is performed with the aim to assess in a clearer manner how they affect the quantitative depth estimations. 4.1. Selection of Sampling Frequency From the results presented above it, was observed that a low sampling resolution can be a strong limitation especially in the case of measurements over time for defects close to the surface. For this purpose, new measurements were performed to evaluate the effect of the sampling resolution on the depth results. In particular, a new dataset was collected, monitoring the heat diffusion into the material bulk with a frame rate of 88 Hz. The new sampling frequency contributed to the increase of the temporal resolution reducing the time step from 25 ms to 11 ms. Indicative results from the time domain analysis of the defects in the Series A and B, which produced the largest deviations, are summarised in Table 2. Apart from the change of the sampling resolution, all other experimental parameters were the same as in the previous measurements (i.e., selection of the sound area next to each detected defect). Table 2. Depth estimations for the defects of Series A and B.
Def. No
Measured Peak Slope Time in s
Calculated Depth in ×10−1 mm
Error (%)
Def. No
Measured Peak Slope Time in s
Calculated Depth in ×10−1 mm
Error (%)
A5 A4 A3 A2 A1
0.0341 0.0341 0.0341 0.0341 0.0341
1.97 1.97 1.97 1.97 1.97
−1.5 −1.5 −1.5 −1.5 −1.5
B5 B4 B3 B2 B1
0.2045 0.1932 0.1818 0.2045 0.2159
4.82 4.69 4.55 4.82 4.96
20.5 17.2 13.7 20.5 24
As can be seen from the results in Table 2, by increasing approximately twice the temporal monitoring resolution, the error production is dramatically reduced. In particular, when studying the heat diffusion with a time step of 25 ms the error production for the defects of Series A was 15%, while by reducing this step to the value of 11 ms the error was calculated to be 1.5%. On the other hand, larger deviations were observed for series’ B defects which however are also reduced if compared with the previous analysis. As discussed in the previous analysis, the large deviations observed on series’ B defects can also be a result of the 3D heat conduction effect, nonetheless from the results in Table 2 it can be seen that a higher sampling frequency can partially overcome the above negative effect. 4.2. Selection of Sound Area As discussed above, an inappropriate selection of a sound area may affect the calculations for depth accuracy, making this decision a crucial parameter when depth estimations have to be performed. As a result, different procedures were followed for the respective depth measurements in both the time and frequency domain analyses. The plot of Figure 13b presents the thermal contrast slope evolutions to time for defect A1, after selecting three different sound areas as illustrated in Figure 13a. In particular, sound area 1 was selected next to the defect A1, while sound areas 2 and 3 were selected next to the top and vertical edges of the surface, respectively. As can be seen from this indicative plotting result, the different sound areas produced contrast slope evolution curves with different behaviours.
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Figure 13. (a) Thermal image of the inspected surface showing the regions from which sound areas Figure 13. (a) Thermal image of the inspected surface showing the regions from which sound areas Figure 13.3 (a) Thermal image of the inspected surface showing the regions fromA1; which areas 1,2, and were selected to calculate the slope of the thermal contrast for Defect andsound (b) temporal 1,2, and 3 were selected to calculate the slope of the thermal contrast for Defect A1; and (b) temporal 1,2, and 3 were selected to calculate the slope of the thermal contrast for Defect A1; and (b) temporal evolution of the correspondent thermal contrast slope curves. evolution of the correspondent thermal contrast slope curves. evolution of the correspondent thermal contrast slope curves.
Moreover, the above described procedure was repeated in the frequency domain. An indicative Moreover, above described procedureinwas repeated in the to frequency domain. An indicative indicative Moreover, plotting result the for the defect C4 is presented Figure 14. Similar time domain analysis, the same plotting result1,for analysis, the same same plotting result the defect is presented Figure 14.surface Similaras to atime domain the sound areas 2, and 3 wereC4 used as well asinthe overall sound area. analysis, The comparison of sound areas 1, 2, and 3 were used as well as the overall surface as a sound area. The comparison of sound areas 1,plots of Figure 14 is revealing that an enhanced similarity was producedcomparison the different regardless the the similarity was produced produced regardless the the different of Figure is revealing that an parameter enhanced similarity was regardless the selection of plots the sound area,14indicating that this has a negligible impact when working selection of the sound area, indicating that this parameter has a negligible impact when working with selection the sound area, indicating that this parameter has a negligible impact when working with phase data. phasephase data. data. with
Figure 14. Phase contrast profiles for defect C4 after selecting three different sound areas from the Figure 14. Phase profiles for defect C4 after selecting three different sound areas from the background and contrast the overall surface. Figure 14. Phase contrast profiles for defect C4 after selecting three different sound areas from the background and the overall surface. background and the overall surface.
4.3. Assessment of Correlation Factor C in Frequency Domain Analysis 4.3. Assessment of Correlation Factor C in Frequency Domain Analysis 4.3. Assessment of Correlation Factor C in Frequency Domain Analysis As presented in the Introduction, depth quantifications using phase data require knowledge of presentedfactor in theC,Introduction, phaseofdata knowledge the As correlation which rangedepth fromquantifications 1.5 to 2, with using the value 1.82require typically adaptedofin As presented in the Introduction, depth quantifications using phase data require knowledge the correlation factor C, which range from 1.5 to 2, with the value of 1.82 typically adapted in experimental studies. Nevertheless, when investigating anisotropic materials such as the present of the correlation factor C, which range from 1.5 to 2, with the value of 1.82 typically adapted in experimental studies. investigating anisotropic materials such asdepth the present CFRP panel, the aboveNevertheless, value may bewhen different, creating uncertainties on the acquired results. experimental studies. Nevertheless, when investigating anisotropic materials such as the present CFRP the above value may be different, uncertainties onathe acquired depth results. In thispanel, direction, the selection of the correlationcreating factor was assessed in graphical manner, plotting CFRP panel, the above value may be different, creating uncertainties on the acquired depth results. Inthe this direction, thezselection of the correlation factor wasmeasured assessed diffusion in a graphical plotting nominal depth of the insertions as a function of the lengthmanner, μ and retrieving the z of the insertions as a function of the measured diffusion length μ data. and retrieving thenominal slope ofdepth the produced linear function, after linearly fitting these experimental Figure 15 the slope of producedresults linearacquired function,from afterthe linearly fitting these experimental data. selecting Figure 15a presents thethe correlation two quantification procedures either presents the correlation results acquired from the two quantification procedures either selecting a
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In this direction, the selection of the correlation factor was assessed in a graphical manner, plotting the nominal depth z of the insertions as a function of the measured diffusion length µ and retrieving the Appl. Sci. 2018, 8, x FOR PEER REVIEW 18 of 22 slope of the produced linear function, after linearly fitting these experimental data. Figure 15 presents the correlation results acquired from thecolumn two quantification procedures eithersurface selecting sound area from the background (left plot) or selecting the entire as aa sound sound area area from the background (left column plot) or selecting the entire surface as a sound area (right column (right column plot). As stated above, the experimental data were fitted by a least square linear fitting plot). Asresulting stated above, the experimental data were fitted by a least square linear used fitting function to high correlation coefficients (0.98). Regardless of the procedure tofunction estimate resulting to high correlation coefficients (0.98). Regardless of the procedure used to estimate depth, the depth, the constant C was measured to be 1.69 in the former case and 1.71 in the the latter one the constant C was measured to be 1.69 in the former case and 1.71 in the latter one (between the range (between the range discussed above and very close to the value used in this study). From the discussed and very close to the value used this From graphical thea graphical above assessment of the correlation factor, it in can bestudy). seen that thethe value used inassessment this study of had correlation factor, it can be seen that the value used in this study had a low impact on the acquired low impact on the acquired results. However, if these graphically retrieved slopes were used for results. However, if these retrieved werewould used for depthaquantifications, the results depth quantifications, thegraphically results presented onslopes the tables provide greater accuracy than this presented on the tables would provide a greater accuracy than this derived using the value of 1.82. derived using the value of 1.82.
(a)
(b)
Figure 15. Correlation results after: (a) selecting a sound area from the background; and (b) selecting Figure 15. Correlation results after: (a) selecting a sound area from the background; and (b) selecting the entire surface as a sound area. the entire surface as a sound area.
5. Conclusions 5. Conclusions In the present study, a CFRP specimen with internal simulated delaminations of various sizes In the present study, a CFRP specimen with internal simulated delaminations of various sizes and and depth locations was investigated by means of PT for the retrieval of quantitative depth depth locations was investigated by means of PT for the retrieval of quantitative depth information. information. Hidden features located in a depth range from 0.2 mm to 1 mm and varying in size Hidden features located in a depth range from 0.2 mm to 1 mm and varying in size from 3 mm from 3 mm to 15 mm were quantitatively characterised using two different analysis procedures to 15 mm were quantitatively characterised using two different analysis procedures through which through which the impact of different analysis parameters was also assessed. The produced results the impact of different analysis parameters was also assessed. The produced results indicated that indicated that the two different analyses provided efficient depth estimations for the inserted the two different analyses provided efficient depth estimations for the inserted features, while the features, while the comparison of temporal and frequency domain quantification in terms of error comparison of temporal and frequency domain quantification in terms of error production showed production showed that frequency domain analysis produced measured depths closer to their that frequency domain analysis produced measured depths closer to their nominal values. Moreover, nominal values. Moreover, the quantification in the frequency domain was further improved by the quantification in the frequency domain was further improved by considering the entire surface of considering the entire surface of the panel as the sound area because the defective zones in the the panel as the sound area because the defective zones in the present case occupy a small region with present case occupy a small region with respect to the entire surface. Contrarily, when working with respect to the entire surface. Contrarily, when working with peak slope time and especially when an peak slope time and especially when an uneven heating application is presented, depth uneven heating application is presented, depth quantification may be performed selecting different quantification may be performed selecting different sound areas for depths determinations, sound areas for depths determinations, ensuring that both the defective and the sound area have ensuring that both the defective and the sound area have received the same amount of heat energy. received the same amount of heat energy. As regards the selection of the experimental and analysis As regards the selection of the experimental and analysis parameters, time resolution had a great parameters, time resolution had a great impact on the determination of the characteristic times used impact on the determination of the characteristic times used for depth estimations and this for depth estimations and this parameter produced large errors when defects near the surface have parameter produced large errors when defects near the surface have to be quantitatively to be quantitatively determined. On the other hand, as frequency is inversely proportional to time, determined. On the other hand, as frequency is inversely proportional to time, the temporal the temporal resolution had an impact on the frequency resolution as well. Contrary to temporal data resolution had an impact on the frequency resolution as well. Contrary to temporal data analysis, the analysis, the low frequency resolution impacted the results of the deeper defects, as the frequency low frequency resolution impacted the results of the deeper defects, as the frequency visibility range visibility range was lower for these features. was lower for these features. For the continuation of this research, and because these quantification methods require the value of thermal diffusivity α to be available, it is highly recommended to also assess the produced depth accuracy when this value is known. In such a manner, the impact degree of this parameter could be more accurately estimated. Moreover, based on this preliminary study, the application of
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For the continuation of this research, and because these quantification methods require the value of thermal diffusivity α to be available, it is highly recommended to also assess the produced depth accuracy when this value is known. In such a manner, the impact degree of this parameter could be more accurately estimated. Moreover, based on this preliminary study, the application of quantitative infrared thermography for depth prediction in different materials and/or for the characterisation of different defects would provide a clearer view in the assessment of these depth prediction methods. In this direction, a comparative study incorporating different methodologies for depth prediction, such as the Logarithmic Peak Second-Derivative Time method [41], techniques based on the development of numerical modelling [42], or the recently developed Pulse Compression Thermography [43–45], which has shown to provide results with enhanced SNR, can define more representatively the strengths and weaknesses of each quantitative technique. Acknowledgments: Authors would like to thank Prof. Xavier Maldague and Dr. Clemente Ibarra-Castanedo from Computer Vision and Systems Laboratory of Université Laval, for the providing of the raw pulsed thermographic data and more importantly for their continuous support and willingness to provide any information throughout the conduction of this research. Author Contributions: P.T. wrote the paper and designed and implemented the experimental case study presented above. M.K. supervised the present research study. Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. Table A1. Depth estimation using peak slope time.
Def. No
Measured Measured Peak Peak Slope Slope Time in s
Calculated Depth in ×10−1 mm
Error (%)
Def. No
Measured Measured Peak Peak Slope Slope Time in s
Calculated Depth in ×10−1 mm
Error (%)
A5 A4 A3 A2 A1
52.95 46.57 18.01 17.99 8.19
0.0254 0.0254 0.0254 0.0254 0.0254
1.70 1.70 1.70 1.70 1.70
−15 −15 −15 −15 −15
D5 D4 D3 D2 D1
0.15 0.29 0.17 0.07 N/D
0.7643 0.6624 0.6879 0.7643 N/D
9.32 8.68 8.84 9.32 N/D
16.5 8.51 10.6 16.5 N/D
B5 B4 B3 B2 B1
2.39 1.40 1.66 0.63 0.03
0.2547 0.2802 0.2547 0.2802 0.3057
5.38 5.65 5.38 5.65 5.89
34.5 41.25 34.5 41.25 47.4
E5 E4 E3 E2 E1
0.08 0.15 0.09 0.06 N/D
0.9936 0.9681 0.9171 0.9936 N/D
10.63 10.49 10.21 10.63 N/D
6.3 4.9 2.1 6.3 N/D
C5 C4 C3 C2 C1
0.57 0.94 0.41 0.34 0.10
0.4331 0.4076 0.4588 0.4076 0.4840
7.01 6.8 7.22 6.8 7.42
16.8 13.3 20.4 13.3 23.6
N/D: Not Detected.
Table A2. Depth estimation using blind frequency. Sound Area Top Left Corner Def. No
Nominal Depth in ×10−1 mm
Blind Frequency fb (Hz)
Measured Depth z in ×10−1 mm
A5 A4 A3 A2 A1
2 2 2 2 2
14.476 15.371 16.267 15.222 15.073
B5 B4 B3 B2 B1
4 4 4 4 4
3.730 3.880 3.880 3.581 3.880
Sound Area All Pixels Error (%)
Blind Frequency fb (Hz)
Measured Depth z in ×10−1 mm
Error (%)
1.74 1.69 1.65 1.70 1.71
−13 −15.5 −17.5 −15 −14.5
15.222 15.222 15.222 15.222 14.028
1.70 1.70 1.70 1.70 1.77
−15 −15 −15 −15 −11.5
3.44 3.37 3.37 3.51 3.37
−14 −15.7 −15.7 −12.2 −12.2
4.029 4.029 4.178 3.581 3.581
3.31 3.31 3.25 3.51 3.51
−17.2 −17.2 −18.7 −12.2 −12.2
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Table A2. Cont. Sound Area Top Left Corner
Sound Area All Pixels Error (%)
Blind Frequency fb (Hz)
Measured Depth z in ×10−1 mm
Error (%)
5.44 5.19 6.51 6.09 6.51
−7.3 −13.5 8.5 1.5 8.5
1.492 1.492 1.193 1.492 1.492
5.44 5.44 6.09 5.44 5.44
−7.3 −7.3 1.5 −7.3 −7.3
0.746 0.596 0.596 0.596 0.596
7.70 8.61 8.61 8.61 8.61
−3.7 7.6 7.6 7.6 7.6
0.746 0.596 0.746 0.596 0.596
7.70 8.61 7.70 8.61 8.61
−3.7 7.6 −3.7 7.6 7.6
0.447 0.447 0.447 0.447 0.596
9.94 9.94 9.94 9.94 8.61
−0.6 −0.6 −0.6 −0.6 −16.1
0.447 0.447 0.447 0.447 0.596
9.94 9.94 9.94 9.94 8.61
−0.6 −0.6 −0.6 −0.6 −16.1
Def. No
Nominal Depth in ×10−1 mm
Blind Frequency fb (Hz)
Measured Depth z in ×10−1 mm
C5 C4 C3 C2 C1
6 6 6 6 6
1.492 1.641 1.044 1.193 1.044
D5 D4 D3 D2 D1
8 8 8 8 8
E5 E4 E3 E2 E1
10 10 10 10 10
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