Comparing the efficiency of defect depth characterization algorithms in the inspection of CFRP by using one-sided pulsed thermal NDT

Infrared Physics and Technology 107 (2020) 103289

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Comparing the efficiency of defect depth characterization algorithms in the inspection of CFRP by using one-sided pulsed thermal NDT

T

A.I. Moskovchenkoa,b, , V.P. Vavilova,c, A.O. Chulkova ⁎

a

Tomsk Polytechnic University, 30, Lenin Avenue, 634050 Tomsk, Russia University of West Bohemia, Univerzitní 2732/8, 301 00 Plzeň, Czech Republic c Tomsk State University, 30, Lenin Avenue, 634050 Tomsk, Russia b

ARTICLE INFO

ABSTRACT

Keywords: CFRP composite Defect depth characterization Thermal quadrupoles Active thermal NDT Neural network

The efficiency of eight algorithms of defect depth characterization (pulse phase thermography – PPT, thermographic signal reconstruction by analyzing the first and second derivatives– TSR, early observation – EO, apparent thermal inertia – ATI, thermal quadrupoles - TQ, non-linear fitting - NLF and neural networks – NN) has been comparatively analyzed on both theoretical and experimental IR image sequences obtained in the inspection of CFRP composite. Synthetic noise-free image sequences have been calculated by means of the ThermoCalc-3D software, while experimental results have been obtained by applying a one-sided procedure of pulsed thermal NDT to the inspection of artificial defects in CFRP. A relative error in the evaluation of defect depth has been chosen as a figure of merit. It has been demonstrated that a simple and robust processing technique is the use of the Fourier transform resulting in phase-domain data (PPT). The technique of TSR ensures maximal values of signal-to-noise ratio and is less susceptible to uneven heating and lateral heat diffusion. The calculation of ATI has allowed the characterization of defects at depths up to 1.5 mm, but it is sensitive to uneven heating thus requiring to carefully choose a non-defect area. The EO method, as well as the technique of TQ, have revealed inferior results in defect depth identification because of a noisy character of raw signals. Nonlinear fitting is a convenient processing technique allowing simultaneous characterization of some test parameters, such as material thermal properties, defect depth and thickness, etc., but this technique is time-consuming and can hardly be applied to full-format images. In the whole defect depth range, minimal characterization errors have been ensured by the use of the NN that is a promising tool for automated identification of hidden defects.

1. Introduction Carbon fibre reinforced plastic (CFRP) is a composite commonly used in high-tech industries, such as aviation, nuclear engineering, car production, building, etc. This is a high-strength and low-mass material composed of a polymer matrix and carbon fibres. There are many types of CFRP with different binding polymers and orientations of fibres. The CFRP samples used in this study were made of a unidirectional carbon fiber fabric and standard filling KPR-150 (Russian standard TU 2225012-93660864-2009). Hidden defects, which inevitably appear in composites at both the manufacture and exploitation stages, may seriously affect CFRP strength thus endangering work performance of this composite, in particular, its lifetime [1]. Typical structural defects in CFRP are delaminations, which may represent either thin air gaps or conglomerates of multiple cracks. Such

⁎

defects appear if a composite has been subjected to various types of impact: mechanical, electrical, water ingress, etc. Certain repair works should follow the detection of defects classified as severe thus requiring to evaluate defect numerical characteristics, i.e. to perform defect characterization. Defect lateral size is a critical parameter, for instance, in aviation. The knowledge of defect depth is important when injecting adhesives or removing some layers of the composite and placing patches [2]. The most usable techniques of nondestructive testing (NDT) are ultrasonic, X ray and thermal, or infrared (IR) thermographic. Ultrasonic NDT is still the most trust-worthy practical technique [2], while thermal NDT is becoming increasingly popular in the last decades being regarded as a rather screening inspection method [3,4]. This method is efficient in the detection of many types of defects, which are typical for composites, and it is non-contact, high productive and illustrative. There are many approaches to determining defect depth in

Corresponding author at: Tomsk Polytechnic University, 30, Lenin Avenue, 634050 Tomsk, Russia. E-mail addresses: [email protected] (A.I. Moskovchenko), [email protected] (V.P. Vavilov), [email protected] (A.O. Chulkov).

https://doi.org/10.1016/j.infrared.2020.103289 Received 21 January 2020; Received in revised form 19 March 2020; Accepted 23 March 2020 Available online 30 March 2020 1350-4495/ © 2020 Elsevier B.V. All rights reserved.

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active thermal NDT (TNDT) procedures [5–8]. Most of them are based on the analysis of temperature evolutions in time. For example, in onesided test procedures, the indications of deeper defects appear with a greater time delay; this principle is used, for example, for producing thermal tomograms. The review of data processing techniques in pulsed thermography can be found elsewhere [9]. Most studies related to IR thermographic techniques have used signal-to-noise ratio (SNR) or probability of detection (POD) as figures of merit for the evaluation of defect detection efficiency [10–17], and few works have analyzed efficiency of defect characterization. The aim of this study is an experimental comparative analysis of several approaches intended for defect depth characterization, including some known techniques, such as pulse phase thermography (PPT), thermographic signal reconstruction (TSR), early observation (EO), apparent thermal inertia (ATI), thermal quadrupoles (TQ), as well as some relatively new data processing algorithms, namely, artificial neural networks (NN) and nonlinear fitting (NLF).

where A is the coefficient varying from 1.5 to 2 (in the case of CFRP A = 1.73 [5]). The Fast Fourier transform (PPT technique) performs transition from the time domain to the frequency domain, where phase images are typically analyzed. A blind frequency can be defined as the frequency at which the phase contrast ΔΦ between the defect and non-defect area tends to zero. In practice, a certain phase threshold applied to ΔΦ/Φnd is usually chosen (2% threshold in this study). Since blind frequencies cannot clearly be defined for experimental data because of noise, they have been defined in this study as the maximum frequencies at which SNR values for the corresponding defects exceeded 1.5. 2.2. Apparent thermal inertia (ATI) method In the ideal case, experimental values of thermal inertia e determined by Eq. (1) at several time points as e = Q / T ( ) should represent a horizontal line if a test body can be regarded as semi-infinite and adiabatic. Balageas et al. suggested evaluating pixel-based apparent thermal inertia as a significant parameter indicating the presence of subsurface defects, which disturb thermal effusivity evolution [19]. In real bodies, one should follow the function e (i,j)/end where the subscript “nd” specifies a non-defect area. This function is close to a straight line of whose deviations correspond to subsurface defects. For example, thermally resistive defects cause a diminution of apparent e (τ) values (Fig. 1). Defect depth can be determined by the formula [12]:

2. Defect depth characterization Some simple defect characterization formulas follow from the classical heat conduction solutions describing flash heating of adiabatic solid bodies. The following formula relates to a semi-infinite adiabatic body:

T 1 = W e

;

e=

C k

(3)

l = Aµ = A ( / fb ),

(1)

Here T is the surface temperature, W is the absorbed energy, e is the thermal inertia, C the heat capacity, is the density, k is the thermal conductivity, and is the time. A basic principle of TNDT is that subsurface defects disturb a regular flow of the heat flux in a body under test and cause the appearance of T ( ) signals, which depend on thermal stimulation parameters Q ( ) , as well as on defect/body geometric characteristics and material thermal properties. An unpleasant feature of TNDT is that T ( ) is linearly proportional to Q ( ) that makes measurement of temperature amplitude on the test object surface unreliable. Therefore, in TNDT, one often deals with either some types of contrast, such as C ( ) = T ( )/ T ( ), or analyzes peculiarities of the T ( ) behavior in time. For example, in the log-log presentation of Eq. (1), the plot of temperature vs. time is a straight line with the −1/2 slope, and any deviation from this line may be associated with hidden defects. However, real procedures of TNDT are characterized by plentiful clutter and noise, and the usefulness of simple analytical approaches is limited.

l=

min

(4)

(e/ end)0.95 min

where min is the time when the ratio e/ end acquires its minimum value. The concept of defect characterization by determining material thermal inertia has been extended by Sun onto thermal tomography [20,21]. Eq. (1) has been modified to allow determining a 3D pixelbased thermal effusivity as a function of three spatial coordinates:

e (x , y , z ) =

d d

Q T (x , y , )

,

with the coordinate z being evaluated by the simple expression:

z=

(6)

.

2.3. Early observation (EO) Classically, in a front-surface TNDT procedure, the evolution of

2.1. Pulse phase thermography (PPT) To some extent, the technique of PPT proposed by Maldague and Marinetti unites advantages of pulsed and thermal wave TNDT [18]. Any type of thermal stimulation function, including a short pulse, or flash, can be represented as a sum of harmonic waves. It is convenient to consider the propagation of single waves in a solid and their interaction with structural inhomogeneities (defects). Each wave is characterized by amplitude, frequency ω, thermal diffusion length μ and velocity v:

µ=

2

;

v=

2

(5)

(2)

High-frequency thermal waves propagate faster but at shorter distances. To detect a flaw at a certain depth, the length of thermal diffusion should be comparable to the defect depth. By other words, deeper defects should be detected with slower thermal waves. By varying frequency, it is possible to determine the so-called “blind” frequency fb associated with the defect depth l. The defect characterization formula has been suggested in the following form [5]:

Fig. 1. Evolution of apparent thermal effusivity. 2

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T ( ) over a subsurface defect starts from zero, then reaches an extremum (maximum or minimum) value and finally decays up to zero. Since heat conduction is a process of diffusion, the longer is observation times the stronger defect temperature ‘footprints” smash. By other words, surface defect indications better reproduce defect shape and size at earlier observation times. The corresponding defect characterization method proposed by Krapez and Balageas requires evaluating defect parameters at the time when the T ( ) signal starts to exceed the noise [22]. The characterization formula is: l=

the layers, the matrix quadrupole equation is as follows [30]: f

Q

where

where min (Crun) is the time when the running contrast Crun = T / Tnd is observed by applying a contrast threshold from 1 to 10%. The formula above has been précised in the following form [22–24]:

l=

1% /0.5655

and l =

5% /0.7291,

A1 B1 A B 1 Rd · · 2 2 · r , C1 A1 C2 A2 0 1 0

Aj = cosh(l j p / j ); Bj = 1/(kj p /

(10) j

) sinh(lj p/ j );

Cj =

kj p / j sinh(l j p / j ); j = 1 and 2 for the first and second layers respectively, θf,θ r are the Laplace temperatures on the front and rear sample surfaces, Q is the absorbed flash energy, Rd is the defect thermal resistance, li is the thickness of the i-th layer, p is the Laplace variable. By solving Eq. (10), one obtains the differential Laplace temperature signal Δθ (Laplace analogue of ΔT). On the sample front surface [30]:

(7)

min (Crun ) ln (2/ Crun ) ,

=

f

(8)

=

QRd sinh2 (l2 p/ ) sinh(L p / )·(sinh((L p/ ) + k p/ · Rd sinh(l1 p / ) sinh(l2 p / )

,

(11)

where τ1% and τ5% are the times when T starts to exceed the noise level by 1 and 5%. A combination of both times has allowed reducing the influence of defect thermal resistance on determining defect depth [25]. In this study, because of a high noise level, Eq. (7) has been used for defect depth characterization with the contrast threshold of 10%.

where L is the sample thickness. The discrete Laplace transform can be applied to a temperature signal in the dimensionless form: imax

m (p ) =

T ( i ) exp( p

i

)

(12)

i=1

2.4. Thermographic signal reconstruction (TSR)

2

2

with the following dimensionless parameters: τ*=ατ/l ; p*=l p/α. Eq. (12) allows determining m values for different Laplace variables p*. By algebraically solving the corresponding equations in the Laplace domain, the following formula for evaluating defect depth has been suggested [31]:

The TSR technique is based on processing temperature derivatives d (ln(T))/d(ln(τ)) and d2(ln(T))/d(ln(τ))2 in the time domain [26,27]. According to Eq. (1), the first temperature derivative starts from −1/2 and decays up to zero when the body temperature approaches the ambient one. In a one-sided test, thermal energy is storing over a thermally insulating defect thus changing the derivative behavior, and, when the defect disturbance is vanishing, the derivative is getting back to the non-defect one. The inversion formula is similar to Eq. (8):

z=1

1 p1

ln

m2 m1

1/2

cosh( p1 ) +

m2 cosh2 ( p1 ) m1

1/2

1

, (13)

where τw is the time of the maximum second logarithmic derivative (see the example in Fig. 2).

where m1 and m2 are the Laplace transforms for p1* and p2* (p2*=4p1*), z = l1/L. Fig. 3 illustrates the algorithm of depth evaluation by using the TQ method.

2.5. Thermal quadrupoles (TQs)

2.6. Non-linear fitting (NLF)

The Laplace transform is a common tool for solving differential equations. In many practical cases, one could stay in the Laplace domain where analytical expressions appear in an evident form thus introducing a concept of “Laplace temperature”. In 1921, Carslaw suggested to replace the heat conduction equation along with the initial and boundary conditions by linear matrix equations thus allowing efficient analysis of multi-layer structures [28]. By using modern computers, the corresponding calculations can be fulfilled in both the Laplace and true temperature domains. The technique of TQs and their use in TNDT was thoroughly summarized by Maillet et al [29]. For a 1D two-layer plate with a thermally resistive defect between

In one-sided TNDT, there is a strong correlation between material diffusivity α and sample thickness L (defect depth l), on one hand, and characteristic observation times, on the other hand. In fact, it is impossible to identify separately the α and L2 parameters which constitute the Fourier number Fo = ατ/L2. Respectively, some analytical multiparametric models implementing a concept of NLF have been proposed to evaluate either material diffusivity or sample geometric characteristics [32–35]. Such models can be analytical or numerical, and the fitting can be performed in the time- or Laplace-domain by applying a least-square technique to minimize a difference between theoretical and experimental data [36,37].

l=

w,

(9)

Fig. 2. Temperature evolution in log-log scale (a), first (b) and second (c) derivatives. 3

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Fig. 3. Defect depth evaluation by using the TQ method.

Fig. 4. Artificial neuron.

Fig. 5. Neural network scheme. Table 1 Model description. Parameters

Material

.

−1. −1

k- thermal conductivity, W m K α – thermal diffusivity, m2.s−1 ρ – density, kg.m−3 C – heat capacity, J.kg−1.K−1 Thickness, mm Defect depth, mm

CFRP

Air

0.56 2.23 × 10−7 1487 1688.8 5 –

0.07 (thin gaps) 5.8 × 10−5 1.3 928.4 0,1 0.5, 1, 1.5, 2, 2.5

In this study, a 1D two-layer analytical model involving a thermal resistance between layers has been analyzed by using the technique of TQs. The front-surface Laplace temperature was found by solving Eq. (10), and the inverse Laplace transform was performed by applying the Gaver-Stehfest algorithm to return to real temperatures. The model included the thermal conductivity, diffusivity and thickness of each layer, as well as the defect thermal resistance and input energy. The unknown parameters were input energy and defect depth (thickness of the first layer). The algorithm provided a best-fit function by Eq. (10) to a given set of experimental data by minimizing the sum of squares of the offsets between experimental and theoretical data. The operation of the fitting algorithm in application to numerical and experimental data will be illustrated below. Fig. 6. Presentation of data used for the training of NN: location of training pixels on the image of temperature derivative (a) and corresponding temperature derivative curves (b).

2.7. Neural networks (NNs) A NN represents a system of interconnected artificial neurons, 4

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Fig. 7. Presentation of synthetic IR thermograms at different observation times (CFRP sample, 5 air-filled defects) at depths of 0.5, 1, 1.5, 2 and 2.5 mm from left to right respectively):

which include a number of inputs with pre-described weights, an activation function and an output. Input signals are multiplied by particular weights and summed up to be afterwards processed with the activation function and then used as the output signals (Fig. 4). A basic advantage of NNs is that, by properly choosing the weights, one can establish complicated relationships between input and output data. Neural networks can effectively be used for both defect detection [38] and characterization [39]. A two-stage algorithm described in [40], first, provides the discrimination between defect and sound areas and, second, allows the estimation of defect depth. Raw pixel-based temperature evolutions can be used as input data, although some data processing algorithms, such as the Fourier transform, principal component analysis, polynomial approximation et al., can reduce input data

size and thus improve defect characterization efficiency. In this study, the input data has been formed as the sequences of the temperature first derivatives (TSR technique); this approach allows high detection efficiency [41]. A NN with a direct propagation of signals, including 3 hidden layers with 15, 15 and 5 neurons with a sigmoidal activation function has been used [41]. The output layer contained a linear activation function, as shown in Fig. 5. The number of layers, neurons and input data features were chosen by trial to reach a compromise between computation time and accuracy. The neural network was trained by feeding it with a set of data which contained both theoretical and experimental results of three test cases (Fig. 6). Each input variable represented a pixel-based value of the logarithmic derivative of temperature (see Section 2.4) which 5

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corresponded either to a true defect depth or material thickness (in “non-defect” pixels). Fig. 6 illustrates the process of choosing input data for training the NN. The training dataset included 100 values of each defect depth and 2000 “non-defect” values extracted from three experimental and one synthetic sequence (400 variables for each depth and 8000 for non-defect). Each variable contained 491 data points. The efficiency of the NN was verified on complementary experimental data obtained by using a similar test setup. 3. Modeling The efficiency of the above-mentioned algorithms in application to defect depth characterization has been analyzed on both theoretical and experimental data. Theoretical temperature profiles have been calculated by using the ThermoCalc-3D software intended for modeling 3D heat conduction in multi-layer solids with discontinuity-like defects. A standard TNDT test has been applied to a 200 × 200 × 5 mm sample made of carbon fiber reinforced plastic (CFRP). The sample contained five 20 × 20 × 0.1 mm air-filled defects, and thermal properties of all materials are given in Table 1 (determined experimentally on the sample described below by using the Parker method). Note that, for the simplicity of the analysis, the CFRP composite has been taken isotropic, i.e. kx = ky = kz. The sample was heated with a square pulse (heating time τh = 0.1 s, power Q = 50 kW.m−2). Pixel-based temperature evolutions have been calculated with a 0.1 s time interval for 20 s thus producing an image sequence including 200 synthetic IR thermograms. For defect characterization, only the image points located over defect centers have been analyzed. It is worth noting that simulation results obtained with the above-mentioned parameters (τh and Q) are identical to those obtained, for example, for τh = 0.01 s and Q = 500 kW.m−2, if defect optimum observation times are, at least, five times longer than τh. Fig. 7

Fig. 8. CFRP reference sample (PTF inserts placed between carbon fabric layers).

Fig. 9. Features of defect depth characterization algorithms applied to synthetic IR image sequences: a – determining “blind” frequency (PPT), b – evolution of apparent thermal inertia (ATI), c – evolution of thermal contrast (EO), d – evolution of 1st derivative (TSR), e – evolution of 2nd derivative (TSR), f – Laplace transform of ΔT(τ) (TQ), g - nonlinear fitting by the analytical model (1.5 mm-depth defect) (NLF), h – 1st temperature derivatives and training scheme (NN). 6

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Fig. 9. (continued) Table 2 Defect depth characterization (synthetic IR image sequences). True defect depth, mm

Depth estimate, mm/relative error, % PPT

ATI

EO

TSR, 1st derivative

TSR, 2nd derivative

TQ

NLF

NN

0.5 1 1.5 2 2.5

0.55 1.08 1.6 2.07 2.92

0.54 0.99 1.47 1.83 2.04

0.46 1.02 1.57 2.14 2.76

0.68 1.08 1.59 2.08 2.6

0.47 0.73 1.02 1.46 1.92

0.49 1.96 1.6 1.7 4.5

0.45 1 1.49 2.06 2.78

0.5 1 1.5 2 2.5

Fig. 10. Relative errors of applying defect depth characterization algorithms to synthetic IR image sequences (negative error values specify lower depth values).

illustrates a classical feature of one-sided TNDT: after flash heating, defect indications appear at time delays dependent on defect depth and experience both diffusion in space and retardation in time.

PTF inserts, they reasonably reproduce air-filled gaps used in the modeling (see Table 1). Thermal stimulation was performed with 2 flash tubes (total energy 14 kJ, pulse duration about 10 ms). IR thermograms were recorded by means of a FLIR A325sc thermal imager in two modes differed by the acquisition frequency (10 and 57 Hz) and process duration (120 and 20 s respectively) that is explained by a quadratic dependence of time parameters on defect depth and the necessity to use a long observation time when applying the Fourier transform. Test results have been

4. Experimentation Experiments have been performed on a 6.2 mm-thick CFRP sample made by using a technique of manual forming of composites. The sample consisted of 25 layers of a carbon fabric with a thickness of 0.2 mm each. The defects were simulated with 0.05 mm-thick folded polytetrafluoroethylene (PTF) film placed between fabric layers (Fig. 8). Note that, due to the folding and non-stick properties of the 7

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beginning of the process that is conditioned by the finite duration of the heat pulse. Note that both models become identical for times longer than 0.5 s, i.e. five times longer than τh = 0.1 s. For the deeper defects, the lateral heat diffusion leads to increasing errors (higher than 10% for l = 2.5 mm) because all algorithms applied are essentially 1D. The best results, except using the NN algorithm, are provided by the TSR technique since maximum derivative times are less sensitive to heat diffusion. In the case of the PPT technique, errors are greater for shallower defects because such defects require higher probing frequencies. It is worth mentioning that the TSR technique using the second time derivative, as suggested in [6] for steel samples, in our case has produced more accurate estimates only for l = 0.5 mm. It seems that the characterization of deeper defects in low-conductive materials might be more efficient by using the first temperature derivative. Eq. (11) has proven to be the worst in the evaluation of defect depth. In this case, there is no strict rule for choosing two values of p1* and p2* (p2*=4p1*), and retrieved values of l = h, are different. The p1* values have been chosen in the range from 0.5 and 5 with the optimum value being p1* = 1.5, as used below in Table 3. The analytical method (NLF) has proven to be the best from the point of view of estimation accuracy, except using a NN, but it is bulky and time-consuming. Therefore, it can hardly be used for evaluating full-format images. The use of a NN for processing synthetic data at points located over defect centers represents a special case where estimation errors tend to zero. However, such NN can scarcely work on experimental data corrupted by noise, uneven heating and complicated sample geometry. Therefore, NNs are to be trained on experimental data obtained on such reference samples which simulate potential test cases as close as possible.

Table 3 Defect depth characterization (experimental data). True defect depth, mm

Defect depth estimate, mm/relative error, % PPT

ATI

EO

0.5 1 1.5 2 2.5

0.51 1.1 1.7 2.4 –

0.62 0.98 1.28 – –

0.68 0.82 1.1 – –

TSR, 1st derivative 0.72 1.19 1.51 1.9 –

TSR, 2nd derivative -* 0.84 1.1 1.6 –

TQ

NLF

NN

0.82 1.2 – – –

0.59 0.97 1.59 – –

0.52 1.07 1.62 2.16 –

* Defect not detected, or too noisy data for quantitative evaluation.

Fig. 11. Infrared thermogram of test sample at 1.1 s after heating.

processed by means of the ThermoFit Pro and MatLab software. Defect depth was evaluated only for 20 × 20 mm inserts thus not taking into account the lateral size of defects. Background subtraction was applied in all cases before further data processing. 5. Defect depth characterization by synthetic data

6. Defect depth characterization by experimental data

Fig. 9 illustrates the features of all characterization algorithms applied to numerical data (synthetic IR image sequences), and the corresponding defect depth estimates are presented in Table 2. The relative error of depth evaluation methods was calculated as (hhtr)/htr·100%, where htr and h are the true and predicted defect depth values respectively. Fig. 10 shows relative errors of defect depth characterization calculated for the data in Table 2. It follows from Table 2 and Fig. 10 that most of the used algorithms ensure characterization errors under 10% for the defects at depths from 0.5 to 2 mm. It is interesting noting that the errors are greater for the depth of 0.5 mm that is explained by the finite duration of the heat pulse and the relatively low acquisition frequency (10 Hz in this case). For example, the temperature evolutions for the numerical and analytical models shown in Fig. 7 reveal a certain discrepancy at the

The characterization formulas above follow from 1D heat conduction solutions and do not take into account lateral heat diffusion, therefore, the temperature over defect centers has been considered. Fig. 11 illustrates the choice of defect areas in the ThermoFit software. First, defect areas have been chosen, then, the 5x5 pixel regions have been determined automatically as the highest signal regions. The reference areas have been chosen manually and separately for each defect because of the presence of the non-uniform heating phenomenon. Thus, a maximal temperature has been supposed to correspond to the maximal temperature over a particular defect. Fig. 12 shows raw and fitted (by the polynomial) temperature profiles. The fitted curves have been used with the TSR, ATI and EO

Fig. 12. Raw experimental temperature profiles in log–log scale before (a) and after (b) polynomial fitting. 8

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Fig. 13. Examples of experimental results: a – apparent thermal inertia map (3 s after heating), b – Fourier phasegram (frequency 0.018 Hz), c – 1st derivative image (3.2 s after heating), d – 2nd derivative image (1.7 s after heating).

(Table 3), shallow defects (l < 1 mm) should be evaluated by using the second derivative, while the first derivative is more appropriate for deeper defects providing the best accuracy of estimation. The PPT method allows identification of defect depth using a simple formula, but it is significantly affected by lateral heat diffusion. Also, unlike thermal inertia and temperature derivatives, “blind” frequencies can hardly be determined automatically. In their turn, the techniques of EO, ATI and TQs are strongly susceptible to uneven heating phenomena thus requiring to carefully choose a non-defect area. Uneven heating patterns can be smoothed by performing image normalization, but, as mentioned above, the division of noisy signals increases high-frequency noise. Fig. 15 illustrates the features of all 8 algorithms applied to the experimental data. The quantitative evaluation of 8 defect depth characterization algorithms applied to experimental data is presented in Table 3 and Fig. 16. The NLF technique is typically applied to raw temperature evolutions, therefore, it seems to be inefficient for the analysis of deeper defects, which produce noisy signals (see the end of the process in Fig. 15g). However, its advantage is the possibility to simultaneously evaluate not only defect depth but also material thermal properties, absorbed energy, heat exchange coefficient, etc. It seems that optimal characterization results can be ensured by using a NN for automated detection of defects and estimation of their parameters. However, the image of defect depth (“depthgram”) shown in Fig. 15e reveals plentiful false indications. The presence of noise and lower amplitude signals from deeper defects may lead to identification of non-defect points as belonging to defect areas. For example, the NN developed in the framework of this study has not been able to correctly identify defects with varying thermal resistance located in different materials and subjected to different types of thermal stimulation. Probably, this problem can be solved by training NNs on extended datasets but this may worsen characterization accuracy [34].

Fig. 14. SNR values for 4 characterization algorithms vs. defect depth.

techniques. The data smoothing has been necessary because a division operation tends to enhance the high-frequency noise adherent to temperature profiles thus making the determining of inflexion points difficult. Raw data has been used with other characterization algorithms. Fig. 13 shows examples of processed experimental IR thermograms. The observation times for each thermogram shown correspond to the maximum value of SNR for the 3rd defect (1.5 mm depth). The SNR magnitudes have been calculated by determining both signal mean values and standard deviations across areas chosen by the operator over the defects and in the neighborhood. It is worth noting that the concept of SNR is well applicable to only 4 characterization algorithms presented in Fig. 13 because the EO technique analyses temperature contrasts at low SNR levels while other algorithms deal with temperature profiles in defect areas only. Fig. 14 shows a comparison of SNR values for 4 defect depths and 5 processing methods (including the raw image with the subtracted background). The defect at the depth of 2 mm has been identified only by applying the techniques of PPT and TSR with the latter one providing the highest SNR. As mentioned above and confirmed experimentally

7. Conclusion In this study, the efficiency of eight algorithms of defect depth characterization has been comparatively analyzed on both theoretical and experimental IR image sequences obtained in one-sided TNDT of CFRP composite. The universal technique, i.e. applicable to any set of raw data, has seemed to be PPT. The technique of TSR ensures maximal values of signal-to-noise ratio and is less susceptible to uneven heating 9

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and lateral heat diffusion. However, the use of the second derivative has been inappropriate for deeper defects and/or low-conductive materials (defect depth l greater than 1 mm in CFRP), while the first derivative has proven to be more efficient in this case. The technique of ATI has allowed the characterization of defects at depths up to 1.5 mm, but it is sensitive to uneven heating patterns thus requiring to carefully choose a non-defect area. The EO and TQs methods have revealed inferior results of defect depth identification because of a noisy character of raw signals. Non-linear fitting is a convenient processing technique allowing simultaneous identification of some parameters, such as material thermal properties, heating characteristics, etc., but this technique is time-consuming and can hardly be applied to full-format images. Also, the fitting has not allowed evaluating defects in CFRP at depths greater than 2 mm. The best defect characterization results have been provided

by using the NN. This technique is promising for automated identification of hidden defects. However, choosing a NN requires proper training on plentiful datasets covering many practical test cases, as well as optimizing NN type and architecture. Funding sources This study was supported by Tomsk Polytechnic University Competitiveness Enhancement Program (scientific equipment), as well as by the Russian Foundation for Basic Research grant # 19-29-13004 (experimentation) and the Russian Science Foundation grant # 19-7900049 (data processing).

Fig. 15. Features of defect depth characterization algorithms applied to experimental IR image sequences: a – determining “blind” frequency (PPT), b – evolution of apparent thermal inertia (ATI), c – evolution of thermal contrast (EO), d – evolution of 1st derivative (TSR), e – evolution of 2nd derivative (TSR), f – Laplace transform of ΔT(τ) (TQ), g – nonlinear fitting by the analytical model (1.5 mm-depth defect) (NLF), h – defect depth map (NN).

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Fig. 16. Relative errors of applying defect depth characterization algorithms to experimental data (negative error values specify lower depth values).

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