1. Introduction
Aluminum alloys, thanks to their low density and ability to resist corrosion, are widely used for manufacturing mechanical components and large structures and, in this regard, many examples can be found in different engineering fields from building to automotive and aerospace.
During the manufacturing processes or in-service conditions, several defects may appear in materials that can affect the structure and its mechanical properties. Therefore, it is very important to check the integrity of the components to reveal these defects.
Several non-destructive techniques (NDT) can be used to detect such defects such as X-ray, ultrasound [
1], eddy current [
2], magnetic method [
3] and penetrant test.
Wilczek et al. [
1] performed a comparison among different NDT techniques such as: X-ray, ultrasonic, eddy current and thermography to detect flaws in aluminum pressure die casting. Regarding the porosity detection in aluminum pressure die casting, the radiographic method allows for analyzing raw casting without surface preparation while eddy current and thermography are not suitable for the detection of fine porosity.
In the work of Postolache et al. [
2] a system architecture based on the eddy current method has been used to detect cracks on aluminum aircraft plates. In particular, superficial and sub-superficial cracks were detected by adopting image filtering techniques based on a 2D stationary wavelet transform, Wiener linear filtering and soft-thresholding.
A non-destructive testing method for thin-plate aluminum alloys based on the geomagnetic field has been proposed in the work of Hu et al. [
3]. This method allows for detecting the artificial groove and natural defects in thin-plate with a thickness of less than 2 mm.
In the case of large structures, it is required a rapid and easy inspection of the components in order to reduce the time of the ordinary maintenance and thus to limit the costs. In this regard, it is very important to develop automatic procedures and algorithms for data analysis to obtain very quickly, the quantitative characterization of defects.
Stimulated thermography [
4,
5,
6,
7,
8] presents the peculiarities suitable for investigation of large areas since it does not require the coupling with the component, is easily automatable and the testing time is relatively short with respect to other traditional well-established NDT techniques. Different thermographic techniques (Pulsed and Lock-in) [
4,
5,
6,
7,
8] and heat sources can be used to detect defects in large aluminum components.
Oswald-Tranta [
9,
10] demonstrated in her works that inductive pulse and lock-in thermography are capable in evaluating surface cracks also on non-magnetic materials such as aluminum. In particular, the lock-in approach improves the signal to noise ratio since a sequence of short pulses is applied. With the aim to detect similar defects, laser spot thermography and vibrothermography techniques were used in the work of Roemer et al. [
11]. In the paper, the effectiveness of the two presented methods has been demonstrated in evaluating very small defects.
In the work of Maldague et al. [
12] several defects were considered for the inspection of aluminum specimens by transient infrared thermography. Authors highlight as flash tubes with heat pulse energy of about 5–20 kJ are sufficient to thermally stimulate the material and a high frame rate is needed to better resolve the thermal process.
In the literature, authors focus their attention on the signal to noise ratio or signal to background contrast, neglecting the influence of the number of analyzed frames on this quantitative parameter. Hence, in this work, a comparison among different algorithms used for processing thermal data derived from a Pulsed thermographic test is provided with the aim of highlighting the strong and weak points of each algorithm in terms of signal to background contrast (SBC), number of detected defects, and the influence of the number of analyzed frames. Another important aim of this work is to demonstrate as a good correlation between two different parameters, the SBC and the aspect ratio r (diameter/depth), for estimating the size and the depth of defects.
The Pulsed Thermography (PT) technique has been applied on an aluminum specimen with flat bottom holes to simulate the presence of defects. Several algorithms have been implemented to elaborate raw thermal data: Pulsed Phase Thermography (PPT) [
12,
13,
14,
15,
16,
17], Thermal Signal Reconstruction (TSR) [
18,
19,
20,
21,
22,
23,
24], Principal Component Thermography (PCT) [
25,
26,
27,
28,
29,
30], Slope and Correlation coefficient (R
2) [
31,
32].
Results show as each algorithm has its own peculiarities and capabilities and a synergic action in defects detection and characterization can be obtained if more algorithms are applied on the same thermal sequence.
2. Theory: Pulsed Thermography
The basic approach of the active/stimulated thermography is based on inducing thermal waves within the specimen by means of an external heat source and monitoring the superficial temperature changes. In literature, there are three classical active/stimulated thermography techniques that differ for the heating source modulation: Pulsed Thermography (PT), Lock-in Thermography (LT) and Stepped Heating Thermography (SHT) [
4]. In each case, thermographic raw data provide few information about the presence of defects because of the low value of the signal to noise ratio. In this regard, a post-processing analysis is necessary to improve the quality of the results by means of different algorithms.
In this work, the PT technique has been used, and different post-processing algorithms were compared, starting from the same thermal sequence.
The PT technique consists of a short heat impulse using a power heating source. The presence of subsurface discontinues changes in the diffusion of heat flow and produces a change of cooling over time.
The one-dimensional solution of the Fourier’s Law for a Dirac delta heating pulse propagation through a semi-infinite homogeneous material is given by this following equation:
where
Q is the energy absorbed by the surface;
T0 is the initial temperature;
α is the thermal diffusivity and
e is the effusivity.
Considering the temperature evolution of the inspected surface, Equation (1) can be rewritten as (
z = 0):
That means a constant cooling slope of value 0.5 in log-log scale [
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32]. In the presence of a defect, Equations (1) and (2) are not valid anymore and a change in slope can be observed due to a different diffusion of thermal waves within the specimen.
Data acquisition in PT is fast and allows the inspection of wide area surfaces. However, as already said, raw PT data are difficult to analyze because of non-uniform heating or reflections. In the next paragraphs, the pre- and post-processing algorithms used to detect defects will be discussed in detail.
2.1. Post-Processing Algorithms: Pulsed Phase Thermography (PPT)
Pulsed phase thermography (PPT) [
12,
13,
14,
15,
16,
17] is a technique that transforms thermographic data from the time domain into the frequency domain using Fast Fourier Transform (FFT).
Any wave form, periodic or not, can be approximated by the sum of purely harmonic waves oscillating at different frequencies. The Continuous Fourier Transform (CFT) can be expressed as:
where
. For the PPT the Discrete Fourier Transform (DFT) is used working with PT data:
where
Re and
Im are respectively the real part and imaginary part of the transformed data, the subscript
n is the increasing frequency, ∆
t is the sampling interval;
N is the total number of thermograms (infrared images). The phase and amplitude maps are finally obtained using the following relation:
Amplitude and phase maps (
Figure 1) are obtained by repeating this process for all pixels (
x,
y) of the field of view. With
N time increments available (with
N corresponds also to the thermograms in the sequence),
N/2 frequency values are available (due to the symmetry of the Fourier transforms [
4].
The quality of the results depends on two important parameters, the sampling rate fs, and the acquisition time (tacq); i.e., the maximum truncation window w(t).
Theoretically, the sampling rate should be high enough to increase the available frequency (fmax = fs/2) and capture early thermal changes.
The truncation window w(t) should be as large as possible to increase frequency resolution and to be able to characterize a wide range of depths, especially deep defects that are detectable only at very low frequencies.
The material thermal properties are critical in the choosing of Δ
t and
w(
t). In fact, the much higher time resolution requirement on high conductivity materials is compensated in part by the need of a smaller truncation window. More frames had to be included for the aluminum to incorporate more data, especially at the beginning of the sequence, where thermal changes are critical. The number of frames
N could be further reduced without loss of pertinent information using a higher sampling rate with a shorter
w(
t) [
15].
Other details about the testing parameters for the PPT technique can be found in references [
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32].
The Fast Fourier Transform (FFT) algorithm, available in software packages such as MatLab®, greatly reduces the computation time and is therefore privileged. It should also be pointed out that the direct implementation of the DFT, as shown in Equation (3) above, requires approximately n2 complex operations. However, computationally efficient algorithms can require as little as n log2(n) operations.
5. Discussion
In the literature, there are several works that show a comparison among the different thermographic techniques and algorithms [
4] in terms of the capability to detect a defect [
32,
33,
34,
35,
36,
37]. However, most of them regard a qualitative evaluation of the results avoiding the quantitative characterization of defects that keep count of their size and depth.
This work proposes an attempt to evaluate the influence of the processed number of frames on the capability of the technique in quantifying the defects [
34]. In particular, a single pulsed thermographic test has been carried out (with three replications) on an aluminum specimen. This type of material has a high diffusivity and so the observed physical phenomenon ends within the first cooling frames. In order to test the right number of frames to choose, different sizes and depths of the imposed defects have been investigated; to detect the presence of superficial defects, few frames are enough to obtain a significant signal contrast. In contrast, deeper defects became visible after a few seconds and then a wider number of frames had to be considered [
37]. Moreover, the number of processed frames changed within different algorithms.
The first important result regards the R
2 algorithm. Indeed, only 32 frames are necessary to detect 19/20 defects (
Figure 11). The motivation could be ascribed to the behavior of the statistical parameter R
2: this parameter, in fact, depends on the shape of the cooling trend and on how it deviates from the linear theoretical trend if a defect is present (
Figure 2). If a large number of frames is considered for the processing, there could be a flattening of the observed phenomena with a consequent loss of sensitivity of R
2.
By using the PCT algorithm (
Figure 10) and the criterion of the signal contrast, the results are less dependent on the chosen number of frames. It is due to the fact that this processing procedure is based on enhancing the correlation between the variables, thus exalting the contrast between defect and sound in the first maps and leaving the noise in the subsequent ones [
27]. However, this algorithm does not provide any information about the depth position of the defects.
Another important result regards the slope and the amplitude parameters and a good linear correlation with the aspect ratio r (
Figure 19). In particular, the best correlation has been obtained in the correspondence of 512 frames for the PPT amplitude and for 1024 frames for the slope parameter. This means that among the proposed algorithms, the slope and PPT amplitude show the better correlation between the SBC value and the size and depth of the defects. In other words, the size and depth of a defect have similar influences on the SBC value.
The results obtained with the application of the TSR and the PPT phase algorithms, are more difficult to handling since they provide several data in different instants of time/frequency. In this regard, the SBC and then the sound standard deviation (noise) have to be evaluated in different data maps. The contrast between the defect and the sound (SBC) is much less especially for the PPT phase (
Figure 10 and
Table 2). The phase maps are connected with the frequencies of analysis and the last maps (high frequencies) are much noisier than the first [
23], and this evidence can have a noticeable impact on the choice of sound zone and on its evaluation. However, the main advantage of these algorithms, as well as the TSR one, is their capacity to estimate the depth of defects, if the thermal diffusivity of the material is known [
37].
A final comparison can be done among the traditional algorithms (PCT, TSR, PPT) and the new ones, R
2 and slope, which are still not used for a quantitative estimation of defects. These latter have shown remarkable results both in terms of the linear trend between the SBC and the aspect ratio r (and so the possibility to evaluate the size and the depth of a defect as explained in the
Section 4.4.1), and the capability to detect a good number of defects. Moreover, it is worth underlining the rapidity of these algorithms in obtaining results in terms of data maps [
31,
32].