Real-time nondestructive testing of composite aeronautical structures with a self-adaptive ultrasonic technique

The experimental set-up used throughout the paper is described in figure 1. It consists in a MultiX parallel acquisition system with 128 channels, and a computer that drives both the system and a linear motorized positioning system to set the probe position. The part under testing is an aeronautical CFRP stringer and the main objective is to control its curved part, also called 'corner radius'. The thickness and the length of the composite are 5 and 380 mm, respectively, and the curvature radius of the front interface is approximately 14 mm (this curvature radius is not rigorously constant along the corner radius). The probe is a linear transducer array (with a central frequency of 5 MHz) composed of 128 elements of 0.5 × 8 mm², with 0.6 mm pitch. In practice, only 42 active elements are used in this section to inspect the curved part of the component. This probe is immersed in the tank over the convex surface, with a water path of 16 mm. Note that, in this section, the SAUL method is introduced for a fixed position of the probe. Real-time results will be presented in the next section by translating the transducer array along the corner radius.

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The paintbrush acquisition mode consists in transmitting a plane wave by firing with the full array and in recording the elementary signals in parallel with all the elements. The experimental Bscan-channels image (channels/time) acquired with the MultiX system is displayed in figure 2(a) (no electronic scanning has been used in reception). We can observe the front surface echo between 22 and 24 µs (see the time of flight curve in figure 2(b)), while the back surface echo is not visible. Since the incident wave is not in the direction normal to the surface, the successive plies inside the material (each ply being approximately parallel to the surface) refract the transmitted field during its propagation and practically almost no energy reaches the back surface. This results in a poor image where both the plies and the back interface of the corner radius can not be identified.

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The incident wave can be partially adapted to the surface according to the processing described in [2] and [6, 7]. First, the times of flight between all the elements of the array and the surface are measured (for instance, by detecting the maxima of the surface echo envelope). Then, these times of flight are used to extract a delay law that will be applied to a second shot. Denoting by t_i the time of flight between an element i and the surface (1 ≤ i ≤ 42), the transmission delay applied to this element is defined by

$$\begin{equation} E_i = \case{1}{2}[ {\max( {t_i }) - t_i }]. \end{equation} \tag{ 1 }$$

A reception delay law can also be applied in order to synchronize each received signal and, for instance, to create several coherent summations of signals using an electronic scanning of a sub-aperture. The reception delay applied to an element i is deduced from the transmission delays as follows:

$$\begin{equation} R_i = \max( {E_i }) - E_i . \end{equation} \tag{ 2 }$$

By applying the transmission and reception adaptive delay laws to the second ultrasonic shot, the new Bscan image in figure 3(a) is obtained. The delay laws are displayed in figure 4(a) and are deduced from the times of flight plotted in figure 2(b). Compared to the first acquisition, the back surface echo can now be identified, which confirms that the delay law calculated with (1) transmits the incident wave with a wave front almost parallel to the front surface. The anisotropy effects due to the fibrous nature of the material are minimized by forcing a normal incidence transmission. However, as the incident wave is not completely adapted to the front surface, the back surface echo has a low amplitude level and the internal composite structure still can not be identified (the plies are not clearly visible). In addition, the elementary signals are not accurately synchronized, which could result in a poor image if an electronic scanning with a sub-aperture of several elements was used in reception.

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For a geometry as complex as a corner radius, the incident wave is not perfectly adapted to the surface since the times of flight used in the delay law computation are not specular (a specular time of flight corresponds to the path along the ray passing through the center of an element and normal to the surface). A technique for measuring these specular times of flight consists in using an electronic scanning in transmission with a sub-aperture and a scanning step of 1 element (all the elements are excited separately, and the same element is used as transmitter and receiver for each shot).

Figure 4(b) shows the new delay laws, obtained with the same experimental set-up. The only difference lies in the times of flight that now correspond to specular paths. Their measurement requires a cycle of 42 shots since the transducer array is composed of 42 active elements. Next, these delay laws are applied to one last shot (transmission once with all the elements). In figure 3(b), one can see that the individual signals are now time coherent (the front surface echo is horizontal), which means that the incident wave is ideally adapted to the geometry. The ply echoes now can be observed.

This method thus provides the optimal delay laws to achieve a normal incidence transmission into the material. However, in its current state, it can not be applied to industrial controls for two reasons. First, since a single element is used at each transmission, the amplitude level of the surface echo is much lower than the one obtained by transmitting with the full array and times of flight may be difficult to be measured. Second, the large number of shots (43 in the present case) may dramatically decrease inspection rates compared to a conventional paintbrush acquisition mode.

The SAUL method is an iterative processing of a conventional paintbrush acquisition. The processing thus begins with the transmission of a plane wave by simultaneously firing with all elements and recording individual signals in parallel separately with the full array. As previously described, the adaptive delay laws are then calculated and used in turn for a second ultrasonic shot.

In the SAUL method, this processing is iterated as many times as necessary, until the incident wave ideally fits the front surface, i.e. new delays laws are calculated after the second shot and are added to the previous ones; then, the resulting delay laws are applied to a third shot; and so on, until the iterative processing converges. Mathematically, the transmission delay applied to an element i (with 1 ≤ i ≤ 42) is calculated as follows:

$$\begin{equation} E_i^{( {j + 1})} = \case{1}{2}\big[ {\max \big( {t_i^{(j)} } \big) - t_i^{(j)} } \big] + E_i^{(j)} , \end{equation} \tag{ 3 }$$

$$\begin{equation} E_i^{( {j + 1})} = E_i^{( {j + 1})} - \min \big[ {E_i^{(j)} } \big], \end{equation} \tag{ 4 }$$

where j (j = 1, 2,...) denotes the shot number in the iterative processing (j = 1 corresponds to the first transmission without delay law, i.e. $E_i^{( j )} = 0$ for j = 0 ∀i). Equation (3) refers to an accumulation of delay laws after each iteration, while (4) is an offset correction ensuring that the minimum delay in the accumulated delay law is still zero. In reception, the delays are such that

$$\begin{equation} R_i^{( {j + 1})} = \max \big[ {E_i^{( {j + 1})} } \big] - E_i^{( {j + 1} )} . \end{equation} \tag{ 5 }$$

For an optimal implementation in electronic systems, it is more convenient to express $E_i^{( {j + 1})}$ and $R_i^{( {j + 1} )}$ only with delays related to the previous shot j. Substitution of (4) into (3) yields to the following expression for the emission delays:

$$\begin{equation} E_i^{( {j + 1} )} = E_i^{( j )} - \frac{{t_i^{( j )} }}{2} - \min \bigg( {E_i^{( j )} - \frac{{t_i^{( j )} }}{2}} \bigg). \end{equation} \tag{ 6 }$$

Next, substituting (6) into (4), the reception delays may be expressed as

$$\begin{equation} R_i^{( {j + 1} )} = \max \bigg( {E_i^{( j )} - \frac{{t_i^{( j )} }}{2}} \bigg) - \bigg( {E_i^{( j )} - \frac{{t_i^{( j )} }}{2}} \bigg). \end{equation} \tag{ 7 }$$

Equations (6) and (7) are the ones implemented in the MultiX systems in order to optimize inspection rates. The application of the first four transmission and reception delay laws ($E_i^{( j )}$ and $R_i^{( j )}$ with 1 ≤ j ≤ 4) in the iterative processing leads to the Bscans images in figure 5. The experimental set-up is unchanged compared to the previous part.

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The set of Bscans in figure 5 illustrates the gradual adaptation of the incident wave to the front surface of the corner radius. Iteration after iteration, the amplitude levels of the front and back surface echoes gradually increase in amplitude, and the received elementary signals progressively become time coherent. At the convergence, the Bscan is identical to the one provided by an electronic scanning in transmission (see figure 3(b)). Note that, in the present case, no delay law is applied to the first shot because we assumed that no information was available about the geometry of the surface. In contrast, if rough information is available about the geometry, a non-zero delay law can be applied at the first shot in order to partially adapt the incident wave to the surface. Thus, the algorithm requires fewer iterations to converge.

The convergence of the SAUL algorithm is demonstrated in figure 6 through simulations performed with the CIVA software platform [12]. These simulations have been simplified by considering a homogeneous and isotropic material (with the same acoustical properties as the epoxy) and by taking into account the propagation of compression waves only. In the simulation model, the interaction of waves with the component boundaries is based on the high-frequency Kirchhoff approximation, while the field propagation is governed by the semi-analytical 'pencil method' [13]. As in the experiment, the delay laws are deduced from times of flight measured from the front surface echo, but this echo is now simulated. In the CIVA model, the configuration (geometry of the component, properties of the transducer array, water path) is identical to the experimental one.

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The simulated incident fields in figure 6 show the evolution of the incident wave front at each shot of the SAUL processing, just before the wave reaches the surface. As expected, the wave progressively fits the surface. At the fourth shot, the incident wave front has the same curvature as the front surface.

Generally, the SAUL algorithm allows us to master a normal incidence transmission through any complex surface using a small number of ultrasonic shots (generally, no more than four or five shots are needed). In order to illustrate this, a second experimental set-up is considered in figure 7.

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A linear transducer array (the probe is the same than previously but ten elements are disabled) is placed in front of the concave surface of the corner radius presented in figure 1. This type of geometry is the most unfavorable (because the curvature radius is smaller than the one of the convex surface and reflections on the flat surfaces may also affect the time of flight measurement) but the algorithm is robust and requires only one additional iteration to converge. Both results in figures 5 and 7 are interesting since they demonstrate that it is possible to control the concave and convex surfaces of a given composite radius using a same conventional non-shaped transducer array.

The third and last example in figure 8 is a composite stiffener with a shoulder geometry; this particular geometry includes both concave and convex surfaces with local curvature radii of 20 mm (for the convex surface) and 5 mm (for the concave one). A linear probe (with 128 elements, 10 MHz central frequency and 0.35 mm pitch) is placed in front of the complex part (its thickness is 3 mm). For this kind of geometry, the algorithm still converges quickly, at the fourth shot.

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In order to demonstrate the robustness of the adaptive method to a lateral misalignment during scanning, figure 9 displays several screenshots of the real-time processing when a linear transducer array (the same probe used for the shoulder geometry) is translated perpendicularly to the axis of a corner radius (the one described in figure 1). The screenshots are presented for five positions of the probe, from x = −15 mm to x = 15 mm, around the top (x = 0) of the corner radius.

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The successive images in figure 9 clearly demonstrate the ability of the real-time processing to adapt itself to significant changes in the geometry, such as the presence of a misalignment between a probe and a corner radius. Even for very eccentric positions of the probe, figure 9 shows that the front and back surface echoes remain horizontal and that the maximum amplitude of the back surface echo is practically unchanged.

In conclusion of this part, it is important to note that the SAUL algorithm is unchanged for matrix probes and does not require specific changes in the hardware design of the MultiX systems.

The SAUL hardware design in the MultiX systems enables real-time inspections at high speed: using a transducer array of 48 elements and five shots in each cycle of iterations, the processing can be enabled with a frame rate of around 500 fps. It is important to note that no convergence criterion has been implemented in the hardware design. The number of iterations is constant during scanning and it is specified at the initial position of the probe. As shown above, a cycle of five shots is sufficient for most geometries encountered in aerospace.

The experimental set-up considered in this paragraph is the one described in figure 1. Two acquisitions were performed by translating the transducer over a distance of 280 mm (the initial scanning position is 40 mm from one end of corner radius) and data were recorded in 2 mm steps at a speed of 100 mm s^–1. An artificial defect (a flat bottom hole with 4 mm diameter and 2 mm depth) was drilled on the concave surface (under the corner radius). It is located at mid-length of the component, at 190 mm from either end (the length of the corner radius is 380 mm). In figure 10(b), the SAUL processing was applied by using a cycle of four shots at each position, while no processing was applied in figure 10(a). In both cases, an electric scanning with a sub-aperture of four adjacent elements and a scanning step of one element was used in reception (which corresponds to 45 sequences in reception). For each scanning step, the mean of four elementary signals was calculated and represented in the form of an electronic Bscan (sequence/time).

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Each electronic Cscan (position/sequence) in figure 10 results from the concatenation of the electronic Bscans recorded at each acquisition step. The comparison of the two Cscans reveals a larger surface echo when the SAUL processing is enabled. This is mainly due to the time coherence of the elementary signals rather than an increase in their amplitude. This surface echo is large enough to enable triggering during scanning and eliminate water path variations. A triggering is essential in order to set an acquisition time window at a given inspection depth below the surface, and to eliminate the surface echo that could hide an echo of interest, such as in figure 10(b).

The SAUL acquisition mode, coupled with a compensation of water path variations, can be better understood with the mechanical Bscans (position/time) displayed in figure 11. Each one represents the evolution of a single sequence (i.e. the average of four received elementary signals at the 19th sequence) as a function of the probe position. By using the SAUL processing without triggering (comparison of figures 11(a) and (b)), we note that the surface echo is much stronger and the defect echo is identified at 150 mm from the initial scanning position. However, the SAUL mechanical Bscan shows that the arrival time of the surface echo varies due to a slight misalignment between the scanning axis and the corner radius one. After triggering, in figure 11(c), the water path variations are corrected so that a 2 µs time window at 3 µs after the surface echo (corresponding to an inspection depth of around 4 mm) can be set in order to image the defect with a Cscan representation.

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The real-time SAUL processing, associated with a correction of water path variations, provides the new electronic Cscan displayed in figure 12. The artificial defect is detected with a suitable signal-to-noise ratio (around 12 dB) at 150 mm. Thus, this experimental result clearly demonstrates that it is possible to detect a defect without any prior accurate knowledge of the geometry and/or the position of a composite component. Nevertheless, it should be noted that the method does not allow for characterization of a defect (especially, its size) because the SAUL imaging is only a representation sequence/scanning of the measured amplitudes. A substantial improvement would be to reconstruct actual images of the inside of the component, which requires an implementation of fast surface reconstruction algorithms in the imaging MultiX systems. In the next section, we test an algorithm introduced in the field of radar systems and based on the computation of an envelope of circles.

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