**4.1 Experiments type-I based on simulated noisy traces**

Type-I experiments were carried out with simulated signal registers. They provide adequate calculation results to confirm the accuracy of the expressions estimated from the theoretical models of the processing techniques proposed in the equations (3), (5) and (8) to predict the distinct SNRs (*SNR2Dtime*, *SNR2DTFlinear* and *SNR2DWVT*). So, those expressions could be validated for an ample range of values in *SNRini* with perfectly controlled characteristics in echo-signals and their associated grain noises. Some results, in a similar context, using these same rather simple simulated registers, have been compared in a previous work (Rodríguez et al 2004a) with the obtained results when a more accurate ultrasonic trace generator was used. A very close agreement between them was observed, which confirms the suitability of these registers to evaluate those expressions.

The testing case proposed to attain this objective is the location of a punctual reflector into a rectangular parallelepiped from 2 external surfaces, perpendicular between them, and using 4 transducers by surface. The general scheme of these experiments, with 4 horizontal (H1, H2, H3, H4) and 4 vertical (V1, V2, V3, V4) transducers is depicted in the Figure 4. Transducers H3 and V2 receive echoes from the reflector whereas the other transducers (H1, H2, H4, V1, V3 and V4) only receive grain noise. To assure compatibility of experiments type-I with experiments type-II, ultrasonic propagation in a piece of 24x24 mm has been simulated assuming for calculations a propagation velocity 2670 m/s very close to that corresponding to methacrylate material. The sampling frequency was 128 MHz.

Fig. 4. Geometry of the inspection case planned to evaluate the different combination methods: detection of a single-flaw in a 2D arrangement with 16 elemental-cells.

Comparative Analysis of Three Digital Signal Processing Techniques for 2D Combination of

**4.2 Experiments type-II with echographic traces measured from an ultrasonic** 

Fig. 6. Perpendicular array transducers and the inspected plastic piece with the hole.

hole

In all the measurement cases, the transducers are driven for transmission and selected for echoe reception in a sequential way. We deal with near field radiations and only one transducer emits and receives at the same time, in our eight-shots successive measurement process. Thus, among all the echoes produced by the isolated reflector in each transducer shot, only those received in the two transducers located in front of the reflector (at the perpendicular projections of the flaw on the horizontal and vertical apertures) will be captured, because, in each shot, the echoes acquisitions are cancelled in the other seven transducers. Additionally, these two transducers in front of the reflector could receive certain amount of noise. And under these conditions, the rest of transducers of the two array apertures, in each plane, only could eventually acquire some noise signal during its shot, but not echoes from the reflector hole. Concretely, in the flaw scheme of the figure 4 (before shown for the simulated type-I experiments), the pulsed-echoes from the discontinuity of the reflector will be received by transducers H3 and V2 (with the apparition time of these echoes being determined by the distance to each transducer and the sound propagation velocity in the piece), and the traces in H1, H2, H4, V1, V3 and V4, will not contain flaw

**prototype** 

reflections.

Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 89

The type-II experiments are based on real ultrasonic echoes measured from an isolated-flaw (hole drilled in a plastic piece) with a multi-channel ultrasonic prototype designed for this kind of tests in laboratory. The two array transducers are disposed in a perpendicular angle and the square plastic piece with the hole are inside and in contact with the radiation area of arrays. There are 4 broadband elemental transducers in each perpendicular array, 8 in the whole system. Transducers work in the 4 MHz frequency band range. The dimensions of the emitting surface of each individual transducer are 6x6 mm, being 24 mm the total length of both arrays. Then, the area of the methacrylate piece to be inspected by the ultrasonic system is 24x24 mm. Arrays manufacturing was ordered to the Krautkramer company. The methacrylate piece has a drilled cylindrical hole in a position similar as used in experiment type I. Then, simulations of experiment type-I are almost coincident with real measurements of experiment type-II. The main difference is that methacrylate generates a very low level of ultrasonic grain noise. Figure 6 shows the disposition of transducers and inspected piece.

The simulation of the echo-traces produced by the reflector was made by integrating a real echographic signal with a synthetic noise-component similar to the grain reflections registered in some industrial inspections, and that are quite difficult to be cleaned. The echographic echo was acquired from one of the 4 MHz transducers of the perpendicular array used for experiments type-II. The sampling frequency was 128 MHz. The echo is shown in figure 5. The "coherent" grain noise, to be associated with the basic echo-signal, was obtained by means of a synthetic white gaussian noise generator. To assure the frequency coherence with the main reflector echo-pulse (simulating an unfavourable case), this initial noise register was passed thought a digital filter just having a frequency response as the ultrasonic echo-pulse spectrum. Finally, the composed traces containing noisy echoes are obtained by the addition of the real echo-signals with the synthetic noise register. Previously, the noise had been unit power normalized and the echo-signal had been multiplied by a constant with the finality of obtaining the desired *SNRini*.

Fig. 5. Ultrasonic echo utilised in type-I experiments.

Several sets of tests were prepared with 11 different *SNRini* (0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 dB). For each *SNRini* , 10.000 tests were performed using the three combination methods described in section 3, and their respective results were compared. The length of the each individual ultrasonic trace was of 2304 points (corresponding to 18 microseconds with a sampling frequency of 128 MHz). 18 microseconds is the time of flight of 48 (24 +24) mm with a propagation velocity of 2670 m/s, very close to the total echo length from the methacrylate piece considered in experiments. The length of the echo-signals contained in these traces was of 98 samples. The size of the final 2D representation is 2304x2304 (5308416) points (corresponding with an inspected area of 24x24 mm). Thus, from 18432 initial points (2304 by transducer), a 2D display with 5308416 points was obtained for the whole piece. To measure the different SNR's, the echo-signal power was measured over its associated area 98x98 points in the 2D display, whereas for the noise power, the rest of the 2D display points were used.

88 Applications of Digital Signal Processing

The simulation of the echo-traces produced by the reflector was made by integrating a real echographic signal with a synthetic noise-component similar to the grain reflections registered in some industrial inspections, and that are quite difficult to be cleaned. The echographic echo was acquired from one of the 4 MHz transducers of the perpendicular array used for experiments type-II. The sampling frequency was 128 MHz. The echo is shown in figure 5. The "coherent" grain noise, to be associated with the basic echo-signal, was obtained by means of a synthetic white gaussian noise generator. To assure the frequency coherence with the main reflector echo-pulse (simulating an unfavourable case), this initial noise register was passed thought a digital filter just having a frequency response as the ultrasonic echo-pulse spectrum. Finally, the composed traces containing noisy echoes are obtained by the addition of the real echo-signals with the synthetic noise register. Previously, the noise had been unit power normalized and the echo-signal had been

Several sets of tests were prepared with 11 different *SNRini* (0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 dB). For each *SNRini* , 10.000 tests were performed using the three combination methods described in section 3, and their respective results were compared. The length of the each individual ultrasonic trace was of 2304 points (corresponding to 18 microseconds with a sampling frequency of 128 MHz). 18 microseconds is the time of flight of 48 (24 +24) mm with a propagation velocity of 2670 m/s, very close to the total echo length from the methacrylate piece considered in experiments. The length of the echo-signals contained in these traces was of 98 samples. The size of the final 2D representation is 2304x2304 (5308416) points (corresponding with an inspected area of 24x24 mm). Thus, from 18432 initial points (2304 by transducer), a 2D display with 5308416 points was obtained for the whole piece. To measure the different SNR's, the echo-signal power was measured over its associated area 98x98 points in the 2D display, whereas for the noise power, the rest of the 2D display points were used.

µsec

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -1

multiplied by a constant with the finality of obtaining the desired *SNRini*.

Fig. 5. Ultrasonic echo utilised in type-I experiments.





0

0.2

0.4

0.6

0.8

1

## **4.2 Experiments type-II with echographic traces measured from an ultrasonic prototype**

The type-II experiments are based on real ultrasonic echoes measured from an isolated-flaw (hole drilled in a plastic piece) with a multi-channel ultrasonic prototype designed for this kind of tests in laboratory. The two array transducers are disposed in a perpendicular angle and the square plastic piece with the hole are inside and in contact with the radiation area of arrays. There are 4 broadband elemental transducers in each perpendicular array, 8 in the whole system. Transducers work in the 4 MHz frequency band range. The dimensions of the emitting surface of each individual transducer are 6x6 mm, being 24 mm the total length of both arrays. Then, the area of the methacrylate piece to be inspected by the ultrasonic system is 24x24 mm. Arrays manufacturing was ordered to the Krautkramer company. The methacrylate piece has a drilled cylindrical hole in a position similar as used in experiment type I. Then, simulations of experiment type-I are almost coincident with real measurements of experiment type-II. The main difference is that methacrylate generates a very low level of ultrasonic grain noise. Figure 6 shows the disposition of transducers and inspected piece.

In all the measurement cases, the transducers are driven for transmission and selected for echoe reception in a sequential way. We deal with near field radiations and only one transducer emits and receives at the same time, in our eight-shots successive measurement process. Thus, among all the echoes produced by the isolated reflector in each transducer shot, only those received in the two transducers located in front of the reflector (at the perpendicular projections of the flaw on the horizontal and vertical apertures) will be captured, because, in each shot, the echoes acquisitions are cancelled in the other seven transducers. Additionally, these two transducers in front of the reflector could receive certain amount of noise. And under these conditions, the rest of transducers of the two array apertures, in each plane, only could eventually acquire some noise signal during its shot, but not echoes from the reflector hole. Concretely, in the flaw scheme of the figure 4 (before shown for the simulated type-I experiments), the pulsed-echoes from the discontinuity of the reflector will be received by transducers H3 and V2 (with the apparition time of these echoes being determined by the distance to each transducer and the sound propagation velocity in the piece), and the traces in H1, H2, H4, V1, V3 and V4, will not contain flaw reflections.

Comparative Analysis of Three Digital Signal Processing Techniques for 2D Combination of

from expressions (3), (5) and (8).

in the mentioned work.

SNRini (dB)

Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 91

electronic instrumentation) and 33.34% of coherent noise (accounting by "grain" noise tied to material texture). Seven experiments were realized: 1 with time domain technique, 3 based on linear time-frequency decomposition using 2, 3 and 4 bands, and finally 3 utilising WVT with 2, 3 and 4 band again. The SNR after the 7 experiments were measured. The results are exposed in Tables 1 and 2, together with the values expected

In the first column of Tables 1 and 2, the initial SNR, *SNRini* of the ultrasonic traces are shown. The experiment 1 in the Table 1 was planned in order to measure the behaviour of the 2D time-combination method in terms of *SNR2Dtime* improvement. The experiments number 2, 3 and 4 had as objective to evaluate the accuracy of the expression *SNR2DTFlinear* corresponding with the linear time-frequency combination. The difference among these 3 cases is the number of bands utilized [parameter *L* in expression (5)]; thus, the experiments 2, 3 and 4 were performed with 2, 3 and 4 bands respectively. The particular linear time-frequency transform used in these latter experiments was the undecimated wavelet packet transform, (Mallat 1989, Shensa 1992, Coifman and Wickerhauser 1992), with Daubechies 4 as mother wavelet, as it was used in the work (Rodríguez et al 2004b) but with some new adjusts included in this case, which provide a better agreement (as it can be seen in Table 1) between estimated and measured expressions of *SNR2DTFlinear* that

Finally, experiments 5 to 7 in Table 2 show the improvements obtained by using the WVT transform in the combination. The differences among these 3 WVT experiments are again the number of bands being involved: 2, 3 or 4, respectively. The SNR related to these 7 experiments are presented in Table 1 and Table 2. The expected SNRs estimated from their theoretic expressions, together with the measured SNRs, are detailed for each case. The measured SNR values, which are shown in these tables, were calculated as the mean of

> 2 bands experiment 2

Table 1. SNRs of the 2D representations obtained by means of the experiments 1 to 4.

 Est. Meas. Est. Meas. Est. Meas. Est. Meas. 0 0 0.11 0 0.34 0 0.05 0 0.75 1 2 2.08 4 3.53 6 5.72 8 8.81 2 4 4.07 8 7.62 12 11.54 16 16.63 3 6 6.06 12 11.46 18 17.53 24 24.57 4 8 8.11 16 15.42 24 23.41 32 32.26 5 10 9.97 20 19.39 30 29.34 40 40.44 6 12 12.01 24 23.43 36 35.28 48 48.42 7 14 14.11 28 27.38 42 41.23 56 56.24 8 16 16.13 32 31.34 48 47.31 64 64.25 9 18 18.16 36 35.32 54 53.24 72 72.17 10 20 20.08 40 39.33 60 59.27 80 80.43

SNR2DTFlinear(dB)

3 bands experiment 3

4 bands experiment 4

different 10.000 SNRs obtained for each set of simulated traces.

SNR2Dtime(dB)

experiment 1

For measurements, an experimental prototype, with eight ultrasonic transceivers, has been arranged for the validation and comparative assessment of the three flaw localization techniques by 2D traces combination in a real NDE context. It includes as emitter-receiver probes two 4 MHz piezoelectric linear arrays of 4 elements each one (as it is shown in figure 6), which are controlled by a Krautkramer NDE system model USPC-2100, disposed in the pulse-echo mode. The main characteristics of this NDE system in the signal receiving stage are the following: a dynamic range of 110 dB; a maximum effective sampling of 200 MHz in the digitalizing section. A signal gain of 44 dB and a sampling rate of 128 MHz were selected in reception for all the signal acquisitions performed in this work. Other general characteristics of this system are: pulse repetition rate of up to 10 KHz per channel, and 15 MHz of effective bandwidth in emission-reception. The high-voltage pulser sections of this commercial system were programmed in order to work with the highest electric excitation disposable for the driven transducers, which is about 400 Volts (measured across a nominal load of 100 Ohm). A relatively low value for the E/R damping resistance of 75 Ohm was selected looking for the assurance of a favourable SNR and a good bandwidth in the received echoes. Finally, the maximum value offered by this equipment for the energy level, contained into the driving spike, was selected.

It must be noted that in the experimental ultrasonic evaluations performed with the two arrays, their elemental transducers were operated with the restriction of that only one transducer was emitting and receiving at the same time. So, the two transducers located in front of the flaw (in this case: transducers H3 & V2) were operated separately as receivers in order to obtain useful information from the artificially created flaw (by drilling the plastic piece), which is clearly smaller than transducer apertures. Thus, only ultrasonic beams of H3 & V2 transducers (which remain collimated into a 6 mm width due to the imposed near-field conditions) attain the hole, whereas the other six elemental transducers radiate theirs beams far away of that hole, and therefore, in any case, they are not covering the artificial flaw and are not receiving echoes reflected from this flaw during their acquisition turns.
