**5. Simulated and experimental flaw detection results for the three combination techniques. Discussion of their performance**

Three sets of experiments are shown in this section. First, the results related to the final SNR calculated for seven type-I simulated experiments using different combination options will be presented in the first section part. Second, 2D displays about the location of an isolated reflector, calculated for a particular combination case and a small *SNRini* are also shown. Third, as results illustrating the type-II experiments, 3 pairs of representations of a real flaw obtained by means of the 3 different combination techniques of section 3 will be shown and commented, analyzing the respective performances of the three techniques. The initial data for these type-II experiments were a set of measured ultrasonic traces acquired with the ultrasonic set-up of section 4.

The first tasks in type-I experiments (with simulated traces) were performed to confirm the accuracy of expressions (3), (5) and (8). In these experiments, 11 *SNRini* were selected (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10). 10.000 sets of measures were generated using a real 4 MHz echo response sampled at 128 MHz and synthetic noise, composed in this case by 66.66% of white Gaussian noise (accounting by the "thermic" noise induced by the usual 90 Applications of Digital Signal Processing

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,

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

Three sets of experiments are shown in this section. First, the results related to the final SNR calculated for seven type-I simulated experiments using different combination options will be presented in the first section part. Second, 2D displays about the location of an isolated reflector, calculated for a particular combination case and a small *SNRini* are also shown. Third, as results illustrating the type-II experiments, 3 pairs of representations of a real flaw obtained by means of the 3 different combination techniques of section 3 will be shown and commented, analyzing the respective performances of the three techniques. The initial data for these type-II experiments were a set of measured ultrasonic traces acquired with the

The first tasks in type-I experiments (with simulated traces) were performed to confirm the accuracy of expressions (3), (5) and (8). In these experiments, 11 *SNRini* were selected (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10). 10.000 sets of measures were generated using a real 4 MHz echo response sampled at 128 MHz and synthetic noise, composed in this case by 66.66% of white Gaussian noise (accounting by the "thermic" noise induced by the usual

**5. Simulated and experimental flaw detection results for the three** 

**combination techniques. Discussion of their performance** 

contained into the driving spike, was selected.

during their acquisition turns.

ultrasonic set-up of section 4.

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

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 in the mentioned work.

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 different 10.000 SNRs obtained for each set of simulated traces.


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

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

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> -5

Transducer H1

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Transducer H3

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Transducer V1

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Transducer V3





Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 93





µsec <sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> -5

µsec <sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> -5

µsec <sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> -5

µsec <sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> -5

Transducer V4

Transducer V2

Transducer H4

Transducer H2

µsec

µsec

µsec

µsec

Fig. 7. Ultrasonic traces from the 8 transducers of figure 4 with a simulated *SNRini* = 3 dB.


Table 2. SNRs of the 2D representations obtained by means of the experiments 5 to 7.

The estimated and measured values of the *SNR2Dtime* (Table 1, columns 2 and 3) and *SNR2DTFlinear* ratios, obtained for 2 bands (Table 1, columns 4 and 5), 3 bands (Table 1, columns 6 and 7) and 4 bands (Table 1, columns 8 and 9), present a very good agreement. Finally, the *SNR2DWVT* (Table 2) for different bands number show a high correlation between estimated and measured values, but in some cases small differences appear. These are due to the fact that the estimated expression for *SNR2DWVT* was obtained by means of approximations, but in any case, the global correspondence between estimated and measured values is also reasonably good.

Apart from SNR improvements, the three techniques described in this chapter allow the accurate detection of flaws inside pieces.

A second type-I experiment was realised to show this good accuracy in the defect detection capability inside the pieces. A new set of ultrasonic traces was generated, simulating again a hole in a rectangular piece as it is depicted in figure 4. In this case, the selected *SNRini* of the initial A-scan was 3 dB.

The echo is the real 4 MHz trace sampled at 128 MHz, and the noise contained in the initial eight traces was composed by white noise and coherent noise with amplitudes of 50% each one. This set of simulated measures is displayed in figure 7, being the units shown in horizontal axis micro-seconds. In these graphics, it can be appreciated that noise and echo amplitudes are similar, thus it is very difficult to distinguish the reflector echo from the noise. In fact, the echo only appears in graphics corresponding to transducers H3 and V2. The real echo-pulse of H3 transducer is located in the middle of the noise beginning approximately at 5.5 microseconds whereas the echo-pulse of V2 transducer begins around 10.75 microseconds.

Using the ultrasonic registers of figure 7, the three combinations of the traces by applying the different techniques exposed in the chapter were performed. The first combination was done using the time domain method and the resulting 2D representation is shown in figure 8.a., where the 24x24 mm inspected area is displayed (the axis units are in mm). The searched hole location is around 8 mm in horizontal axis and 15 mm in vertical axis. It can 92 Applications of Digital Signal Processing

2 bands experiment 5

Table 2. SNRs of the 2D representations obtained by means of the experiments 5 to 7.

The estimated and measured values of the *SNR2Dtime* (Table 1, columns 2 and 3) and *SNR2DTFlinear* ratios, obtained for 2 bands (Table 1, columns 4 and 5), 3 bands (Table 1, columns 6 and 7) and 4 bands (Table 1, columns 8 and 9), present a very good agreement. Finally, the *SNR2DWVT* (Table 2) for different bands number show a high correlation between estimated and measured values, but in some cases small differences appear. These are due to the fact that the estimated expression for *SNR2DWVT* was obtained by means of approximations, but in any case, the global correspondence between estimated and

Apart from SNR improvements, the three techniques described in this chapter allow the

A second type-I experiment was realised to show this good accuracy in the defect detection capability inside the pieces. A new set of ultrasonic traces was generated, simulating again a hole in a rectangular piece as it is depicted in figure 4. In this case, the selected *SNRini* of the

The echo is the real 4 MHz trace sampled at 128 MHz, and the noise contained in the initial eight traces was composed by white noise and coherent noise with amplitudes of 50% each one. This set of simulated measures is displayed in figure 7, being the units shown in horizontal axis micro-seconds. In these graphics, it can be appreciated that noise and echo amplitudes are similar, thus it is very difficult to distinguish the reflector echo from the noise. In fact, the echo only appears in graphics corresponding to transducers H3 and V2. The real echo-pulse of H3 transducer is located in the middle of the noise beginning approximately at 5.5 microseconds whereas the echo-pulse of V2 transducer begins around

Using the ultrasonic registers of figure 7, the three combinations of the traces by applying the different techniques exposed in the chapter were performed. The first combination was done using the time domain method and the resulting 2D representation is shown in figure 8.a., where the 24x24 mm inspected area is displayed (the axis units are in mm). The searched hole location is around 8 mm in horizontal axis and 15 mm in vertical axis. It can

*SNR2DWVT*(dB)

3 bands experiment 6

 Est. Meas. Est. Meas. Est. Meas. 0 0 4.93 0 8.64 0 12.88 1 6 8.90 9 12.81 12 18.08 2 12 11.91 18 19.01 24 25.31 3 18 16.76 27 28.02 36 38.92 4 24 21.63 36 35.70 48 50.45 5 30 27.65 45 45.32 60 64.33 6 36 34.63 54 56.13 72 80.90 7 42 41.53 63 63.17 84 94.67 8 48 48.91 72 78.46 96 111.31 9 54 56.88 81 90.69 108 127.91 10 60 64.24 90 101.73 120 142.04

4 bands experiment 7

*SNRini* (dB)

measured values is also reasonably good.

accurate detection of flaws inside pieces.

initial A-scan was 3 dB.

10.75 microseconds.

Fig. 7. Ultrasonic traces from the 8 transducers of figure 4 with a simulated *SNRini* = 3 dB.

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

acquired not only from the emitting transducers.

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Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 95

this type of ultrasonic traces combination methods (using perpendicular NDE transducers) from echoes coming from two ultrasonic imaging array apertures, where this particular restriction (for only isolated reflectors) will be solved, by means of an improved procedure, that includes an additional processing step involving additional echographic information

a) time domain method b) wavelet method, *L*=2 c) WVT method, *L*=2

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d) wavelet method, *L*=3 e) wavelet method, *L*=4f) wavelet, *L*=4, scale in dB

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>0</sup>

g) WVT method, *L*=3h) WVT method, *L*=4i) WVT, *L*=4, scale in dB

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>0</sup>

Fig. 8. Different 2D representations, after the combination of the traces shown in the figure 7;

different methods and *L* values were used.

be deduced that by using this time domain technique, the flaw is not very well marked and a lot of noise appear, but it is must taken into account that, in the initial traces shown in figure 7, the echo level was under noise level, in some cases.

The linear time-frequency transform used for second combination in this comparative analysis was the undecimated wavelet packet transform with Daubechies 4 as mother wavelet, as in the previous set of experiments. Figures 8.b, 8.d and 8.e show the 2D representations obtained using wavelets with 2, 3 and 4 bands. In these graphics, which amplitudes are in linear scale, it can be clearly distinguished the mark corresponding to the hole. Figure 8.f represents the same result than 8.e, but with the gray scale of amplitudes measured in dB, in order to appreciate with more detail the low levels of noise.

Finally figures 8.c, 8.g and 8.h show the 2D representations obtained using WVT with 2, 3 and 4 bands and using a linear scale for amplitudes. Figure 8.h and 8.i correspond to the same results, but figure 8.i is displayed with its amplitude scale expressed in dB. Thus, in figure 8.h, the noise has disappeared but in figure 8.i the low level noise can still be observed. It must be noted that, for all the cases, the 2D representations of figure 8 mark the flaw that we are looking for, although in the initial traces, shown in figure 7, the echoes coming from the flaw were very difficult to see.

Additionally, in the first strip of the figure 8, the 2D graphic resulting when time domain method is used, is shown. It can be seen its performance in contrast with the wavelet method with minimum quality (*L*=2) and WVT option with minimum quality (*L*=2), in such a way that a quick comparison can be made among improvements applying the different methods.

In that concerning to results of type-II experiments, displays of 2D representations, obtained by combination of experimental traces acquired from the ultrasonic prototype described in section 4 are presented in figure 9. Two scales have been used for each 2D result: linear and logarithmic scales. With the logarithmic scale, the small flaw distortions and secondary detection indications, produced by each combination method, can be more easily observed and quantified. It must be noted that the logarithmic scales have an ample resolution of 60 dB, giving a better indication of techniques performance.

In all these cases, the initial traces had a low level of grain noise because these echo-signals correspond to reflections from the small cylindrical hole drilled in a plastic piece made of a rather homogeneous material without internal grains. The patterns of figure 9 were obtained using similar processing parameters than those used with the simulated traces in the type-I experiments, and only two bands were considered for frequency decomposition. The results of the figure 9, using the time-combination method, present clear flaw distortions (more clearly visible in 9.b) with shadow zones in form of a cross, but even in this unfavourable case, a good spatial flaw location is achieved.

The mentioned crossing distortions appear already very attenuated in the results shown in figures 9.c and 9.d, corresponding to the linear time-frequency combination technique (wavelet using 2 bands), and practically disappear in the results of figures 9.e and 9.f obtained by using to the WVT combination technique.

Similar good results could be also achieved in many practical NDE cases with isolated-flaws patterns, but this performance could be not extended to other more complicated testing situations whit flaws very close among them, i.e. with two or more flaws located into a same elemental cell and thus being insonifyed by the same two perpendicular beams. Under these more severe conditions, some ambiguity situations, with apparition of "phantom" flaws, could be produced [Rodríguez et al 2005]. We are working order to propose the extension of 94 Applications of Digital Signal Processing

be deduced that by using this time domain technique, the flaw is not very well marked and a lot of noise appear, but it is must taken into account that, in the initial traces shown in

The linear time-frequency transform used for second combination in this comparative analysis was the undecimated wavelet packet transform with Daubechies 4 as mother wavelet, as in the previous set of experiments. Figures 8.b, 8.d and 8.e show the 2D representations obtained using wavelets with 2, 3 and 4 bands. In these graphics, which amplitudes are in linear scale, it can be clearly distinguished the mark corresponding to the hole. Figure 8.f represents the same result than 8.e, but with the gray scale of amplitudes

Finally figures 8.c, 8.g and 8.h show the 2D representations obtained using WVT with 2, 3 and 4 bands and using a linear scale for amplitudes. Figure 8.h and 8.i correspond to the same results, but figure 8.i is displayed with its amplitude scale expressed in dB. Thus, in figure 8.h, the noise has disappeared but in figure 8.i the low level noise can still be observed. It must be noted that, for all the cases, the 2D representations of figure 8 mark the flaw that we are looking for, although in the initial traces, shown in figure 7, the echoes

Additionally, in the first strip of the figure 8, the 2D graphic resulting when time domain method is used, is shown. It can be seen its performance in contrast with the wavelet method with minimum quality (*L*=2) and WVT option with minimum quality (*L*=2), in such a way that a quick comparison can be made among improvements applying the different

In that concerning to results of type-II experiments, displays of 2D representations, obtained by combination of experimental traces acquired from the ultrasonic prototype described in section 4 are presented in figure 9. Two scales have been used for each 2D result: linear and logarithmic scales. With the logarithmic scale, the small flaw distortions and secondary detection indications, produced by each combination method, can be more easily observed and quantified. It must be noted that the logarithmic scales have an ample resolution of 60

In all these cases, the initial traces had a low level of grain noise because these echo-signals correspond to reflections from the small cylindrical hole drilled in a plastic piece made of a rather homogeneous material without internal grains. The patterns of figure 9 were obtained using similar processing parameters than those used with the simulated traces in the type-I experiments, and only two bands were considered for frequency decomposition. The results of the figure 9, using the time-combination method, present clear flaw distortions (more clearly visible in 9.b) with shadow zones in form of a cross, but even in this unfavourable

The mentioned crossing distortions appear already very attenuated in the results shown in figures 9.c and 9.d, corresponding to the linear time-frequency combination technique (wavelet using 2 bands), and practically disappear in the results of figures 9.e and 9.f

Similar good results could be also achieved in many practical NDE cases with isolated-flaws patterns, but this performance could be not extended to other more complicated testing situations whit flaws very close among them, i.e. with two or more flaws located into a same elemental cell and thus being insonifyed by the same two perpendicular beams. Under these more severe conditions, some ambiguity situations, with apparition of "phantom" flaws, could be produced [Rodríguez et al 2005]. We are working order to propose the extension of

measured in dB, in order to appreciate with more detail the low levels of noise.

figure 7, the echo level was under noise level, in some cases.

coming from the flaw were very difficult to see.

dB, giving a better indication of techniques performance.

case, a good spatial flaw location is achieved.

obtained by using to the WVT combination technique.

methods.

this type of ultrasonic traces combination methods (using perpendicular NDE transducers) from echoes coming from two ultrasonic imaging array apertures, where this particular restriction (for only isolated reflectors) will be solved, by means of an improved procedure, that includes an additional processing step involving additional echographic information acquired not only from the emitting transducers.

Fig. 8. Different 2D representations, after the combination of the traces shown in the figure 7; different methods and *L* values were used.

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

the proposed methods in a real NDE context.

**7. Acknowledgment** 

**8. References** 

Innovation (R&D Project DPI2008-05213).

PhiladelphiaPA

*Ultrasonics* vol. 40, pp 263-267.

7 (10).

than the wavelet technique, which also offers a good performance.

addressed by means of a specifically extended imaging procedure.

Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 97

Two types of experiments have been performed to evaluate these techniques. Results of the first type, involving simulated noisy signal traces, have confirmed the accuracy of our theoretical SNR expressions proposed for the three combination variants. The first type experiments also demonstrate a great capability for accuracy detection of internal flaws. Results from the second type, using an experimental ultrasonic prototype, permit to validate

More concretely, the three combination methods described and applied in this chapter, based on different processing tools (the Hilbert, Wigner-Ville, and Undecimated Wavelet packet Transforms) produce accurate 2D displays for isolated-flaws location. Additionally, these methods drastically improve the SNR of these 2D displays in relation to the initially acquired traces, very especially with the two latter processing cases, being the best flaw discrimination results obtained with the WVT option, but with a mayor computational cost

These good results for isolated-flaws patterns could be not directly extended to other more complicated testing situations with flaws very close among them, because some ambiguous flaw indications could be produced. In a future work, this particular restriction will be

This work was supported by the National Plan of the Spanish Ministry of Science &

Chang Y F and Hsieh C I 2002 Time of flight diffraction imaging for double-probe technique

Chen C.H. and Guey J.C. 1992 On the use of Wigner distribution in Ultrasonic NDE *Rev. of Progress in Quantitative Nondestructive Evaluation*, vol. 11A, pp. 967-974,. Claasen T.A.C.M. and Mecklenbrauker W.F.G. 1980 The Wigner Distribution - A tool for time-frequency signal analysis *Philips J. Res.*, vol. 35, pp. 217-250, 276-300, 372-389.

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#### **6. Conclusion**

Three variants of a recent digital signal processing procedure for ultrasonic NDE, based on the scanning with a small number of transducers sized to work in near field conditions (located at two perpendicular planes to obtain different ultrasonic perspectives), are evaluated. They originate distinct techniques to fuse echo information coming from two planes: time-domain, linear time-frequency, and WVT based, 2D combination methods.

Fig. 9. Different 2D representations after combination of real traces in experiments type-II, with linear scale (a, c, e) and logarithmic scale (b, d, f).

Two types of experiments have been performed to evaluate these techniques. Results of the first type, involving simulated noisy signal traces, have confirmed the accuracy of our theoretical SNR expressions proposed for the three combination variants. The first type experiments also demonstrate a great capability for accuracy detection of internal flaws.

Results from the second type, using an experimental ultrasonic prototype, permit to validate the proposed methods in a real NDE context.

More concretely, the three combination methods described and applied in this chapter, based on different processing tools (the Hilbert, Wigner-Ville, and Undecimated Wavelet packet Transforms) produce accurate 2D displays for isolated-flaws location. Additionally, these methods drastically improve the SNR of these 2D displays in relation to the initially acquired traces, very especially with the two latter processing cases, being the best flaw discrimination results obtained with the WVT option, but with a mayor computational cost than the wavelet technique, which also offers a good performance.

These good results for isolated-flaws patterns could be not directly extended to other more complicated testing situations with flaws very close among them, because some ambiguous flaw indications could be produced. In a future work, this particular restriction will be addressed by means of a specifically extended imaging procedure.
