**1. Introduction**

In certain practical cases of quality control in the manufacturing industry, by means of ultrasonic non-destructive evaluation (NDE), it is very difficult to detect certain types of internal flaw using conventional instrumentation based in ultrasonic transducers located on a unique external surface of the piece under inspection. In these cases, the detection problems are due to the especial flaws orientation or their spatial location, and some technological solutions for it are still pendent to be proposed.

In addition, it is convenient, in a more general scope, to improve the flaw-location in two dimensions, by using several ultrasonic transducers emitting beams from distinct places. In fact, the utilization of more than one detection transducer provides complementary information in the NDE of many pieces. These transducers can be located at the same or at different planes depending on the piece shape and the detection necessities. In any case, the result of such arrangement is a set of ultrasonic traces, which have to be carefully fussed using digital signal processing techniques in order to extract more accurate and more complete detection results.

The usual trend for reducing the mentioned limitations in flaw detection is to increase the number of ultrasonic channels involved in the testing. On the other hand, it is important to reduce this ultrasonic channels number in order to minimize technological costs. In addition, it should be noted that the detection capability also depends on other important factors, because, from a more general point of view, still some physical limitations of the ultrasonic beams remain for a) certain angles of the scanning (Chang and Hsieh 2002), b) for certain complex geometries of the industrial components to be tested (Roy et al 1999) or c) for biological elements in medical diagnosis (Defontaine et al 2004, Reguieg et al 2006).

Schemes have been preliminarily proposed in order to improve flaw detection in difficult conditions, trying to resolve these type of aspects well with two transducers and additional digital signal processing of echoes (Chang and Hsieh 2002), or well with several arrays of few elements (Engl and Meier 2002). Other posterior alternative proposals, based on perpendicular scanning from two planes with a reduced transducers number and ultrasonic

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

representation of the signals.

processed signals and a high computational cost.

the measured echo-responses, will be discussed.

associated to the investigated reflectors.

**SNR** 

Echographic Traces Obtained from Ultrasonic Transducers Located at Perpendicular Planes 81

using a 2D product operator. The SNR was used as a quality index to evaluate both methods; and the resulting evaluation data showed a better performance of the product operator. Nevertheless, their performances were limited in both cases by the time

A technique in this same line that introduces the combination in the time-frequency domain, based on the Wigner-Ville transform (WVT), was preliminary applied in (Rodríguez 2003). This technique took into account the temporal and the frequency information of the ultrasonic traces. A better SNR result than with the time domain method (Rodríguez et al 2004) was obtained. But this option presented two drawbacks: a lost of linearity of the

In (Rodríguez et al 2004b) a new method was presented, performing the combination in the time-frequency domain with a low computational cost by the use of a linear transform (based on the wavelet transform (Daubechies 1992); its 2D SNR performance seemed to be

The present chapter summarizes these three combination techniques previously proposed by the authors for flaw detection from perpendicular transducers. A comparative analysis (based on theoretic and experimental results) of their performances over a common set of specific experiments is made. The objective is to establish the respective advantages and inconveniences of each technique in a rather rigorous frame. For experimental evaluations, we have arranged an ultrasonic prototype to generate (from 2 planes) ultrasonic near-field beams collimated along the inspected piece, and to acquire the echoes from the transducers involved in our experiments. The different combination results calculated in each case, from

**3. Description of processing techniques for combination. Expressions of** 

A number of distinct combination techniques to fuse several ultrasonic traces, coming from perpendicular transducers, have been proposed by the authors. There are two important parameters that define all these techniques: a) the initial type of the traces representation,

To choose the best representation for the processing of signals is an open general problem with multiples solutions; the two most popular representations are in time or in frequency domains: a) the direct time domain is very useful for NDE problems because the spatial localization of possible defects or flaws (in the material under testing) is closely related with the apparition time of the echoes; b) the frequency domain is less used in this type of ultrasound based applications because does not permit a spatial localization; in addition, the spectrum of the ultrasonic information with interest for testing in some industrial applications, is almost coincident with the mean spectrum of the "grain" noise originated from the material texture, which some times appears corrupting the signals waveforms

An interesting possibility for introducing spectral information in these applications is the use of time-frequency representations (Cohen 1995) for the echo-graphic signals. This option shows in a 2D format the time information for the different frequency bands in which the received ultrasonic signals range. Therefore, each point of a 2D time-frequency representation corresponds with one spectral frequency and with one time instant. Two different time-frequency techniques, the wavelet transform (Daubechies 1992, Shensa 1992)

closed to that obtained in (Rodríguez 2003) with Wigner-Ville transforms.

and b) the particular operator utilized in their combination process.

beams overlapping, were reported (Meyer and Candy 2002, Rodríguez et al 2004). But an extensive research in order to find simple and complete solutions to these problems is still needed. In particular, the authors are currently investigating techniques for ultrasonic radiation from perpendicular planes using arrays of few radiators working in near field conditions. In parallel, we are developing digital signal processing tools for improving the signal to noise ratio (SNR) in the echoes acquired in NDE of media with complex internal structure (Lázaro et al 2002, Rodríguez et al 2004a, Pardo et al 2008).

In this technological context, a set of novel ultrasonic signal combination techniques have been developed to be applied in flaw detection ultrasonic systems based on multiple transducers. These combination techniques use a spatial-combination approach from the echographic traces acquired by several transducers located at different external planes of the piece under testing. In all these alternative techniques, the A-scan echo-information, received from the different transducers involved, is fused in a common integrated twodimensional (2D) pattern, in which, each spot displayed incorporates distinct grades of SNR improvement, depending on particular processing parameters.

In this chapter, some linear and non-linear digital processing techniques to fuse echo-traces coming from several NDE ultrasonic transducers distributed on two perpendicular scanning planes are described. These techniques are also applied to the flaw detection by using a 2D combination of the ultrasonic traces acquired from the different transducers. The final objective is to increase the detection capabilities of unfavorable-orientation flaws and also to achieve a good 2D spatial location of them.

Individual ultrasonic echo-signals are measured by sucesively exciting several transducers located at two perpendicular planes with electrical short-time pulses. Each transducer acquires a one-dimensional (1D) trace, thus it becomes necessary to fuse all the measured 1D signals with the purpose of obtaining an useful 2D representation of the material under inspection. Three combination techniques will be presented in this chapter; they are based on different processing tools: Hilbert, Wavelets and Wigner-Vile transforms. For each case, the algorithms are presented and the mathematical expressions of the resulting 2D SNRs are deduced and evaluated by means of controlled experiments.

Simulated and experimental results show certain combinations of simple A-scans registers providing relatively high detection capacities for single flaws. These good results are obtained in spite that the very-reduced number of ultrasonic channels involved and confirm the accuracy of the theoretical expressions deduced for 2D-SNR of the combined registers.
