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·Computer Processing and Simulation
An Evaluation Approach to NDT Ultrasound Processes by Wavelet TransformG. Cavaccini, M. Agresti, G. Borzacchiello
Alenia Un'Azienda Finmeccanica - Pomigliano d'Arco (Naples, Italy)
E. Bozzi, M. Chimenti, O. Salvetti
Consiglio Nazionale delle Ricerche - Istituto di Elaborazione delle Informazioni - Pisa (Italy)
The simulation of characteristic spectrum and waveform of the ultrasonic transducer was performed: an accurate reproduction of the transducer waveform is essential both for simulating the wave propagation and for assuring a reliable fitting between simulated and experimental data as well.
The probe frequency spectrum distribution d(f) is created by adding two distorted normal branches (left and right with respect to the central frequency f0), where the distortion is realised by exponential damping factors and skewness addends:
where s i, m i and si are, respectively the left/right standard deviations, the damping coefficients and the skewness coefficients.
The transducer waveform w(t) - amplitude vs. time - was obtained adding sine contributions:
d = wave damping coefficient,
t0 = delay
j = phase.
Fig 1: Simulated frequency spectrum (top) and signal waveform (bottom) of the 5 MHz probe.|
They were considered the multiple reflections due to first echoes, as well as the attenuation of sound waves as they travel away from their source. To reflect the "structure" of experimental waveforms and noising perturbations, an heuristic corrective factor Fc(t,f0), depending on the central frequency of the transducer, was introduced that multiplies the wave propagating through the part-defect configuration
The front echo has been calculated by:
We calculated several waveforms and we compared them with the US signals obtained by inspecting some composite material, typically used during manufacturing of Eurofighter 2000 Typhoon (EFA) parts. In particular, we report two examples relative to EFA laminated area of a sandwich made of Hexcel 8552/IM7 carbon epoxy material (see Figure 2). To inspect the part, a contact scanning was performed, using a Krautkramer USD15 pulser-receiver.
Fig 2: Left. Central cavity (air), with part thickness = 3.3 mm, defect-part front face distance = 1.5 mm, defect thickness = 0.1 mm. Right. Resin enrichment area, with part thickness = 3.3 mm, defect-part front face distance = 1.5 mm, Defect thickness = 0.1 mm.
Preliminary One-Dimensional Wavelet Analysis
Matlab tools were used; the Daubechies 5 wavelet was chosen, because it seem to approximate in a realistic way experimental data.
Simulated signals were processed so to obtain time-scale plots, where x-axis represents time, y-axis represents the scale and the colour at each x-y point represents the magnitude of wavelet coefficient. The analysis of time-scale plots permits to point out similarities in wave's structures. This can be used as basis for recognising, and for some aspects characterising, the defects.
Fig 3: Time-scale plot-Central cavity case.
|Fig 4: Time-scale plot-Resin enrichment case.|
Preliminary Two-dimensional Wavelet Analysis
In order to obtain a C-Scan map, the ultrasound transducer is moved along two directions across the specimen to reach the scanning position (i, j), and the peak value P (i, j) of the echo signal inside a predefined time gate is measured. The map is represented by a multi- level digital image, whose pixels have a luminance value proportional to P (i, j).
Assuming that the time gate is located in correspondence of the back-wall echo, the signal measured in presence of porosity is smaller than that obtained in normal conditions: hence, the C-Scan map shows a pattern, normally irregular, of small round blobs, darker with respect to undefected areas.
In order to assess the porosity content of the inspected specimen, an image processing procedures should extract from the image some geometrical and photometric features and to analyse them. The two-dimensional wavelet transform can be used as an intermediate step to filter and reduce data; for this purpose using the MATLAB environment and the Wavelet and Image Processing Toolboxes we begun to study the effectiveness of this approach and we developed a graphic interface and some modules for file management and data pre-processing.
In particular, the interface allows to select the wavelet family and to define a set of weighting parameters wk in order to process an input image S and to obtain the output image O, given by
O = w1 H + w2 V + w3 D
where H, V and D are the horizontal, vertical and diagonal detail images produced by wavelet analysis.
In the following example, the input image (see figure 5) contains 9 round blobs with diameter increasing from 5 to 21 pixels in steps of 2 pixels; the minimum value of luminance of all blobs is zero.
Figure 6 shows the sum of the horizontal and the vertical detail images at level 1 obtained by applying the wavelet bior 1.3 to the input image; the pixel values of the image in figure 6 are expanded to the full interval 0-255.
Using a 53 ´ 48 rectangular area centred on each blob of figure 6 we calculated the histograms of photometric values; table 1 reports the minimum luminance value of the filtered blobs.
|Fig 5: Input image||Fig 6: Output image produced by bior 1.3 wavelet.||Fig 7: Thresholded output image.|
|Table 1: Minimum value of luminance Lmin of filtered blobs of figure 6.|
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