·Table of Contents
·Methods and Instrumentation
Signal Processing for Ultrasonic Testing of Material with Coarse StructureT. Stepinski and L. Ericsson, Uppsala University, Signals and Systems, Uppsala, Sweden
|z(kT) = s(kT);||y(kT) ³c|
|z(kT) = 0;||y(kT)< c|
The subsequence length (bandwidth) c, required for target detection can be determined interactively by the operator. The bandwidth measure can be equivalently expressed in number of windows or Hz, as these units differ only by a multiplicative constant. Note that the thresholding operation is very simple and can be done in real-time while watching the result.
|Fig 1: Transients with phase angles f =0° (left) and f =90° (right)|
Application of the NCD algorithm in ultrasonics differ from telecommunication in that not only the phase, f , is unknown but also the envelope, A(t), and carrier frequency, f0, of the transients, (cf. ). Thus, the ultrasonic response signals must be modelled by a transient prototype that can be used for all target echoes within the inspected volume. Below we propose a simple model employing two parameters, cut-off frequencies flower and fupper , .
The NCD algorithm includes specification of the transient prototype, estimation of the grain noise statistics, followed by the computation of an optimal filter. The structure of the algorithm is displayed in Fig. 2. It should be noted that the filter construction process is part of the calibration procedure for the utilised transducer. The actual processing of the acquired ultrasonic data, employing the resulting filter, is very simple and may be performed in real time.
|Fig 2: Structure of the noncoherent detection algorithm.|
According to Fig. 2, the complete process of constructing a filter for target detection includes the following detailed steps:
|Fig 3: Example of estimated autocorrelation and power spectrum of grain noise.|
|Fig 4: Example of signal prototype, and its spectrum, flower=0.5 MHz, fupper=1.4 MHz.|
|Fig 5: Filter calculated from the noise correlation matrix and the signal prototype from above.|
An attractive property of the NCD algorithm is that small variations of the transient parameter values result in only small variations of the filter output. Consequently, near-optimal parameter values can easily be determined automatically using a suitable performance measure.
The parameters of the signal prototype must be tuned so that the transient covers the same spectral region as the target echoes that should be detected. While this operation may be performed manually by the operator it is not viable in an industrial environment. Therefore an automated procedure, based on a well-defined performance measure, has been developed.
The type of performance measure to be used during filter construction depends on whether target echoes can be localized in the acquired ultrasonic data or not. If a special calibration block is available, the exact defect locations should be known. In this case the actual signal-to-noise ratio (SNR), i.e., target echo energy divided by noise power, can be computed and used as a performance measure, . This method will be utilized in the evaluation below.
It is also possible to construct a "blind" performance measure working on data from an unknown object. Such an algorithm has to mimic the operator's way of looking at an unknown image, i.e., judging it as "good" if it has an ordered structure with a few peaks and "bad" if it is "noisy". One way of formalizing these vague criteria, which has turned out to be quite successful , is to utilize the concept of entropy, known from information theory. Signals that have an amplitude distribution with high entropy are characterized by a high degree of "disorder". In ultrasonic NDE we normally look for a few pulses (echoes from flaws), i.e., an ordered signal. Thus, from an operator's perception point of view, interesting results should be obtained if the ultrasonic data is filtered to yield low entropy amplitude distributions.
Regardless of the performance measure used during the filter construction procedure the basic idea is the same: the prototype parameters (flower and fupper) are varied in a systematic manner and the performance of the resulting filter is evaluated by applying it to the selected ultrasonic data. When a known test block is available, the set of data would typically be a B-scan containing one defect echo surrounded by grain noise. The coordinates of the defect and noise regions are then supplied to the filter construction algorithm so that the SNR enhancement (SNRE) can be automatically calculated for each set of prototype parameters.
|Fig 6: Two echoes separated in time by 2 µs.||Fig 7: Two echoes separated in time by 2 µs, after NCD processing.|
The NCD technique had no problems to resolve two echoes separated in time by 2 µs, see Fig. 7.Further reduction of the distance resulted in a smooth transition to one, wide echo. The SSP/CPC algorithm optimised for noise suppression also processed the same signal, see Fig. 8a. Obviously, in this case the temporal resolution is not good enough to detect both the echoes. By increasing the distance in time between the echoes the temporal resolution for the SSP/CPC, using the current parameter setting, was estimated to 6 µs, see Fig. 8b. It should be noted that when decreasing the distance below 6 µs the peak corresponding to the smaller echo disappears very abruptly.
|Fig 8a: Two echoes separated in time by 2 µs, after SSP/CPC processing.||Fig 8b: Two echoes separated in time by 6 µs, after SSP/CPC processing.|
One should also note that the SSP/CPC output gives the impression of high temporal resolution due to its sharp shape. Unfortunately, this has nothing to do with the resolution but stems from the fact that SSP/CPC is a nonlinear algorithm optimised for the detection single targets.
The temporal resolution of the SSP algorithm may be improved by increasing the bandwidth of the Gaussian filters in the filter bank. However, at the same time the clutter suppression performance is deteriorated. In order to get a temporal resolution comparable to the NCD the filter bandwidth had to be increased by a factor of three.
For illustration it is shown how this change affects the results for real ultrasonic data. Two B-scans of three side-drilled holes in stainless steel block, described in the next section, are shown in Fig. 9.
Fig 9a shows the B-scan obtained after processing using parameters optimal for signal enhancement while the modified parameter setting resulted in the image shown Fig. 9b. Evidently, the signal to noise ratio has been significantly reduced compared to Fig. 9a.
|Fig 9a: Three side-drilled holes after SSP/CPC processing with parameters obtained for optimal signal enhancement.||Fig 9b: Three side-drilled holes after SSP/CPC processing with parameters modified to obtain improved temporal resolution|
|Fig 10a: Back wall echo through 200mm of stainless steel.||Fig 10b: Back wall echo through 200mm of stainless steel after NCD processing|
The side-drilled holes were difficult to detect using the 2.25 MHz V325-SU transducer (cf. B-scan in Fig. 11). The same B-scan after NCD respective SSP/CPC processing is shown in Fig. 12a and 12b. The processing result is quite impressing, the results illustrate the fact that the NCD can yield better signal enhancement than the SSP/CPC.
|Fig 11: B-scan of three side-drilled holes obtained using V325-SU transducer. The holes are weakly pronounced at transducer positions 50 mm (Æ 10), 100 mm (Æ8) and 150 mm (Æ5)|
|Fig 12a: B-scan from Fig. 11 after processing with NDC||Fig 12b: B-scan from fig. 11 after processing with SSP/CPC|
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