Geometrical Feature Extraction from Ultrasonic Time Frequency Responses: An Application to Nondestructive Testing of Materials
© Soledad Gómez et al. 2010
Received: 30 December 2009
Accepted: 17 March 2010
Published: 28 April 2010
Signal processing is an essential tool in nondestructive material characterization. Pulse-echo inspection with ultrasonic energy provides signals (A-scans) that can be processed in order to obtain parameters which are related to physical properties of inspected materials. Conventional techniques are based on the use of a short-term frequency analysis of the A-scan, obtaining a time-frequency response (TFR), to isolate the evolution of the different frequency-dependent parameters. The application of geometrical estimators to TFRs provides an innovative way to complement conventional techniques based on the one-dimensional evolution of an A-scan extracted parameter (central or centroid frequency, bandwidth, etc.). This technique also provides an alternative method of obtaining similar meaning and less variance estimators. A comparative study of conventional versus new proposed techniques is presented in this paper. The comparative study shows that working with binarized TFRs and the use of shape descriptors provide estimates with lower bias and variance than conventional techniques. Real scattering materials, with different scatterer sizes, have been measured in order to demonstrate the usefulness of the proposed estimators to distinguish among scattering soft tissues. Superior results, using the proposed estimators in real measures, were obtained when classifying according to mean scatterer size.
Signal processing is an essential tool in nondestructive material characterization. Modern technologies can take benefit of more sophisticated algorithms allowing to classify and characterize materials precisely. One of the techniques that takes advantage of all these advances is the nondestructive testing (NDT) using ultrasounds. Thanks to the advances in signal processing it is now easy to find applications of NDT using ultrasonics in materials, that some years ago was very hard to find [1–3].
The Signal Processing Group (GTS) of the Universidad Politécnica de Valencia published a technique  that allows to characterize dispersive materials by means of pulse-echo inspection with ultrasonic energy. The aforementioned technique was based on extracting time of flight-dependent parameters from the ultrasonic A-scan. This technique involves assuming a Linear Time Varying (LTV) model for the ultrasonic inspection of dispersive material. The extracted parameters were affected by the physical properties of the material and automatic classifiers could be used.
In this paper we introduce a novel technique to extract parameters, based on the shape analysis of time frequency responses, that complement or in some situations improve the performance of the previously published methods.
This work is going to be structured as follows. In Section 2 we describe a simple model that demonstrates how physical properties of scattering materials affect the time frequency representation (TFR) of the A-scan. Later, in Section 3, we briefly review the traditional parameter estimators presented in . In Section 4 a new technique based on computing geometrical descriptors from the TFR is introduced. A comparative study of the traditional versus the new proposed technique is presented in Section 5. An example of application to characterize mean scatterer size on soft dispersive materials is also shown in this section. Finally in Section 6, conclusions are presented.
2. Ultrasonic Pulse Modeling in the Frequency Domain
Equations (7) and (8) predict a downshift in the central frequency and a pulse narrowing due to Stochastic scattering attenuation. Similarly, and as it was expected, (9) predicts faster attenuation in depth for materials with larger mean grain size. All these behaviors affect the shape of the A-scan TFR and can be used to design algorithms for material classification, based on the amplitude, frequency, or bandwidth profiles. This shape dependence can also be used for scatterer mean size estimation. The TFR of a register obtained in NDT of scattering materials can be modeled using (6). The parameters , , and will affect the shape of the TFR.
3. Conventional Parameter Extraction for Material Characterization: The Ultrasonic Signature (US) Concept
As already mentioned, information about the material is included in the A-scan. Among some other possibilities to extract information about the materials [5, 7], the analysis of the variant impulse response (or equivalently the variant frequency response) of the LTV is a feasible alternative. The time-variant characteristic of the model leads naturally to a nonstationary analysis of the recorded signal.
This technique proposes the use of a short-term frequency analysis of the signal to isolate the evolution of the different frequency components. This can be done by means of explicit implementation of a bank of filters or, more usually, by means of some type of linear or nonlinear time-frequency transformation, including nonconstant bandwidth analysis like wavelet transform. From the time-frequency signal we obtain the US which is a one-dimensional signal hopefully encompassing the relevant information needed for every particular purpose. The US  is obtained by computing for every time instant, along a finite discrete time interval, a spectral parameter; some possible alternatives are
4. An Alternative Technique to Conventional Parameter Extraction for Material Characterization
2-D shape analysis can be applied to the TFR of the ultrasonic A-scans for material characterization. The motivation of this idea was based on the observation that the mean scatterer diameter, , affects TFR shapes (see Figure 1). It is expected that using shape-related parameters applied to the TFR, we will be able to classify materials with different scatterer sizes. Additionally, if a process of binarization of TFR is employed, previous to the extraction of geometrical parameters, the obtained parameters should be less affected by noise.
The application of geometrical parameters to TFR diagrams provides an innovative way to complement classical techniques based on one dimensional US and an alternative way of obtaining similar meaning and less variance estimators (as we will show in Section 5).
We are going to see in the next section the set of geometrical parameters that allow us to classify materials according to scatterer size.
4.1. Geometrical Descriptors
From , the binarized TFR generated with the mixed threshold, we can calculate many geometrical descriptors [8, 9]. Our contribution, at this point, is to work with shape or geometrical parameters having a physical meaning related to the expected changes produced in the TFR. It is expected that geometrical descriptors will provide a most intuitive representation of the model in comparison with the classical signal-processing parameters. For example, we can establish visual relations between orientation parameters and physical variations of attenuation or frequency along depth.
The most representative geometrical descriptors that have proven to give good classification results are given below.
If we use the area parameter to distinguish between materials with similar attenuation coefficient but including scatterers with different sizes, it is expected that materials with higher scatterer sizes get lower value of the area descriptor.
4.1.2. Center of Gravity
By using first-order moments, the center of gravity or centroid of a binary representation can be calculated.
We can use the eccentricity parameter to distinguish between materials with similar attenuation coefficient but including scatterers with different sizes. For lower scatterer sizes eccentricity is expected to be higher than for higher scatterer size materials. Seeing TFR diagrams depicted in Figure 1, we can notice how materials with higher value of have more circular shapes than those having lower . So, it is expected that the higher the lower the eccentricity value is.
4.1.5. Boundary Signature (BS)
The BS is a 1-D representation of an object boundary. One of the most simple ways to generate the BS of a region is to plot the distance from the center of gravity of the region to the boundary as a function of the angle, . Figure 3 illustrates this concept. The changes in size of binarized TFR result in changes in the amplitude values of the corresponding BS. It is expected that the higher the value of is, the lower the amplitude of the corresponding BS. Moreover, the BS not only provides information about area changes but also provides the angular direction of such changes. To compute the BS we need to compute for each angle, , the Euclidean distance between the center of gravity and the boundary of the region. As will be demonstrated, it is expected that different values of , for the model or material under test, will correspond with different BSs for the binarized TFR.
4.1.6. Frequency-Derived Parameters
Some frequency-derived parameters have been also tested such as centroid frequency, central frequency, or bandwidth.
To compute the centroid frequency evolution with depth we divide the binzarized TFR into small rectangles along the -axis and then we compute the center of gravity (described above) for every rectangle, the final result is the evolution of centroid frequency along horizontal direction.
The process to compute the bandwidth evolution is similar to centroid frequency computation. In the case of bandwidth the width of each rectangle is computed, thus obtaining the evolution of bandwidth with depth.
5.1. Application of Conventional and Geometrical Descriptors to Simulated Signals
Simulated signals have been generated according to the model presented in Section 2.
From the observation of Figures 6 and 7 we can conclude that both methods are equivalent when estimating the central frequency. This is quite obvious, if we take into account, that the central frequency estimator is computed using the nonbinarized TFR diagram and it computes the maximum of each block along -axis (2-D shape analysis is not applied). However, the estimator behavior changes when extracting 2-D geometrical parameters from the binarized diagrams (centroid and fractional bandwidth estimators). If we compare the fractional bandwidth estimator computed using the conventional technique with the fractional bandwidth estimator computed over binarized TFR diagrams, it can be appreciated the lower variance (represented by shorter vertical bars) but higher bias (represented by higher value markers). If we compare centroid frequency parameter computed with both presented techniques, we observe that we get lower variance (vertical bars) and bias (markers) when geometrical estimator is employed. For the centroid frequency parameter, superior performance of the geometrical estimator is obtained in high noise conditions.
It is also worth mentioning that if we compare the centroid estimator in Figures 6 and 7, benefits of using the proposed geometrical estimators are as big as the mean scatterer diameter ( ) increases. Note, that the bias increases when increases for the conventional centroid estimator.
5.2. Application of Conventional and Geometrical Descriptors to Distinguish Variable Size Scatterers in an Agar-Agar Matrix
Composition of the test pieces.
The measurement equipment was a PC with an ultrasonic board IPR-100 (Physical Acoustics) working in pulse-echo mode with 400 V of attack voltage, 40 dB in the receiver amplifier, and damping impedance of 2000 Ohms. The transducer frequency was chosen to be 1 MHz (K1SC transducer probe from Krautkramer and Branson). Received signal was acquired with the Tektronix 3000 oscilloscope ( = 50 MSamples/s).
The set of 8 test pieces was separated in two subsets: the odd subset (composed by test pieces 1, 3, 5, and 7) and the even subset (composed by test pieces 2, 4, 6, and 8). Both subsets were measured separately and individual estimators were computed and compared between subsets. The measurement procedure was as follows: uniformly distributed A-scans were obtained around each test piece contour. Individual A-scan TFRs were obtained using the Spectrogram (by means of the Short-Time Fourier Transform). Final TFR for each test piece was obtained averaging individual A-scan TFRs. After thresholding the final TFR, geometrical descriptors presented in Section 4 were calculated for each subset. The parameters and graphs obtained after processing each subset were similar, for that (and for representation purposes) all parameters and graphs presented in this section were averaged for even and odd subsets, thus representing an only value for each parameter for every value of .
The area values obtained in Table 2 agree with the expected behavior described in Section 4. It can be noticed that higher scatterer sizes get lower value of the area descriptor. This trend is coarsely maintained among all scatterer diameter sizes ( ).
The orientation parameter values presented in Table 2 also agree with the expected behavior described by (7) since it predicts a downshift in the TFR shape (see Figure 1). Physical explanation is based on the fact that the higher the value of , the higher the attenuation of the ultrasonic energy at high frequencies. As a result of that, higher values get higher negative slope (with respect to horizontal axis). The orientation parameter allows to distinguish coarsely between small scatterer test pieces ( and mm) and large ( and mm).
The eccentricity parameter values presented in Table 2 show that the higher the lower the eccentricity value is. This behavior agrees with theoretical equations and allows to classify all the test pieces.
To sum up, from Table 2 and Figures 9(b) and 10, it is important to stress that area and orientation parameters can classify test pieces in two categories (large and small scatterer sizes) whereas eccentricity, centroid frequency and BS provide better results since they are able to distinguish among the four different scatterers sizes.
In this paper we show that parameters extracted from the TFR of ultrasonic A-scans can be used for material characterization/classification. The novelty of this work is based on the use of TFRs as input information in 2D-shape analysis algorithms, specifically geometrical descriptors. This technique compliments traditional classification parameters (attenuation, longitudinal ultrasonic velocity, etc.) with shape-related parameters. Additionally, for some parameters, the new technique allows to obtain lower variance estimators. When binarized TFRs are processed and 2-D geometrical modeling, inherent in our approach, is used, a new set of estimators can be derived. The proposed geometrical estimators can provide better estimates and moreover, they are less sensitive to noise than conventional estimators. Thanks to this superior performance, in terms of bias and variance, a better classification of scattering materials can be achieved. This behavior has been validated through simulations.
The results were applied to real test pieces created at the laboratory. Traditional estimators could hardly be used to classify according to mean scatterer size. However, estimators based on geometrical descriptors of the binarized A-scan TFR could easily distinguish among the different scattering sizes. Concretely, area and orientation parameters can classify test pieces in two categories (large and small scatterer sizes) while eccentricity, centroid frequency and BS provide better results since they are able to distinguish among the four different scatterers sizes.
This work was supported by the national R + D program under Grant TEC2008-02975 (Spain), FEDER programme and Generalitat Valenciana PROMETEO 2010/040.
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