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On the Uncertainty of Time-Frequency Domain Resolutions for Ultrasonic Velocity Evaluation of Surface Elastic WavesEdouard G. Nesvijski, Tatiana E. Nesvijski
Center of Technology, Federal University of Santa Maria, Santa Maria, RS, Brazil
Nondestructive characterization of materials and structures contains a great possibility to organize a "safe belt" for infrastructure reliability and environment protection. Acoustic methods of nondestructive evaluation (NDE) of materials have held leading position among other NDE methods for practical applications. A lot of academic institutions and manufacturing companies are engaged in research and development of new approaches to automation and measuring: data acquisition, signal processing, dynamic imaging, computer-personnel interface, etc. However, some basic problems of acoustic measurements have been studied for a long time. The most critical of them is uncertainty of time-frequency domain resolution of ultrasonic velocity evaluation for testing of materials and structures. This uncertainty is critical for velocity evaluation of different types of surface waves: Lamb, Love, Stoneley, and some modes of leaky waves. All these types of waves (except Rayleigh waves case) are dramatically dependent on frequency domain due to their high velocity-frequency dispersion characteristics. The uncertainty of ultrasonic frequency domain is a core obstacle for application of surface waves for NDE needs.
Most construction materials, such as ceramics, concrete, wood, metal-matrix composites, etc. are inhomogeneous materials and their analysis by ultrasonic means is a complicated task. Several problems may be considered here:
All the above-mentioned represent only a part of existing problems.
Presently most ultrasonic equipment for measurements of wave velocity in construction materials uses ultrasonic pulses of high intensity for generation of ultrasonic waves. Ultrasonic velocity through material ("pitch-catch") or pulse-echo methods are applied for materials testing. The first approach has problems with changing pulse form during wave propagation from generator to receiver. The second one is more complicated as there are also reflections from flaws or the opposite edge of the specimen as well as double propagation distance and accordingly considerable changes of form and frequency spectrum of receiving pulses. In a number of papers [1, 2] such materials are considered as a low-pass filters, but this model seems to be very simplified. Some experimental works  demonstrate that such construction materials may be better represented as "comb" filters. Such a model describes spectrum as pass-in and pass-off gates for propagating pulse. As a result parts of initially generated pulses are dropped out, and phase spectrum also suffers some transformations. These effects lead to impossibility of describing velocity dispersion characteristic as a monotonically changing dispersion function. It may physically explain why the fastest components of the propagating wave are not necessarily the highest frequency components of the pulses.
Unlike pulse velocity through material and pulse-echo ultrasonic testing methods surface waves techniques seem to be more applicable as allow to test materials using one-side approach. But the problem of the uncertainty of time-frequency domain resolution for ultrasonic velocity evaluations is still very important for surface waves techniques. It may be explained by the following:
The problem of measurements of wave velocities is still open for most of construction materials because of great attenuation of pulses and due to the fact that "velocity" definition for them does not fully correspond to physical-acoustical definition of the phenomena. However, many authors continue to use measured values of pulse velocity for calculations of many physical properties of materials such as modulae of elasticity, plasticity, porosity, strength, etc. [4, 5]. Application of the discrimination method for measurements of pulse arrival time is based on threshold trigger switching when amplitude of the arriving pulse is higher than the threshold level. As the arriving wave is represented by quasi-periodical signal then loss of the fastest components of the signal may occur due to high attenuation of pulses or their level may be lower than the threshold level (Figure 1).
|Fig 1: Loss of the fastest components of the signal due to high attenuation of pulses, when their level is lower than the threshold level ( TH ).|
The other situation when the threshold is fixed for negative level may lead to loss of the positive phase of the arriving wave (Figure 2).
|Fig 2: Loss of the positive phase components of the signal, when the threshold ( TH ) is fixed for negative level|
Presence of noise makes this problem even more serious because the threshold level has to be elevated (Figure 3).
|Fig 3: Loss of the fastest components of the pulse due to high level of noise and accordingly elevated level of the threshold ( TH )|
The above-mentioned problems make us to look for new approaches to uncertainty of ultrasonic velocity evaluation. One of the approaches may be based on application of time-frequency convolution, which describes frequency structures of propagating waves as well as phase-time changes of propagating pulses. The general algorithm of time-frequency convolution  may be presented by (1) as a mathematical model of an ultrasonic pulse U( t ) in time domain t
|Fig 4: Ultrasonic pulse in time domain||Fig 5: Ultrasonic pulse in frequency domain|
In the Figure 5 FFT of the pulse from the Figure 4 is presented:
In the Figure 6 a model of convolution function of the same pulse is presented:
|Fig 6: Convolution of ultrasonic pulse|
This work is an attempt to underline some problems, which have been on the way of the progress of ultrasonic testing of materials and structures for a long time. Presently different composite and inhomogeneous materials are used as construction materials. Their structures differ considerably from other traditional homogeneous materials, such as metals, and accordingly their ultrasonic testing is bringing new problems that require solutions. High attenuation of pulses and wave velocity dispersion are among them. On the other hand, application of different types of surface waves require accurate analysis of spectral composion of received ultrasonic pulses as well as a correct registration of time of the first wave arrival. These problems have to be discussed and ways to solve the uncertainty of time-frequency domain resolution for ultrasonic velocity evaluations have to be found for further progress in the NDE testing of construction materials.
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