Dx atlas crack

In particular, ZAM distribution belongs to the category of quadratic time-frequency representations and, especially, to the group of reduced interference distributions RIDs. The ZAM distribution is derived by choosing the kernel function as follows: where is a window function that leads to smoothing along the frequency axis. Thus, the following expression can be obtained that defines the ZAM distribution: ZAM distribution was selected among RIDs due to its advantage of significantly reducing cross-terms between signal components, through its cone-shaped kernel function 4 [ 7 ].

Smoothing was performed using Hamming windows of -samples and -samples for time and frequency, respectively. Taking the ZAM distribution of the time series of beam responses to the VAM stimulation, that is, , a more detailed exploitation of the modulation effects can be achieved by analyzing the mean amplitude and fluctuation of at the main sidebands around the high-frequency component, that is, , along with the mean amplitude and fluctuation of at the excitation frequency, that is,.

From this perspective, changes in the mean value and the dynamic range of amplitude fluctuation, combined with the inspection of the spectral characteristics of this fluctuation, could correlate with the crack depth and provide insight into the way the presence of the crack affects the beam response during VAM stimulation.

Tests were performed on Plexiglas beams to obtain nonlinear modulation responses for further signal processing. The coil was placed in the field of a permanent magnet and was excited by two waveform generators using sinus signals. A miniature transducer was used to pick up the vibration response, which was transferred to an acquisition system and stored for further analysis. A very narrow cut was initially introduced to the beam. Next, the beam was subjected to controlled dynamical loading which caused crack propagation.

Due to the structure of Plexiglas, the propagation of the crack could not be accurately controlled resulting in arbitrary crack depths. A Bruel and Kjaer piezoelectric charge transducer was used for the high-frequency excitation. A schematic representation and a photo from the actual implementation set-up are depicted in Figures 1 a and 1 b , respectively.

During the experiments two continuous sine waves were simultaneously introduced to the beam. The first was the high-frequency ultrasound probe wave at kHz. The second wave was the low-frequency vibration at a frequency of Hz, equal to the resonance frequency of the intact beam. Figure 2 depicts an excerpt from the measured response for the uncracked and the three different crack depth cases a to d , respectively.

As it can be seen from Figure 1 , strong modulation components are present and increase with increasing crack depth. Apparently, from these plots it is clear that a series of sidebands is evident, with the at Hz and Hz being the most noticeable, compared to the rest.

From the latter, it is clear that the amplitude is inversely proportional to the crack depth, whereas the amplitude fluctuation is highly increased as the crack depth also increases. Moreover, there is a clear periodicity in the amplitude modulation for the case of Figure 4 b ; a noticeable, yet not so intense, one is evident in the amplitude modulation of.

As it is clear from Figure 5 , the low excitation frequency Hz modulates the amplitude of Figure 5 b , whereas mainly the first harmonic of , that is, Hz, causes the amplitude fluctuation Figures 5 a and 5 c , resp.

Similarly to the spectral characteristics of the amplitude modulation of ZAM transform seen in Figure 5 , here the low excitation frequency Hz modulates the frequency fluctuation Figures 6 a and 6 c , resp.

Figure 8 depicts the along with the defined in 2. Apparently, the surpasses in terms of higher sensitivity in the crack depth change, as it better captures crack changes, even in small crack depths. When comparing the presented work with the one of Zaitsev et al.

Both works conclude that the damage index based on the amplitude modulation is better than the one based on the frequency modulation.

Nevertheless, the latter damage index of [ 6 ] unexpectedly increases nonmonotonically as the severity of crack increases; here, as it is derived from Figure 7 second and third rows , the damage indices based on the frequency fluctuation range and std of the ZAM distribution increase monotonically with the crack depth, exhibiting, though, reduced sensitivity in the small cracks identification. This, in turn, is compensated by the damage index based on the inverse of the ZAM amplitude.

Moreover, the analysis in [ 6 ] is prone to the mode-mixing effect; that is, a single intrinsic mode function IMF derived from the Empirical Mode Decomposition employed in [ 6 ] consists either of signals of widely disparate scales or a signal of a similar scale residing in different IMF components. Mode-mixing is often a consequence of signal intermittency, which could not only cause serious aliasing in the time-frequency distribution, but also make the physical meaning of individual IMF unclear [ 9 ].

The proposed analysis here does not produce any mode-mixing effect, as it is clearly shown in the time-frequency distributions of Figure 3 , making the relevant damage indices more robust to any signal intermittencies.

In this work, the investigation of the vibroacoustic modulation of cracked beam is approached in the time-frequency domain, using time-frequency analysis based on the Zhao-Atlas-Marks ZAM distribution. ZAMs efficient time-frequency representation of the vibrational information, with reduced cross-terms between signal components through its cone-shaped kernel function, allowed for detailed monitoring of the VAM effects on beam behavior due to the existence of a crack.

The hypothesis adopted here, that is, the characteristics of modulation responses in time domain might be proved more sensitive compared to those in the frequency domain and the combination of both could lead to damage indices that are more sensitive and robust, was proved valid. Considering the responses at the ZAM domain and, especially, the reduction of mean ZAM amplitude at the sidebands and excitation high frequency with the increase of the crack depth a new damage index was formed, that is,.

The latter led to a more sensitive response compared to the one based on the spectral characteristics of the beam response, that is, , better capturing crack changes, even in small crack depths.

The promising results presented here enable more efficient applications of the proposed method in nondestructive damage detection applications. The authors declare that there is no conflict of interests regarding the publication of this paper.

Trochidis et al. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Trochidis, 1 L. Hadjileontiadis , 2 and K. There are crack groups who work together in order to crack software, games, etc. If you search for Dx Atlas Crack, you will often see the word "crack" amongst the results which means it is the full version of the product. The word "serial" means a unique number which identifies the license of the software as being valid.

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