## 4 The Integration of the Streamed and Crack Growth Signals
### Detectable Fatigue Crack Energy with Respect to Background Noise  
In the previous section, the decomposition of streamed signal is shown as a feasible way to identify the crack signals from the streamed signals with low SNR. However, the window size selection is an important variable to determine the position of the crack signal. Several window sizes, including 200 \(\upmu\)s, 400 \(\upmu\)s, 600 \(\upmu\)s, 800 \(\upmu\)s, and 1000 \(\upmu\)s, are selected, and the AE feature extraction is repeated. The window size is limited to 200 \(\upmu\)s in order to obtain good frequency resolution in the range of 20-400 kHz. The crack signal is embedded at 51 ms. Figure 12 shows the spectra of frequency centroid. The embedded crack signal can be identified clearly, as shown in Figure 12a,b by the decrease of frequency centroid in the range of 260-270 kHz near 51 s, as indicated by the color change in the spectra. The spectra of frequency centroid obtained from the original streamed signal are shown in Figure 12c, which has uniform distribution of frequency centroid throughout the streamed signal and no indication of the crack signal. Similarly, the spectra of AE power can also be used to identify the crack signal, as shown in Figure 13. However, as \(SNR\) is one, the amplitude related feature of AE power could cause artificial outlier signals, as observed near 115 s in Figure 13. If \(SNR\) is greater than one, AE power also separates the crack related activity from the secondary sources. However, the spectra of peak frequency fail to distinguish the crack signal, as seen in Figure 14. If \(SNR\) is greater than one, all three features identify the position of the embedded crack signal when the window size is less than 1 ms.  
For improving the efficiency of signal processing method, a larger window size is preferable to reduce the computational time. The window size is increased up to 8 ms, and the \(SNR\) is kept the same as 1.0. It is identified that if the window size is larger than 2 ms, the background signal dominates the crack signal, as shown in Figure 15. The distinction between outlier and mean feature is reduced with the increase of window size.  
Figure 12: The spectra of frequency centroid (unit: kHz), (**a**) embedded streamed signals (\(SNR\) = 1.0), (**b**) zoomed embedded stream signals, and (**c**) original streamed signals.  
Figure 13: The spectra of AE power (unit: V*s\({}^{2}\)), (**a**) embedded streamed signal (\(SNR\) = 1.0), (**b**) windowed embedded stream signal to 45–60 ms, and (**c**) original streamed signal.  
While small window size improves the resolution of crack detection, large window size can reduce the computational cost of the identification process. Figure 16 shows the prediction error and the number of windows used to divide the streamed waveform. The predicted error is calculated by  
\[Predicted\ error\ (\%)=\frac{|p(t)-e(t)|}{e(t)}\times 100 \tag{2}\]  
where \(p(t)\) is the predicted embedded time and \(e(t)\) is the actual embedded time. While Figure 15 indicates that the window size of 200 us has more indicative change in the spectra of frequency centroid,  
Figure 14: The spectra of peak frequency (unit: kHz), (a) embedded streamed signal (\(SNR=1.0\)), and (b) original streamed signal.  
Figure 15: The spectra of frequency centroid by selection of different window size, (a) three-dimensional (3D) suface plot (b) projected to xy plane, and (c) window of (b) with the time window of 40 ms to 60 ms.  
the minimum error is at the window size of 1 ms as this is the duration of the embedded crack signal. It is recommended to have the window size less than 1 ms, as typical AE signals due to the fatigue crack growth in metals have short duration.