## 4 The Integration of the Streamed and Crack Growth Signals
### The Application of Signal Decomposition to the NAVAIR Test Rig  
In the previous section, the decomposition of streamed signal is shown to detect the crack signal with the proper selection of the window size. The smaller the window size is used, the more accurate the crack detection is achieved. Therefore, in this section, different window sizes are applied to the streamed signals that were recorded from the NAVAIR test rig. It is important to note that the complexity of gearbox structure, source mechanisms, and AE method causes the AE source identification highly challenging. The purpose is to identify the unusual AE signals (typically burst types) that are embedded into the streamed signals as outliers, which indicate the divergence from the normal operation. Fifteen (15) streamed waveforms are selected from the acoustically stable times of each testing day (the experiments are started in mornings and ended in about 3-4 h). The streamed signals are decomposed with different window sizes of 6 ms, 2 ms, and 1 ms. The frequency centroid is extracted from each window. In order to reduce the influence of operational condition, the frequency centroid is normalized to each mean value.  
The outliers are determined as the AE data outside the dashed blue lines, as shown in Figure 17. The overall outlier considers the mean value of all data recorded throughout from day 1 to day 6. The individual outlier considers the mean value of individual day and identifies the limits for the outlier per day. As shown in Figure 17, both methods of outlier identification have similar cumulative outliers. With the decrease of window size, more outliers are observed, especially in the test day 2. The streamed signals from the test day 2 are plotted in Figure 18. There are several burst signals that are detected inside the streamed signals. The windowed frequency spectra using 1 ms duration indicate the peak frequency and the frequency centroid values are 152 kHz and 230 kHz, respectively. The values are similar to the characteristics of crack signal obtained in the laboratory. The crack size is measured using replica, and is shown in Figure 19. The crack grows gradually until the test day 4 and then exponentially. The crack length data of test days 2, 3, 4, and 6 are measured from the replica inserted into the gearbox; the data of test day 5 is obtained by curve fit. It is important to note that the test duration of each day is about 3-4 h, where above 2000 streamed waveforms are recorded. In this paper, only 15 streamed waveforms per day are analyzed. Therefore, the exponential change in the crack length cannot be observed from the outlier plots in Figure 17. The AE method cannot detect the crack size; however, it can predict the presence of unusual behavior in data, which can be used as the indication for performing more quantitative nondestructive evaluation methods.  
Figure 16: The relation of the predicted error and the number of the windows in relation to the window size.  
Figure 19: The crack growth behavior of fatigue experiment conducted at the NAVAIR facility.  
Figure 17: The outlier prediction with different window sizes.  
Figure 18: The burst signals detected in the test day 2 and their frequency spectra using the windowed time histories.