# A Wear Debris Signal Processing Method Based on Inductive Monitoring for Aero-Engine
## 4 Debris Detection Based on Histogram in the Sliding Window  
The main reason for a false alarm is that the amplitude of the noise signature exceeds the threshold. Thus, the noise signature is mistaken for the debris signature. Here, there exists an important issue, that is, the determination of the threshold. Take the signal illustrated in Figure 3 as an example, there occurs a change in working conditions, which is a challenge to the algorithm for debris detection in real-time monitoring. The signal amplitude may increase due to the changes in working condition even if there is no debris passed through the inductive sensor. For monitoring algorithms based on absolute thresholds, it is likely to be mistaken for debris, which results in a high false alarm rate. In addition, the sensor system can only acquire the data up to the current time during real-time monitoring. In other words, the complete data can not be available until the test is over, which is another problem for monitoring algorithms based on absolute thresholds. Figure 6: Results of excessively large time interval: (**a**) T = 0.04 s and (**b**) T = 0.004 s.  
Figure 7: Results of excessively small time interval: (**a**) T = 0.0004 s and (**b**) T = 0.004 s.  
Regarding the issues above, a new monitoring method for debris detection is proposed. Based on the results in the time domain analysis, a sliding window is added to the energy value signal, and the debris signature detection is executed by the data distribution in the histogram. The movement of sliding window is illustrated in Figure 8. The fixed-length window iterates forward by one energy value in each round, until the entire energy value signal is traversed. For the data falling into the sliding window, a histogram with a fixed number of bins is performed, whose upper and lower boundary are the maximum and minimum value of the data in this sliding window. The main parameters of this section are the width of sliding window and the number of bins of histogram. Width of sliding window is equal to the number of energy values in the window. Due to the histogram and statistical requirements, the width of sliding window cannot be small. However, it cannot be too large, since this method detects debris signature by iterative local identification. The number of bins is related to the capability of debris detection. After verification, the width of the sliding window is set to 80 and the number of bins is set to 4, which are suitable for general application. The data distribution of the typical debris signature and noise signature are illustrated in Figure 9. For the debris signature, the histogram shows an unusual distribution, only a few data fall into the highest bin, while most of the data are concentrated into the lowest bin, and there are several blank bins in the middle. In sharp contrast to the debris signature, the histogram of the noise signature is more even. The reason is that the energy value is extremely high when the debris signature falls into the sliding window, and the upper boundary is the maximum value of the data in this sliding window. Therefore, the upper boundary can be extremely high when the debris signature is included in the sliding window, which results in the concentration of the data being in the lowest bin and the blank in the middle bins. Figure 8: Schematic diagram of the movement of sliding window. In order to evaluate the concentration of the data quantitatively, the threshold is set as the percentage of data falling into the lowest bin. Specifically, the threshold is set to 95%. The detection results of this method and the actual results provided by the suppliers are illustrated in Table 1 and Figure 10. The error between the detection time and the actual time has disclosed the effectiveness of this method.