## 4 Practical Example of the Proposed Method
Figure 12: Spectrogram of acoustic signals measured at near blower of air-conditioner (AC): (**a**) case of normal AC with impulsive noises and beep sounds; (**b**) case of faulty AC with abnormal noises. Figure 13: Band-pass filtered acoustic signals: (**a**) normal AC with impulsive noises and beep sounds; (**b**) faulty AC with an abnormal noise. Figure 14a compares the magnitude at the rotation frequency of around 13 Hz in the spectrum obtained with a 0.5-s-length time window (considering the time resolution and frequency resolution) and 50% overlap for the envelope of the normal and noise-defective signals shown in Figure 13. This figure shows only the magnitude at the rotational frequency according to the conventional method, and it is not possible to distinguish between the normal and the noise-defect signals due to impulsive noise at around 3 s. Figure 14b shows a graph considering the baseline magnitude of the low frequencies obtained by the method proposed in this study. The noise-defective signal shows almost no difference from Figure 14a, whereas the normal signal has a value close to zero overall. In particular, the value showed very dramatic improvement at around 3 s, at which the impulsive noise was mixed into the normal signal. To confirm the practicality of the proposed method, it was applied to 500 ACs that were under production. At this time, the detection rate was verified by also putting five ACs into the assembly line that had been investigated for noise-defects by the interference between foreign substances and the fans. Figure 15 shows the results of the proposed method for 500 normal ACs and the 5 noise-defective ACs for verification. The detection value used for the result is the mean of the values shown in Figure 14. Figure 15a shows the mean values obtained over time (0.5-s-length time window and 50% overlap) for only the magnitude of the rotation frequency in the envelope spectrum according to the conventional method. Figure 15b shows the difference between the magnitude at the rotational frequency and the baseline magnitude of the lower frequencies, which is the method proposed in this study. In Figure 15a, the five defects are not clearly distinguished from the 500 normal conditions. In comparison, Figure 15b shows the proposed method, and the 500 normal conditions and 5 defects are well distinguished. The practical application was verified by using acoustic signals measured in an assembly line producing ACs. The measured ACs were 500 normal units and 5 units with noise-defects. The detection performance was degraded because it was difficult to distinguish between the normal and the defects in the presence of impulsive noises using the conventional envelope analysis method. By eliminating the effects of the impulsive noises with the proposed method, the distinction between the normal and the defects became clear, and the detection performance was improved. However, the samples used in the real test for validation are 500 normal ACs and only 5 defective ACs caused by interference between the foreign materials and the fans. In the future, we will have to verify more defective ACs and various types of defects or other rotating machinery. Figure 14: Comparison of detection methods. (**a**) Conventional method using the peak value at the rotational frequency; (**b**) the proposed method using difference between the magnitude at the rotational frequency and the baseline magnitude of the lower frequencies.