## 5 Conclusions  
In this study, the simple time-frequency envelope analysis has been proposed to improve the degradation of the detection performance when impulsive noises contaminate the measured signals for condition monitoring and fault detection of the rotating machinery. When the impulsive noise is mixed in one time, the baseline of the envelope spectrum slightly increases, and the sharpness of the peak related to the defect becomes dull. When the impulsive noises are mixed in multiple times, the peaks related to the time interval between the impulsive noises can be observed to increase in the baseline of the envelope spectrum. This makes the sharpness of the peak indicating a defect that is very blurry and makes it impossible to distinguish between normal and defective signals.  
Impulsive noise occurs for a very short time, so its effect can be eliminated by conducting envelope analysis on each section divided into several sections through a time window. The difference between the baseline magnitude was increased by the effect of the impulsive noise and the magnitude at the rotational frequency, which was used as an index for detecting defects. The improvement effect of the proposed method was verified through two methods: the simulation of a mathematically modeled signal and practical application to an assembly line that produces ACs.  
For the simulation of synthetic signals, the models based on CS process representing typical properties of rotating machinery were used. Impulsive noise caused by unpredictable sources was modeled as single rectangular wave with short time. The proposed method was inspired by frequency characteristics of single rectangular wave in which the magnitude decreases as the frequency increases. The performance of the proposed method was verified by comparing to conventional method depending on the number of impulsive noises contained in the measured signal.  
The real test in the assembly line producing ACs was implemented to verify the proposed method. The measured dataset using microphones consist of 500 normal ACs and 5 noise-defect ACs. The proposed method shows the ability to clearly differentiate the noise-defects from the normal even in the presence of impulsive noises, and contributes to the possibility of using a microphone, a non-invasive sensor, for fault detection. 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. Moreover, the approaches of big data and deep learning will be required for the development of the PHM framework.  
Figure 15: Comparison of detection results: (**a**) conventional method; (**b**) the proposed method.  
**Author Contributions:** Conceptualization, D.-H.L.; methodology, W.-B.J. and S.A.; formal analysis, C.H.; writing--original draft preparation, D.-H.L.; writing--review and editing, S.A.; visualization, S.A.; supervision, W.-B.J.; project administration, C.H. and W.-B.J.; All authors have read and agreed to the published version of the manuscript.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1I1A3064576).  
**Data Availability Statement:** Not applicable.  
The authors declare no conflict of interest.