# An Application of Instantaneous Spectral Entropy for the Condition Monitoring of Wind Turbines
## 7 Conclusions  
The Instantaneous Spectral Entropy (ISE) has been discussed as a potential time-dependent damage index. The Shannon Spectral Entropy (SSE) definition was used for this aim. The goal of this research was to perform damage event detection retrospectively on acquired vibration time histories, recorded from a wind turbine gearbox. The Continuous Wavelet Transform (CWT) was applied to define the time-frequency representation needed to extract the ISE. In this regard, a sensitivity analysis has been carried out on the parameters of the Generalised Morse Wavelet (GMW), to investigate their effects on the final results. Some suggestions were made based on the experimental data analysed here. However, further studies will be needed to assess these findings on different datasets, also considering different sampling frequencies and varying the duration of the recorded measurement time series.  
The pure ISE was found to be significantly affected by spikes, i.e., very fast, short-termed transients of the instantaneous entropy. For this reason, its moving mean has been preferred as a more stable time-dependent index. The procedure successfully detected the occurrence of bearing faults on experimental data, recorded before and after a bearing failure and concatenated to emulate a time-varying structural condition. The moving mean of ISE returned some isolated false alarms as well; however, only an actual alteration of the machine condition caused a permanent deviation from the baseline.  
As an entropy-based approach, the ISE is inherently limited by its dependence on the input force. That is to say, measurements corresponding to highly different wind speeds cannot be directly compared for anomaly detection. Future works will also include the automation of the selection procedure for acquisitions related to similar wind speeds.  
Finally, the relatively low computational burden and rapid execution time suggest that the method can be further extended to real-time, online applications. This can be achievedusing a small moving window of recent history over the data stream. These potential applications will be further investigated in future works as well.  
Conceptualization, M.C. and C.S.; methodology, M.C. and C.S.; software, M.C.; validation, M.C.; investigation, M.C.; resources, C.S.; data curation, M.C.; writing--original draft preparation, M.C.; writing--review and editing, C.S.; visualization, M.C.; supervision, C.S.; project administration, C.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The experimental data utilised for this research were retrieved from a public dataset, available at [[http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dswid=-2411](http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dswid=-2411)]([http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dswid=-2411](http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dswid=-2411)) (accessed on 24 June 2021).  
The Authors would like to thank [PERSON], [PERSON], and [PERSON] of the Lulea University of Technology for making their experimental data publicly available.  
The authors declare no conflict of interest.