# Mechanical Incipient Fault Detection and Performance Analysis Using Adaptive Teager-VMD Method
## 5 Conclusions  
In this work, we present a fusion algorithm based on CTEO and parameter-optimized VMD to solve the difficulty of early fault feature extraction for low-speed and heavy-load devices. The application of both simulated and real data shows that the proposed  
Figure 20: Analysis of the obtained modes and reconstructed result based on optimal VMD (BORF). (**a**) Modes. (**b**) Signal-reconstructed result. (**c**) Spectrum. framework separates the feature components more effectively and preserves effective feature representations more accurately than other signal approaches. 1. CTEO is an exact value of the conventional TEO, which can further enhance the impulse component in the signal and improve the signal-to-noise ratio of the faulty signal. It should be noted that the early failure signals of large, low-speed, and heavy machinery are very sparse and weak. It is easy to cause VMD to misjudge fault signals as \"noise\" and fail to decompose them into corresponding IMF components accurately. The use of CTEO to preprocess the raw vibrational signal effectively enhances the signal energy of the impulse component in the signal, which can help VMD properly decompose the impulse signal characterized by the fault into the corresponding IMF components. 2. Based on the nature of the logistic map and the sine map, we propose a 3D logistic-sine complex chaotic mapping. It extends the two-dimensional search space of FOA to a three-dimensional search space, which can effectively restrain FOA algorithms from getting trapped in local optimal solutions and improve the global search power and convergence rate. 3. The FOA algorithm based on 3D-LSCCM was used to search for the optimal combination value of the key parameter [\(K\), \(\alpha\)] of VMD to ensure that the VMD algorithm could adaptively obtain the best decomposition performance. 4. The fault signal is decomposed using the optimal VMD method to obtain several IMF components, which are selected to include shocks based on the mean kurtosis criterion for the IMF components. The selected IMF components are then reconstructed to extract fault characteristic frequencies more efficiently. Finally, the experimental results show that the combined CTEO and optimal VMD approaches have excellent performance and advantages in extracting early fault characteristics of mechanical devices. 5. In the actual operation of large, low-speed, and heavy-duty mechanical devices, in addition to the low-speed and large load of the mechanical devices themselves, there may be some intermittent operating characteristics. For this condition, the validity of the proposed method needs to be further verified. Conceptualization, B.X., F.Z. and H.L. ; methodology, H.L. ; software, B.X. ; validation, P.H. and H.L. ; formal analysis, P.H. ; investigation, F.Z. ; resources, F.Z. ; project administration, F.Z. ; data curation, H.L. and P.H. ; writing--original draft preparation, H.L. ; writing--review and editing, H.L. and P.H. ; funding acquisition, B.X. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China (grant no. 51975433, 51975430), the Research Project of Hubei Provincial Department of Education (grant no. B2022203). Not applicable. The authors acknowledge the editors and reviewers for their constructive comments and all the support on this work. The authors declare no conflict of interest. * [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] Online Unbalanced Rotor Fault Detection of an IM Drive Based on Both Time and Frequency Domain Analyses. _IEEE Trans. Ind. Appl._**2017**, _53_, 4087-4096. [CrossRef]
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