# Mechanical Incipient Fault Detection and Performance Analysis Using Adaptive Teager-VMD Method
###### Abstract
[[https://doi.org/10.3390/appl310058](https://doi.org/10.3390/appl310058)]([https://doi.org/10.3390/appl310058](https://doi.org/10.3390/appl310058))  
Footnote †: journal: Applied  
**Citation:** [PERSON]; [PERSON], [PERSON]; [PERSON]; [PERSON] [PERSON] Mechanical Incipient Fault Detection and Performance Analysis Using Adaptive Teager-VMD. _Appl. Sci._**2023**, 13, 6058. [[https://doi.org/10.3390/appl310058](https://doi.org/10.3390/appl310058)]([https://doi.org/10.3390/appl310058](https://doi.org/10.3390/appl310058))  
Footnote †: journal: Applied  
**Citation:** [PERSON]; [PERSON]; [PERSON] Mechanical Incipient Fault Detection and Performance Analysis Using Adaptive Teager-VMD. _Appl. Sci._**2023**, 13, 6058. [[https://doi.org](https://doi.org)]([https://doi.org](https://doi.org))an efficient time-frequency analysis method, but its resolution of time and frequency is fixed [3]. The wavelet transform (WT) is suitable for frequency localization analysis but is limited by choosing the appropriate wavelet basis function [4]. The S transform has excellent adaptive time-frequency analysis capability, but it is affected by the degree of identification [5; 6]. The Wigner-Ville distribution method represents the instantaneous time-frequency relationship of the signal, but it is constrained by the resolution in both the time and frequency domains [7; 8]. The high-order statistics method effectively eliminates the influence of symmetric distribution noise but tends to cause interference with the higher-order spectrum [9]. Empirical mode decomposition (EMD) suffers from fundamental problems such as mode mixing, fitting overshoot, and end effect, which limit its application in engineering to a great extent [10; 11; 12; 13]. Local mean decomposition (LMD) trends produce signal mutations during demodulation [14; 15]. Intrinsic time-scale decomposition (ITD) has shortcomings such as waveform distortion and false components [16; 17]. Scholars have made many improvements to the above methods; however, limited by the theoretical framework, these improvements make it difficult to eliminate their own problems. Fortunately, an effective non-recursive method, termed VMD, was proposed in 2014 [18]. In contrast to recursive mode decomposition methods, VMD can decompose a signal into intrinsic mode functions with an estimated center frequency and limited bandwidth. Thus, the problem of solving mode bandwidth is transformed into a constrained optimization problem, and each mode is solved. Moreover, it effectively overcomes the defects of EMD, LMD, and ITD, and it has been widely studied and applied in electromechanical equipment fault diagnosis [19; 20; 21; 22]. However, the critical parameters of VMD, such as the total mode number \(K\) and mode frequency bandwidth control parameter (quadratic penalty term \(\alpha\)), must be set in advance, which is highly empirical and blind. Therefore, VMD is not a model-adaptive method in the actual application process. Several recent studies have focused on VMD parameter setting. Based on personal experience and convenience, [PERSON] et al. solved the difficult problem of milling chatter detection by combining VMD with energy entropy [23]. In [24], a kind of FFT method was introduced to determine the optimal parameters of VMD, but FFT has essential defects in processing nonlinear and non-stationary information [25]. [PERSON] et al. [26] used a PSO algorithm to realize the optimization of adaptive values \(K\) and \(\alpha\). [PERSON] et al. [27] proposed a PSO-based VMD approach for the self-selection of the intrinsic parameters and set the minimum mean envelope entropy as the optimality function. The method improves the function of the original VMD and makes it self-adaptive. To avoid the PSO algorithm falling into the local optimal solution, some scholars have proposed corresponding optimized algorithms, referred to as quantum particle swarm optimization (QPSO) [28]. As the classical improved algorithm of standard PSO, QPSO can enhance the global searching ability significantly.