# Mechanical Incipient Fault Detection and Performance Analysis Using Adaptive Teager-VMD Method
###### Abstract
However, the tendency toward precocity still occurs. With the vigorous development of intelligent optimization technology, [PERSON] et al. [29] introduced an original bionic intelligent optimization approach inspired by fruit fly foraging behavior in 2012, called the fruit fly optimization algorithm (FOA). Recently, it has been extensively studied in many areas of engineering optimization [30]. Compared with the PSO algorithm, the FOA algorithm is easy to program and implement with few control parameters and is convenient for embedding specific search links for the problem [31]. However, FOA is also a heuristic optimization algorithm, and there is still the challenge of falling into the local optimal solution. [PERSON]. [32] proposed a three-dimensional underwater sensor network coverage enhancement optimization algorithm based on an improved fruit fly optimization algorithm (UFOA). [PERSON] et al. [33] developed a method of adding mutation strategies to a chaotic FOA algorithm, which improves the premature problem to some extent. However, the proposed mutation strategy does not have a strict mathematical definition or detailed comparative analysis. The weak nature of the vibration impulse represents an early defect of the device, making direct analysis in both the time and frequency domains difficult [34]. The Teager operator improves the shock energy in the vibrational signal and is characterized by excellent real-time performance, high resolution, and low computational complexity. Fault feature identification requires that the input data be stable and can reliably represent this type of signal. Consequently, screening of sensitive signals is particularly important. The minimum permutation entropy criterion was explored to select the basis function to compute the statistical properties of the signal [35]. The correlation coefficient and variance contribution rate between the reconstructed signal and the original signal are used to determine the optimal choice from the obtained stability criterion [36]. Based on the aforementioned introduction, this work introduces an adaptive CTeager-VMD for early fault feature extraction methods. The main highlights are summarized below: (1) The original vibrational signal is enhanced using the complete Teager operator. (2) A three-dimensional logistic-sine composite chaotic map (LSCCM) is constructed to promote the global search capability and convergence rate of the FOA. (3) The improved FOA is used to seek the optimal parameters \(K\) and \(\alpha\) of the VMD, and it makes the VMD adaptive to achieve the best processing power. (4) The enhanced vibrational signal is decomposed into several IMFs using the optimized VMD. According to the mean kurtosis criterion, sensitive IMFs with impact components are selected and used to reconstruct a fresh signal. Next, the envelope spectrum of the fresh signal is calculated, and the characteristic information of the incipient fault is obtained. Finally, the proposed method is evaluated using synthetic and measured signals and compared with other excellent methods. The proposed CTeager-VMD method is able to unambiguously identify the characteristic frequency of the micro-impact. The evaluation and comparison results sufficiently verify the superiority and stability of the proposed method. The subsequent sections of this paper are organized as follows. Section 2 introduces the proposed adaptive VMD method in detail. In Section 3, the performances are compared by simulated experiments. In Section 4, the performance of the proposed method is verified and evaluated. Finally, the conclusions are summarized in Section 5.