CEEMDAN-Based Permutation Entropy: A Suitable Feature for the Fault Identification of Spiral-Bevel Gears

Abstract

A spiral-bevel gear is a basic transmission component and is widely used in mechanical equipment; thus, it is important to monitor and diagnose its running state to ensure safe operation of the entire equipment setup. The vibration signals of spiral-bevel gears are typically quite complicated, as they present both nonlinear and nonstationary characteristics and are interfered with by strong noise. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method has been proven to be an effective method for analyzing this kind of signal. However, the fault feature information after CEEMDAN is not obvious and needs to be quantified. Permutation entropy can be used to quantify the randomness, complexity, and mutation of vibration time-series signals. This paper proposes to take the CEEMDAN-based permutation entropy as the sensitive feature for spiral-bevel gear fault identification. First, the raw vibration signal is decomposed by the CEEMDAN method to obtain a series of intrinsic modal functions (IMFs). The IMFs which included greater amounts fault information are selected as the optimal IMFs based on the correlation coefficient. Next, the permutation entropy values of the optimal IMFs are calculated. In order to obtain accurate permutation entropy values, the two key parameters, namely, embedding dimension and delay time, are optimized by using the overlapping parameter method. In order to assess the sensibility of the permutation entropy features, the support vector machine (SVM) is used as the classifier for fault mode identification, and the diagnostic accuracy can verify its sensibility. The permutation entropy of CEEMDAN-based/EEMD-based/EMD-based features, combined with SVM, is applied to identify three different fault modes of spiral-bevel gears. Their respective diagnostic accuracies are 100%, 88.33%, and 83.33%, which indicate that the CEEMDAN-based permutation entropy is the most sensitive feature for the fault identification of spiral-bevel gears.