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.
Spiral bevel gears are basic transmission components which are widely used in mechanical equipment. These components are important elements used in the monitoring and diagnosis of running states for ensuring the safe operations of entire equipment setups. The vibration signals of spiral bevel gears are typically quite complicated, as they present both nonlinear and nonstationary characteristics. In previous studies, multiscale permutation entropy (MPE) has been proven to be an effective nonlinear analysis tool for complexity and irregularity evaluations of complex mechanical systems. Therefore, it is considered that MPE values can be used as the sensitive features for spiral bevel gears fault identifications. However, if the MPEs are used to directly construct the feature vectors, some problems will be encountered, such as large numbers of characteristic quantities, high dimensions, and issues related to diagnosis accuracy and efficiency, which have been proven difficult to obtain at the same time. In order to improve the accuracy and efficiency of fault recognition in spiral bevel gear evaluations, locality preserving projection (LPP) methods can be applied to reduce the high dimensionality feature vectors constructed by MPEs. They have the ability to extract low-dimensional sensitive information from high-dimensional feature data. In order to directly obtain the diagnostic results, classifications are necessary. When compared with traditional neural networks, it has been found that extreme learning machines (ELMs) have the advantages of faster training speeds and stronger learning abilities. In summary, this study proposed the use of MPE values which could be optimized and dimensionality reduced by LPP as the feature vectors, along with ELMs as the classifiers of the fault mode identifications, in order to carry out valuable research of fault diagnosis methods for spiral bevel gears. The proposed method was applied to the diagnoses of four types of fault state spiral bevel gears. Then, the MPE-LPP-ELM results were compared with those obtained using MPE-PCA-ELM and MPE-ELM methods. Their respective diagnostic accuracy is 100%, 98.75%, and 98.75%, and diagnostic time is 0.0023 s, 0.0033 s, and 0.0078 s. It was determined in this study that the results confirmed the accuracy and superiority of the proposed method.
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