A Novel MPE-LPP-ELM Recognition Method for the Fault Diagnosis 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