# Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder's Latent Space
###### Abstract  
This paper presents a method of pitting failure detection in toothed gears based on the reconstruction of the gear case vibrational signal. The effectiveness of the proposed method was tested in an experiment on a power circulation test stand. The autoencoder deep neural network architecture, semi-supervised training, and validation, along with the latent data convex hull-based clustering, are presented. The proposed method offers high efficiency (0.99 F1-measure) in gear state prediction (100% in failure detection, 98.9% in normal state prediction) and provides more capabilities in terms of generalization in comparison with linear machine learning techniques such as principal component analysis and nonlinear like the generative adversarial network. Moreover, it is distinguished by high sensitivity while also being able to detect even slight surface damage (initial pitting). These findings will be of particular relevance to a range of scientists and practitioners working with gear drives who are willing to implement machine learning in signal processing and diagnosis. gear fault diagnosis; semi-supervised deep learning; autoencoder; generative adversarial network; vibrational signal; anomaly detection +
Footnote †: journal: Medical Engineering and Aeronautics  
requires data from the worn mechanical component and proper signal feature selection, which provides information about the relevant faults. In the case of high-power geared transmissions, extensive fatigue testing is required to obtain reliable data for training. Another aspect is that such neural networks are trained only to predict predefined failures such as pitting or tooth fracture and may not cover all possible failures occurring during real operation. To overcome the above-mentioned disadvantages, a specific neural network architecture known as an autoencoder may be used [13]. An autoencoder is a type of deep neural network that can reconstruct its input. Usually, they are used for feature extraction [14; 15; 16; 17], however, they can also work as anomaly detectors [11; 14; 18]. For this purpose, the autoencoder neural network is trained with the aid of unlabeled data in which there are no or very few abnormal states. These kinds of data are usually easy to collect because they refer to the normal operation of the system. As a measure of fault (abnormal state), the training loss function is selected. If the autoencoder fails to reconstruct the input with sufficient accuracy (obtained while training), it means that an abnormal state (failure) has occurred. Another technique that can be used for unsupervised anomaly detection is the generative adversarial network (GAN), widely used for image generation [19]. This type of network is trained to generate data, making use of the game between the generator and discriminator. If the network is trained on data for a normal state, the probability output space of the discriminator calculated for abnormal data is then used to predict an abnormal state. GANs have been used for anomaly detection in time series data [20], image and tabular data [21], and fault detection in unbalanced datasets [22; 23]. Several papers related to the predictive maintenance of gears and generally of rotating machinery based on its vibrations have adopted a semi-supervised or unsupervised learning approach. The main reason for using such techniques is the problem of heavily imbalanced datasets occurring in industrial practice. Usually, there are no extensive test results to construct a proper dataset with a uniform distribution of each feature, but there are a lot of data related to the proper operation of the mechanical system. For such imbalanced datasets, unsupervised or semi-supervised learning approaches are suitable. In [14], the authors presented an unsupervised approach based on an autoencoder to monitor and detect anomalies in industrial machines. The authors compared their models with supervised machine learning ones and achieved 91% accuracy, 98% precision, and 83% recall.