# Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder's Latent Space
###### Abstract
Planetary gear trains were also within the interests of the researchers [15], who proposed the supervised method based on a stacked autoencoder. Model training and validation were performed on a dataset with artificially induced gear teeth failures. The recognition rates varied depending on gear state from 95% to 97%. The authors of [16] used stacked autoencoders with a relatively simple architecture (one hidden layer) in order to extract the features of faulty planetary gear vibrational signals. In [11], the complex expert system was proposed to monitor the condition of helicopter transmissions. The dataset consisted of measurements from 23 accelerometers mounted in various places within the helicopter driveline, which provided 80 time signals. The authors used a convolutional autoencoder and unsupervised classifier that combined K-nearest neighbors, isolation forest, angle-based detection, and the local outlier factor. The anomaly detection was based on averaging the outputs from these two models. The method was highly efficient, giving 100% of the true positive rate and 0.03% of the false positive rate, but was limited in terms of generalization on the type of anomaly. In [18], the authors investigated spur gear train vibrations collected for different artificially-induced teeth failure types. They used sparse stacked autoencoders for feature extraction and supervised learning, which resulted in 97% accuracy. Researchers have also used GANs as anomaly detectors [23] where the bearing and gear teeth were under investigation. To detect an abnormal state, the anomaly score was used on the discriminator output, which resulted in accuracy from 95% to 98% and an F1-score from 97% to 99%, depending on the test case. The use of GANs has also been proposed for general time series anomaly detection [20]. The authors compared three models: cumulative sum chart, MAD-GAN (multivariate anomaly detection with genera tive adversarial networks) and TAnoGAN (time series anomaly detection with generative adversarial networks). Depending on the model, the authors achieved a 90% accuracy, 72% recall, and 61% precision. It may be seen, based on the literature review presented, that there are many supervised methods that might not be suitable for imbalanced datasets. Moreover, many models have been trained and validated on artificially-induced teeth failures, and are rarely focused on the pitting type of failure. Taking the above into account, the novelty of the work as well as its aim is to:  
* Construct a dataset as a result of extensive fatigue tests of gears with real gear pitting failure of different severity rates;
* Propose a robust semi- or unsupervised model for failure detection;
* Ensure the high-performance metrics of the model;
* Construct a model that gives a general perspective on gear pitting wear prediction. In this paper, we explore the experimental data from a helical gear setup using semi-supervised machine learning techniques. In Section 2.1, we describe the setup and data collection, and in Section 2.2, we discuss the data preprocessing for the algorithms. In Section 2.3, we commence with a simple analytic solution, based on principal component analysis (PCA). Finally, in Section 3, we present the three methods for pitting failure detection in gearboxes, namely, the autoencoder as a basic anomaly detector (Section 3.1), autoencoder and convex hull-based classification in its latent layer (Section 3.2), and a generative adversarial network for anomaly detection (Section 3.3). All models based on neural networks used in this study were subjected to neural ablation tests in order to choose a model architecture with the maximum performance and reasonable learning time. A representative example of the ablation test is given in Appendix A. We discuss and conclude the results in Sections 4 and 5, respectively.