# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
###### Abstract
CNN, as one of the most effective DL models, has been extensively applied for fault diagnosis of rotating machinery. [PERSON] et al. [6] describe the roadmap (1990-2020) of machine learning applied to machine fault diagnosis (gears, bearings, motors engines, etc.) with three stages, traditional machine learning, deep learning, and transfer learning theories, while highlighting future research trends. Some of the related papers dealing with wavelet transform, gear fault detection, and CNN-based classification are mentioned in the next paragraphs. For a broader perspective, we start with two overview studies and then present individual papers in more detail. A systematic review of machine fault diagnosis applications (classification, health prediction, and transfer diagnosis) using CNN or its variants is presented in [PERSON] et al. [7], published in 2020. Public datasets (such as CWRU, PHM09, or Paderborn) containing bearing/gear/rotor fault types are described as well. Very good performance results, with accuracy > 94.5%, were obtained for all the diagnosis applications trained and tested with the public datasets. In helical gear fault classification, on the PHM09 dataset, with six health conditions, an accuracy of 99.33% was achieved by a 1D-CNN model with FFT preprocessing of the raw signal. To improve the performance on the same task, a deep adversarial convolutional neural network (DACNN), which implements a transfer learning strategy, named adversarial domain adaptation was proposed. This model reached a 99.4% accuracy on the PHM09 dataset. A comprehensive synthesis [8] of 59 studies published from 2016 to 2022 presents the deep learning methods for fault diagnosis of rotating machinery using vibration signals. In the study, all DL techniques (CNN, DBN, RNN, SAE, GNN, and GAN) applied to detect faults in bearings, gearboxes, and motors are mathematically described. An important conclusion was that, in the studied papers, the most used DL technique was CNN (39%), followed by SAE (28.8%), and GNN (20.3%). The performance results of DL-based fault diagnosis systems are presented, with details regarding the pre-processing approaches (FFT, WT, CWT, and time-domain to image), architecture, and dataset (public or private) used in training/testing. The best accuracy for fault gearbox diagnosis is 99.58%, and it was reached by a CNN-based system with WT processing working on a private dataset. The best-performing systems based on SAEs achieved accuracies of 99.14% and 99.43%, respectively, for private datasets of gearbox defects. Two GNN-based fault diagnosis methods for gears, developed in 2021, reached accuracies of 98.31% and 98.7%, respectively, for private datasets. The approach proposed in [PERSON] et al. [9] preprocesses multisensor raw data for dimension reduction (using PCA), resulting in RGB images that are further used as input to an improved CNN with residual networks. The test rig of the SEU gearbox dataset (provided by Southeast University) used in the experiments contains a planetary gearbox and a parallel gearbox. Five health conditions--a health state and four severe faults at the gear tooth level (named shortly: chipped, miss, root, and surface) were under observation. An average testing accuracy of 99.98% was reached. In [PERSON] et al. [10], CNN-based defect detection models use 1D and 2D grayscale images (elongated in shape, much longer than wide), representing the vibration image of the acquired raw data from a helical gearbox. The best-performing model, with an accuracy of 99.63%, uses the information acquired on all three axes by a triaxial accelerometer. The same helical gear defects were detected in [PERSON] et al. [4] with an accuracy of 99.73% through machine learning techniques (SVM--support vector machine), working with features associated with GMF harmonics and sidebands. Special interest is dedicated to scenarios with limited gear fault vibration samples in real-world working conditions. Discrete wavelet decomposition (db8 wavelet bases) is applied to a small sample in [PERSON] et al. [11].