# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
###### Abstract
The best performance results were obtained for the combination of the FSST technique and sensor-type fusion strategy. In industrial working environments, highly noised vibration signals are acquired, and noise attenuators are included in the classification deep learning model. In [PERSON] et al. [19], an FFT-based cross-attention module with soft thresholds for noise elimination is inserted in a deep residual shrinkage network (DRSN). The proposed CA-DRSN model, tested on the SEU gear dataset and the Paderborn bearing dataset, outperforms other methods, proving to be robust and noise-resistant at high noise levels. For gear fault detection, under two working conditions, the highest accuracies achieved for low noise are 99.9% and 99.8%, respectively, and for high noise, 97.4% and 98%, respectively. The current work proposes a method for diagnosing the defect type of a helical gearbox by observing variations in the vibration signal of the test rig. The measurements are performed for three different motor velocities, three loads for each velocity, and four health states of the gearbox. Small fluctuations in speed, around the nominal speed, are present. Vibration signals are represented as 2D grayscale images generated by CWT for a specific frequency range. Two of the four condition (health) states are structural defects on a pinion tooth flank, namely incipient localized pitting and localized wear. The other two states are poor lubrication and the normal state. Vibrations at the speed reducer case and the rotation velocity at the speed reducer output are measured by using a triaxial accelerometer and a tachometer, respectively. In defect detection (classification),models based on 2D-CNN and trained on grayscale images obtained from the CWT-based representation of vibration signals, are proposed. The following research goals guide the present study:  
* Development of three 2D-CNN-based models trained on the CWT-based representation of the vibration signals measured on individual accelerometer axes (\(X\), \(Y\), and \(Z\)) to detect four health states of a helical gearbox, regardless of the selected load level or speed on the test rig. * Fusing the CWT-based representations of the signals on individual axes for use as input to a 2D-CNN model with the aim of improving the performance in the proposed defect detection task. * Comparing the performance of different defect detection models on the same dataset of observations. This paper is structured as follows: Section 2 is dedicated to related studies that emphasize the importance of CWT and Morlet wavelet for fault diagnosis. In Section 3, we describe the test rig, the defects in the input shaft pinion of the speed reducer, and data acquisition, followed by data processing based on transforming the raw vibration signals into images using the CWT. Section 4 contains the methodology for solving the defect detection task and the description of the 2D-CNN-based architecture of the proposed models. The experimental results and comparison with previous published approaches are presented in Section 5. In the last section, we draw conclusions and mention directions for future work.