# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
## 6 Conclusions  
A two stages speed reducer gearbox with parallel axes and helical gears was employed for gear fault detection. Four condition states were under observation: D1, low oil level in the speed reducer; D2, normal state; D3, incipient and localized pitting on the pinion tooth flank of the first reducer stage; and D4, localized wear on the pinion tooth flank (first reducer stage). A triaxial accelerometer was utilized to record the acceleration on the reducer housing. Three different working speeds and three load levels for each speed were the working conditions used to reveal the gearbox condition states. Helical gearbox defect detection models were developed by applying continuous wavelet transform (CWT) to the raw vibration signals and using convolutional neural networks (CNNs). A carefully chosen filter bank is able to capture the most important frequency components of the vibrations generated during the gear meshing process. Some of the unwanted noise is also eliminated. Through CWT, the vibration signal was decomposed into 2D time-frequency grayscale images. The first research goal, RG1, was achieved, and the three 2D-CNN-based models built using the CWT-based representation of the vibration signals measured on individual accelerometer axes (\(X\), \(Y\), and \(Z\)) proved to perform very well, with accuracies higher than \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Defect Detection Model** & **Features Type** & \
\begin{tabular}{c} **No. of Features** \\ **on Three Axes** \\ \end{tabular} & **Classifier** & **Accuracy** \\ \hline GMF and sidebands-based model [4] &
\begin{tabular}{c} Band powers, \\ 6 GMFs and 2 \\ sideband pairs \\ \end{tabular} & 90 & SVM-cubic & 99.73\% \\ \hline
2D-CNN- based model with raw data [10] & \
\begin{tabular}{c} Extracted by \\ 2D-CNN \\ \end{tabular} & 576 &
\begin{tabular}{c} 2 hidden layers \\ +softmax \\ \end{tabular} & 99.63\% \\ \hline
2D-CNN- based model with CWT-processed data & \
\begin{tabular}{c} Extracted by \\ 2D-CNN \\ \end{tabular} & 768 &
\begin{tabular}{c} 2 hidden layers \\ +softmax \\ \end{tabular} & 99.91\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracies achieved by several defect detection models applied to the same dataset. Figure 13: Comparison of performances (F1 scores) at the level of classes (defects) of the CNN-based models using raw data versus CWT-processed data for individual axes. 99%. The information acquired on the \(Y\)-axis is the most relevant one in detecting the four states of the gearbox, and the corresponding model reached an accuracy of 99.54%. The fourth 2D-CNN-based model implemented within the research goal RG2 uses as input the fusion of the CWT-based representations of the signals on individual axes and solves the proposed defect detection task with a very high accuracy of 99.91%. The conclusion of the last research goal, RG3, is that in solving the proposed defect detection task on the same dataset of observations measured on all three accelerometer axes, the model proposed in the current paper, with an accuracy of 99.91%, outperforms two other models. One model is an SVM-based model that uses as features the band powers of six regular GMF harmonics and the first two sideband pairs for each harmonic, achieving an accuracy of 99.73% [4]. The second model is a 2D-CNN-based model trained on raw data without a processing step, reaching a 99.63% accuracy [10]. Thus, the importance of CWT-processing of vibration signals to better distinguish specific states of the gearbox was proved. The present study focuses on the fault detection of the proposed two-stage speed reducer with helical gears (which generate relatively low noise at the gears level, even at high rotation speed). For double helical gears and spiral bevel gears, we assume that the proposed fault detection model gives good results. For spur and bevel gear pairs, which are noisier, and for noisy industrial environments, a noise mitigation step is applicable. These assumptions need to be confirmed on other test platforms.