# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
###### Abstract  
This paper studies the relevance of CWT (continuous wavelet transform) processing of vibration signals for improving the performance of CNN-based models that detect certain types of helical gearbox faults. Gear tooth damages, such as incipient and localized pitting and localized wear on helical pinion tooth flanks, combined with improper lubrication, are the faults under observation. Vibrations at the housing level for three rotating velocities of the AC motor and three load levels (for each velocity) are acquired with a triaxial accelerometer. Through CWT, the vibration signal is decomposed into 2D time-frequency grayscale images, with a filter bank of ten voices per octave in the frequency band of interest. Three 2D-CNN-based models trained on the CWT-based representation of the vibration signals measured on individual accelerometer axes (\(X\), \(Y\), and \(Z\)) are proposed to detect the four health states (one normal and three faulty) of the helical gearbox, regardless of the selected load level or speed on the test rig. These models achieve an accuracy higher than 99%. By fusing the CWT-based representations of the signals on individual axes for use as input to a 2D-CNN, the best-performing model for the proposed defect detection task is generated, reaching an accuracy of 99.91%. h _Article_  
1 Faculty of Industrial Engineering, Robotics and Production Management, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania1
arithmetic mean value, mean of absolute values, mean square value, root mean square, variance, standard deviation, geometric mean, peak value, peak to peak, peak to rms, impulse factor, clearance factor, shape factor, or zero cross rate. Higher-order moments of the signal, like moment of the third order, coefficient of skewness, moment of the fourth order, kurtosis, and energy operator [1], are also useful. Parameters observing the level of chaos in a mechanical system, such as the largest Lyapunov exponent, the approximate entropy, and the correlation dimension estimation, can indicate the emergence or progress of a fault in gears or bearings [3]. Statistical frequency-domain features extracted from stationary vibration signals help in fault diagnosis and classification. Spectral information can be obtained by applying the fast Fourier transformation (FFT) to the acquired signal. Among statistical frequency-domain condition indicators, one can mention the mean frequency of the power spectrum, spectral centroid, spectral spread, spectral skewness, spectral kurtosis, spectral flatness, spectral crest, spectral slope, spectral entropy, Shannon entropy, and so forth [1,3]. In the spectrum of a gearbox, one can find important functional frequencies, such as gear mesh frequencies (GMFs), their harmonics, and sideband pairs associated with the GMFs and harmonics [4]. For nonstationary vibration signals, plenty of mathematical methods are available for the derivation of the spectral content of time-varying signals. Hence, time series are transformed into another feature space, namely time-frequency images. Time-frequency imaging is an ever-developing group of techniques that transform time-series data into the time-frequency domain using various methods. One can mention the short-time Fourier transform (STFT), Gabor transform (STFT with the window of the Gaussian function profile), wavelet transform (WT), Stockwell or S-transform, and Wigner-Ville distribution (WVD) [5]. All these differ in terms of achievable resolution in time and frequency. Models based on deep learning (DL), a branch of machine learning, learn abstract features from raw vibration data and time-frequency images without the participation of the experts' experiences. Several types of DL models, such as deep belief network (DBN), stacked auto-encoder (SAE), recurrent neural network (RNN), convolutional neural network (CNN), graph neural network (GNN), and generative adversarial network (GAN), are mentioned in the literature.