# Detection of Fitting in Gears Using a Deep Sparse Autoencoder
## 1 Introduction  
Gears are one of the most critical components in many industrial machines. Health monitoring and fault diagnosis of gears are necessary to reduce breakdown time and increase productivity. Pitting is one of the most common gear faults and normally difficult to detect. An undetected gear pitting fault during the operation of the gears can lead to catastrophic failures of the machines. In recent years, many gear pitting fault detection methods have been developed. Following the same way to classify machine fault diagnostic and prognostic methods by [1; 2], gear pitting fault detection methods can be classified into two main categories, namely model-based methods and data-driven methods. The model-based techniques rely on accurate dynamic models of the systems, while the data-driven approaches use data to train fault detection models. Model-based approaches obtain the residuals between actual system and output. These residuals are then used as the indicator of the actual faults [3; 4]. However, the model-based approaches require not only expertise in dynamic modeling, but also accurate condition parameters of the studied system. On the other hand, data-driven approaches do not require the knowledge of the target system and dynamic modeling expertise. In comparison with model-based techniques, data-driven approaches can design a fault detection system that can be easily applied when massive data is available. Data-driven techniques are appropriate when a comprehensive understanding of system operation is absent, or when it is sufficiently difficult to model the complicated system [5]. Data-driven-based gear pitting fault detection methods in general relies on feature extraction by human experts and complicated signal processing techniques. For example, Reference [6] useda zoomed phase map of continuous wavelet transform to detect minor damage such as gear fitting. References [7; 8] used the mean frequency of a scalogram to get features for gear pitting fault detection. Reference [9] extracted condition indicators from time-averaged vibration data for gear pitting damage detection. Reference [10] used empirical mode decomposition (EMD) to extract features from vibration signals for gear pitting detection. Reference [11] combined EMD and fast independent component analysis to extract features from stator current signals for gear pitting fault detection. Reference [12; 13] applied spectral kurtosis to extract features for gear pitting fault detection. Reference [14] extracted statistical parameters of vibration signals in the frequency domains as an input to artificial neural network for gear pitting fault classification. One challenge facing the abovementioned data-driven gear fault detection methods in the era of big data is that features extracted from vibration signals depend greatly on prior knowledge of complicated signal processing and diagnosis expertise. Besides, features are selected per the specific fault detection problems and may not be appropriate for different fault detection problems. An approach that can automatically and effectively self-learns gear fault features from the big vibration data and effectively detect the gear fault is necessary to address the challenge. As a data-driven approach, sparse coding is a class of unsupervised methods for learning sets of overcomplete bases to represent data efficiently. Unlike principal component analysis (PCA) that learn a complete set of basis vectors efficiently, sparse coding learns an overcomplete basis. This gives sparse coding the advantage of generating basis vectors that are able to better capture structures and patterns inherent in the input data. Recently, sparse coding-based methods have been developed for machinery fault diagnosis [15; 16; 17; 18]. However, these methods used manually constructed overcomplete dictionaries that cannot guarantee to match the structures in the analyzed data. Sparse coding with dictionary learning is viewed as an adaptive feature extraction method for machinery diagnosis [19].