## 3 Methodology
### Feature Extraction  
The dataset at its primary state is quite large, but it is useful in training a classifier model. However, the dimensionality of the input data should be as small as possible to obtain high classification accuracy with low computational resources. Often, based on application and amount of available data, feature extraction can be omitted, and the data are directly used to train the classifier. In the feature extraction technique, the data dimension is reduced from the initial data by transferring it into a smaller and more tractable set of data for future processing. In the raw data set, because of the different types of working conditions and machine inputs, the number of variables becomes very large and will demand higher computing resources for the next step. The main objective of feature extraction is to convert the raw data into a smaller subset of significant variables that efficiently represent the target classes. Thus,  
Figure 6: Characteristic signals of three mother wavelets. feature extraction is a crucial step for easier calculation and reservation of important information for ultimate decision making. Before performing feature extraction from the current signals, the line component of the 60 Hz component is removed using a notch filter. Then data from 17 bearing conditions are merged. The raw signal and the filtered signal for three bearing conditions are shown in Figure 7. It is not easy to differentiate between faulty and healthy condition signals from the non-filtered signals by visual inspection, but the filtered version is more discernable. The filtered signal is decomposed up to 11 levels with each of the Haar, db4, and sym4 wavelets. From the 11-level decomposition, we obtained the detailed coefficients from level 1 to 11 (cD1 to cD11) and one approximation coefficient (cA) for each wavelet. The decomposed signals are presented in Figures 8-10. Due to the high dimension of data containing an excessive amount of information, wavelet decomposition coefficients cannot be directly used as the input of classifiers. To reduce the data dimension and extract the most important characteristic information, feature extraction methods are applied to the wavelet coefficients at every decomposition level. In this study, 11 statistical features are used for feature extraction from 11 approximation coefficients and the detail coefficient of each wavelet. The initial dataset has 2720 instances containing three different conditions of bearing (healthy, inner race fault, and outer race fault). Each instances is essentially a current signal having a duration of 1 s, sampled at 64 KHz. In the feature extraction stage, each instance is decomposed to 11 levels. Therefore, after decomposition for each instance there are 11 detail and 1 approximation coefficients (total 12 coefficients). Thus, for each coefficient, the features mentioned in Table 3 are calculated, which is \(12\times 11=132\) features. Finally, after adding the label at the last column, we have a feature matrix of \(2720\times 133\). Figure 7: (**a**) Raw and (**b**) filtered signals of three types of bearing states. Figure 8: Wavelet decomposition of the ‘Haar’ mother wavelet of a healthy bearing. Figure 9: Wavelet decomposition of the ‘db4’ mother wavelet of the outer fault bearing.