## 2 Materials and Methods
### 1D-CNN: Design and Configuration  
The present model was inspired by applications of 1D-CNN in human pattern recognition and fault diagnosis systems [30,31]. This model, however, has fewer layers to reduce training time, and it only requires a single raw input (vibration signal). The design process is presented in Figure 2 and was as follows. Firstly, the following parameters were adjusted: number of layers, quantity and size of filters for each layer, and training and optimization algorithms. Hyper parameters for the network were also adjusted. These were: number of signals per category, signal length, ratio training/testing, learning rate, learning training cycles (epochs) and training lot size (batch size). The recommended values are detailed in Table 3. Secondly, CNN structure was created as shown in Table 4. By determining the number of layers of the network model, it is possible to select both the quantity and dimensions of the filters of each convolutional layer. Table 5 presents the performance of each of the configurations that have been selected by adjusting a few options reported in the literature; in this case, the network structure in bold fonts was the best option. The internal structure and configuration of the Kernels filters are shown in Figure 3.  
For data mining, the network applies algorithms to automatically identify and select the most significant features from raw data. For this purpose, the convolution operation (Convolutive Layer) is applied to the input data, resulting in a vector with greater length and whose maximum clustering criterion (Max-Pooling Layer) is applied to extract the most representative features. The same procedure is repeated four times, but as can be seen in Table 4, the number of Kernels is increased for each Convolutive plus Max-Pooling set. This variation is performed to generate feature maps with the capacity to represent adequately the non-linearity of the signals. Figure 4 sequentially shows the generation of the first three values of a feature map by using a filter with a length of three samples and a sliding pass of one sample (stride). This operation is applied to each convolutional layer. The parameters that are regulated for this operation are the quantity and size of the filters (u), and the sliding factor of the window (stride). Figure 1: Data organization: 80% of data were used to train 1D-CNN and 20% were used to test it. From training data, 75% were used to train the network, while 25% were used to validate it. Figure 2: Design and configuration of the proposed 1D-CNN method to detect spindle failures. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Analysis** & **Batch\_Size** & **Seq\_Len** & **Learning\_Rate** & **Epochs** & **n\_Classes** & **n\_Channels** & **Flatten** \\
2 RPM & 100 & 1200 & 0.001 & 50 & 7 & 1 & \(75\times 144\) \\
5 RPM & 100 & 3000 & 0.001 & 50 & 7 & 1 & \(188\times 144\) \\
10 RPM & 100 & 6000 & 0.001 & 50 & 7 & 1 & \(375\times 144\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyper parameters configuration for the 1D-CNN. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Layer** & **Type** & **Filters Size** & **Stride** &
\begin{tabular}{c} **Filters Number** \\ **(Kernels)** \\ \end{tabular} & **Padding** \\ \hline
1 & Convolutive 1 & 64 & 1 & 18 & ‘same’ \\
2 & Max-Pooling 1 & 2 & 2 & 18 & ‘same’ \\
3 & Convolutive 2 & 2 & 1 & 36 & ‘same’ \\
4 & Max-Pooling 2 & 2 & 2 & 36 & ‘same’ \\
5 & Convolutive 3 & 2 & 1 & 72 & ‘same’ \\
6 & Max-Pooling 3 & 2 & 2 & 72 & ‘same’ \\
7 & Convolutive 4 & 2 & 1 & 144 & ‘same’ \\
8 & Max-Pooling 4 & 2 & 2 & 144 & ‘same’ \\
9 & Fully-Connected & 100 neurons & & & \\
10 & Softmax & 7 classes & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 1D-CNN structure. Figure 3: Internal structure of 1D-CNN network.