# A Novel Capsule Network Based on Wide Convolution and Multi-Scale Convolution for Fault Diagnosis
## 4 Experimental Analysis
### Case Study 1: Generalization Experiment under Different Working Conditions  
The generalization of the proposed WMSCN algorithm under different loads is tested in this experiment. According to different operating conditions, such as rotational speed, loads, etc., the experimental data is divided into three different datasets, as shown in Table 2. The specific  
Figure 3: Data enhancement diagram. Figure 2: Fault bearing test bench. experimental steps are as follows: first, use one of the three datasets A, B, and C to train the WMSCCN model; then, test the trained model on a non-training dataset. For example, if you use dataset A to train the WMSCCN model, you can choose the B or C dataset for the model testing. The proposed WMSCCN algorithm takes the vibration data as an input and requires no other preprocessing. It is an end-to-end intelligent fault diagnosis algorithm. Two classic algorithms and five advanced algorithms are developed for comparative experiments: artificial neural network (ANN), support vector machine (SVM) [32], WDCNN [22], CNN based on vibration images (VI-CNN) [33], New CNN based on LeNet-5 [19], multiscale CNN (MSCNN) [34] and adaptive weighted multiscale CNN (AWMSCNN) [35]. The architecture of the last five models implemented in this paper is exactly the same as the references. The input of ANN and SVM is the amplitude at different frequencies obtained by fast Fourier transform (FFT) transformation. Among them, the radial basis function (RBF) is selected as the kernel function of the SVM and the network structure of ANN is 1024-500-200-10. Both VI-CNN and the New CNN based on LeNet-5 convert vibration signals into image data as an input. For specific conversion methods, refer to literature [33] and literature [19], respectively. The input of WDCNN, MSCNN, and AWMSCNN is consistent with the input of the proposed WMSCCN algorithm, and both are original signals. Therefore, the types of input data of the comparison algorithm include frequency domain data, image data, and original data, which are more comprehensive. In this paper, the accuracy rate is selected as the evaluation index. Figure 4 shows the diagnostic accuracy under different settings, where A\(\rightarrow\)B indicates that the WMSCCN model is trained on dataset A and tested on dataset B. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset Name** & **Rotational Speed (rpm)** & **Loads (hp)** & **Damage Size (in.)** \\ \hline A & 1772 & 1 & 0.007, 0.014, 0.021 \\ B & 1750 & 2 & 0.007, 0.014, 0.021 \\ C & 1730 & 3 & 0.007, 0.014, 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dataset details under different operating conditions. Figure 4: Comparison of diagnostic performance under different loads. From the experimental results, SVM + FFT has the worst fault diagnosis performance under different loads, with an average accuracy of only 63.36%. New CNN based on LeNet-5 (referred to as New CNN) and VI-CNN, which take image as an input type, cannot effectively identify fault features under different loads because they directly stack the original data into images and input them into the variation in CNN. As a result, the diagnostic accuracy decreased, with average accuracy rates of 80.86% and 84.99%, respectively. Surprisingly, the ANN + FFT algorithm achieved a relatively good performance. Compared with the above four algorithms, the average accuracy of AWMSCNN, MSCNN, WDCNN, and the proposed WMSCCN algorithm with the original signal as input exceeds 90% and the generalization is better. The improvement in performance may be because the original time series data is more effective for fault feature extraction under variable operating conditions than frequency data and image data. In the case of the same input, the proposed WMSCCN algorithm shows a strong generalization. Although under the conditions of A\(\rightarrow\)B and B\(\rightarrow\)C, the accuracy of the proposed WMSCCN algorithm is 2.93% and 0.18% lower than WDCNN, respectively.