# Bearing Fault Diagnosis Method Based on Improved VMD and Parallel Hybrid Neural Network
## 3 Materials and Methods
### Data Set Processing  
The effectiveness of the proposed fault diagnosis method is verified by experiments on the public data set [32] of XJTU. The test bearing model adopted is LDK uer204. The experimental platform is mainly composed of a speed controller, digital force display, rotating shaft, motor, and test bearing, as shown in Figure 5. During the experiment, the radial force can be adjusted by the hydraulic loading system, and the speed can be adjusted by the AC motor to set different working conditions. There are three kinds of working conditions in the experiment, and the data from five experimental bearings are collected  
Figure 4: Flow chart of parallel hybrid neural network fault diagnosis.  
under each type of working condition. Table 1 lists the details of the bearings selected in this paper, including bearing life and fault location. The experimental data were collected by a dt9837 signal collector with a sampling interval of 60 s, a sampling frequency of 25.6 kHz, and a single sampling time of 1.28 s.  
Because the bearing fault data set is too large to analyze all the fault signals, this paper selects the vibration signals in the horizontal direction of two bearing data sets under each working condition in the experiment [33], and each bearing data set selects the data of the last five CSV files for processing and analysis. Each CSV file contains 32768 sampling points, with a total of six fault types. The experimental data set constructed is shown in Table 2 below.  
The original data set needs to be preprocessed before the fault signal processing so that after the fault signal processing, the data set can be directly brought into the fault diagnosis  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bearing Data Set** & **Speed/Radial Force** & **Number of Files** & **Lifetime** & **Fault Element** \\ \hline Bearing 1\_1 & 35 Hz/12 kN & 123 & 2 h 3 min & Outer race \\ Bearing 1\_4 & 122 & 2 h 2 min & Cage \\ \hline Bearing 2\_1 & 37.5 Hz/11 kN & 491 & 8 h 11 min & Inner race \\ Bearing 2\_2 & 161 & 2 h 41 min & Outer race \\ \hline Bearing 3\_3 & 40 Hz/10 kN & 371 & 6 h 11 min & Inner race \\ Bearing 3\_5 & 114 & 1 h 54 min & Outer race \\ \hline \hline \end{tabular}
\end{table}
Table 1: XJTU bearing datasets.  
Figure 5: Experimental platform.  
model as an input for learning. Data truncation and sample generation are required for the new fault data set before data set preprocessing. To make each group of samples contain effective information on the fault, this paper selects the appropriate sample length by taking the number of points of one revolution of the bearing as a reference and calculates the range of 640-731.43 through the sampling frequency and the corresponding speed in three working conditions. Considering the influence of data abundance, the length of each training sample is set to 1024 data points. To enhance the generalization ability of the model. In this paper, the sliding window overlapping sampling method [34] is employed to generate training samples. The generation formula is as follows:  
\[L=\left(\frac{l-W}{B}+1\right) \tag{12}\]  
where \(L\) is the number of newly generated samples, \(l\) is the number of data points of the original fault signal, \(W\) is the length of the new training sample, and \(B\) is the step size of the sliding window.  
In this paper, the step length of the sliding window is 1/4 of the sample length, that is 256 data points, and the number of newly generated samples can be calculated to be 637. To facilitate statistics and analysis, the first 600 samples are employed as training samples. Therefore, the size of each type of fault set generated after data truncation is (600, 1024). From each type of fault set, the training set and test set are constructed by randomly selecting data in the ratio of 8:2. To accelerate the convergence speed of the training model, the min max function is employed to normalize the experimental data. The newly generated bearing fault data set is shown in Table 3.