# Multi-Sensor GA-BP Algorithm Based Gearbox Fault Diagnosis
## 3 Simulation Analysis  
### Data Processing  
The simulation data was from the Bearing Data Center of Case Western Reserve University in the United States. The sampling bearing model is 6205-2 RS JEM SKF deep groove ball bearing, the motor speed is 1797 r/min, and the sampling frequency is 12 kHz. The four damage diameter states of the inner ring of the bearing: Normal, 0.007 inches, 0.014 inches, 0.021 inches, respectively, using (1, 2, 3, 4) to represent the fault state. The matrix form is [1 0 0 0], [0 1 0 0], [0 0 1 0], [0 0 0 1]. In this present study, the data of four-fault states of the inner ring of the bearing were selected, and the data of each state was divided into 29 groups with 4096 points in each group, a total of 116 groups of data. Then, a feature extraction was perform, and a total of 19 time-frequency domain feature indicators were selected. The time frequency processing results of these 19 feature indicators are shown in Table 1.  
In each state, the front 20 sets of feature index data were selected for training. The remaining 9 sets of data were used as the test set. The training set is input into the BP algorithm and the GA-BP algorithm. At this point, the input layer is 19 layers and the output layer is 4 layers. The value of \(a\) is dependent on the accuracy of output data and the Mean Squared Error (MSE) which MSE represents the fit of the model pair to the data. The accuracy and \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{3}{c}{**Time Domain Features**} & \multicolumn{3}{c}{**Frequency Domain Features**} & \multicolumn{3}{c}{**Time-Frequency Features**} \\ \cline{2-9}  & \multicolumn{2}{c}{**Root Mean Square**} & \multicolumn{1}{c}{\multirow{2}{*}{...}} & \multirow{2}{*}{**Kurtosis**} & \multicolumn{1}{c}{**Barycenter Frequency**} & \multicolumn{1}{c}{...} & \multicolumn{1}{c}{**P13**} & \multicolumn{1}{c}{...} & \multicolumn{1}{c}{**P83**} \\ \hline \multirow{4}{*}{Normal} & 1 & 0.0823 &... & 0.0068 & 1161.104 &... & 45.6012 &... & 0.1492 \\ \cline{2-9}  & 2 & 0.0846 &... & 0.0072 & 1123.906 &... & 44.6706 &... & 0.1578 \\ \cline{2-9}  &... &... &... &... &... &... &... &... \\ \cline{2-9}  & 29 & 0.0829 &... & 0.0069 & 1168.689 &... & 38.1235 &... & 0.1646 \\ \hline \multirow{4}{*}{0.007\({}^{\
u}\)} & 1 & 0.2445 &... & 0.0598 & 2446.6 &... & 9.4725 &... & 1.0977 \\ \cline{2-9}  & 2 & 0.2466 &... & 0.0608 & 2446.023 &... & 9.0168 &... & 1.1224 \\ \cline{2-9}  &... &... &... &... &... &... &... &... \\ \cline{2-9}  & 29 & 0.2470 &... & 0.0610 & 2500.594 &... & 8.4057 &... & 1.0324 \\ \hline \multirow{4}{*}{0.014\({}^{\
u}\)} & 1 & 0.1252 &... & 0.0157 & 3126.209 &... & 16.9972 &... & 6.1315 \\ \cline{2-9}  & 2 & 0.1286 &... & 0.0165 & 3136.342 &... & 17.2573 &... & 6.1819 \\ \cline{2-9}  &... &... &... &... &... &... &... &... \\ \cline{2-9}  &... &... &... &... &... &... &... &... \\ \cline{2-9}  & 29 & 0.1203 &... & 0.0145 & 3073.158 &... & 18.9016 &... & 5.3250 \\ \hline \multirow{4}{*}{0.021\({}^{\
u}\)} & 1 & 0.2318 &... & 0.0537 & 2877.327 &... & 18.0769 &... & 1.5097 \\ \cline{2-9}  & 2 & 0.2245 &... & 0.0504 & 2836.955 &... & 19.8080 &... & 1.7618 \\ \cline{2-9}  &... &... &... &... &... &... &... &... \\ \cline{2-9}  & 29 & 0.2259 &... & 0.0510 & 2846.9183 &... & 17.1866 &... & 1.9061 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time-frequency characteristic parameters.