# Multi-Sensor GA-BP Algorithm Based Gearbox Fault Diagnosis
## 4 Experiments  
### Experimental Data Acquisition  
There are 19 input parameters, which include 8 time-domain parameters, 3 frequency-domain parameters, and 8 energy ratios of the Wavelet Packet of 3-layer decomposition. Time-domain parameters include root mean square, root square amplitude, absolute mean, skewness, kurtosis, variance, maximum value, and minimum value. The frequency-domain features include barycentric frequency, mean square frequency, and the frequency variance. In addition, time-frequency indicators include P\({}_{13}\), P\({}_{23}\), P\({}_{33}\), P\({}_{43}\), P\({}_{53}\), P\({}_{63}\), P\({}_{73}\), and P\({}_{83}\). As shown in Table 1, due to limited space, not all are listed. According to the working data of the nuclear gearbox gears provided by the cooperative enterprise, the gear speed was set to 480 r/min, 650 r/min, 750 r/min and 800 r/min. As shown in Table 4 for the experimental conditions. Due to the presence of multiples in the frequency of engagement in the experiment. According to [PERSON]'s principle, the sampling frequency is 10 KHz to ensure that no distortion occurs in the signal. When carrying out the effect of speed on the results, the most significant change in signal was found at 800 r/min. Therefore the experimental conditions were chosen as, the sampling frequency is 10 KHz, the speed is 800 r/min and the load is 20 N.m.  
As shown in Table 5 for the gear condition, \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Load (N.m)**} & **Number of** & **Sampling Time** & **Sampling Frequency** & **Sampling Frequency** \\  & **Experiments** & **(Seconds)** & **(KHz)** & **(r/min)** \\ \hline \multirow{6}{*}{20} & & & & & 480 \\ \cline{3-6}  & & & & & 650 \\ \cline{3-6}  & & & & 5 & 750 \\ \cline{3-6}  & & & & 800 \\ \cline{3-6}  & & & & 480 \\ \cline{3-6}  & & & & 650 \\ \cline{3-6}  & & & 10 & 750 \\ \cline{3-6}  & & & & 800 \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental gear example conditions. Figure 9: Diagnostic results before and after fusion of evidence. In order to verify the effectiveness of the proposed method in practical production, the experimental data collected on the gearbox test bench have been used for gear fault diagnosis. To this end, the test rig was designed first, the linear acceleration sensor mounting position arrangement selected, the gear selection and other equipment configuration, and the test bench structure diagram, shown in Figure 10. For the next, the gear fault detection test bench was established, as shown in Figure 11. The test bench consists of a gearbox (including a large gear with 36 teeth and a small gear with 25 teeth), drive motors, and so on. Three acceleration sensors were mounted in the gearbox housing near the vibration source. The experiment focuses on the health monitoring of an active gear with four states: normal, single pitting, double pitting, and triple pitting, 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]. The degree of the condition is shown in Figure 12. The collected experimental data for each state is divided into 48 groups, each group of data consists of 4096 points, with a total of 192 groups of experimental data vibration signal for each state Please refer to Figure 13.  
By selecting the frequency domain features from the grouped experimental data, 19 common time-frequency domain features can be extracted. Each state can thus constitute of points, simplifying the original data set and largely improving the speed of gear fault monitoring operations. In each state, the front 34 sets of data are selected for training and the remaining 14 sets are used as the test set. The training set is fed into the BP algorithm and the GA-BP algorithm, at this point, the input layer is 34 layers, the output layer is 4 layers, and the hidden layer is obtained according to Equation (5), where 10 layers were selected. Therefore, the structure of the BP algorithm and the GA-BP algorithm are 34-10-4.