# Gearbox Fault Diagnosis Based on Multi-Sensor and Multi-Channel Decision-Level Fusion Based on SDP
## 3 Fitting Fault Identification Based on SDP Technology
### Single-Channel Fault Diagnosis  
Based on the SDP technique, the choice of parameters for the time lag coefficient \(l\), the mirror symmetry plane angle \(\theta\), and the angular gain factor \(\xi\) were all important for the fault state identification. In addition, the SDP image was able to accommodate information from multiple measurement points of the gear, contributing to determining the gear fault state more intuitively than the common time-domain vibration signal. Previously [45], a decision-level fusion approach based on a single-channel of sensors for the gearbox gear tooth fault diagnosis was used in order to monitor the gear fault state more comprehensively than a single sensor by fusing the sensors that were arranged in the different planes of the gearbox. Nonetheless, the single-channel of a single sensor that was located in the gearbox lead to inaccurate single-channel diagnosis results as the fault data in the other directions were not collected. Hence, with respect to this problem, a multi-sensor multi-channel fault diagnosis method has been proposed in this paper. Next, a comparison between the single-channel fault diagnosis method and the multi-channel fault diagnosis method for gearboxes will be explained. Based on the single-channel fault diagnosis algorithm, a mix SDP image fusing the information of multiple single-channels is proposed in this subsection, 1 st measuring point converted to darkorange image, 2 nd measuring point converted to turquoise image, and 3 rd measuring point converted todarkorchid image, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Testing Frequency** & **Experiment** & **Sampling Time (s)** & **Load (N-m)** & **Rotation Speed** (r/min) \\ \hline \hline \multirow{4}{*}{12.8} & \multirow{4}{*}{30} & \multirow{4}{*}{1} & 0 & \multirow{4}{*}{900} \\  & & & & \(\cdots\) & \\ \cline{1-1}  & & & 30 & \\ \cline{1-1}  & & & 0 & \\ \cline{1-1}  & & & & 1000 \\ \cline{1-1}  & & & 30 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental gear work. Figure 7a depicts the raw vibration signals of the three channels of the multi-channel sensor, and the conversion of the SDP technology can make the raw vibration time domain signals into the SDP images, as shown in Figure 7b, which can then visualize the health status of the detected object. The SDP image technology belongs to feature-level fusion, but the feature-level fusion is located in the middle level of the fusion theory hierarchy and is more complex compared to decision-level fusion, which requires a certain feature filtering capability. The decision-level fusion theory is the highest-level fusion process, which can fuse various information sources in order to realize the final decision result. Therefore, in this section, single-channel data was selected to be used for mirroring in order to achieve decision-level fusion of data. The framework flowchart of the single-channel fault diagnosis is shown in Figure 8.  
Figure 8: Fault diagnosis framework based on single-channel gear pitting level. Figure 7: The SDP image under three measuring points; (**a**) Original vibration signal; (**b**) SDP image conversion. The selection of the parameters for the SDP technique can affect the fault state identification, as shown in Figure 9 for the Y-direction channel of sensor one with different time lag coefficients \(l\) and angular gain factors \(\xi\) for measuring the SDP image arms with different pitting states. The differences in the varying time lag coefficients \(l\) and angular gain factors \(\xi\) were manifested in the images in terms of the arm shape, the thickness, and the concentration areas. Ten sets of comparison experiments were performed, and the time lag coefficient \(l\) gradually rose from 0 to 10 in steps of one and the angular gain factor \(\xi\) gradually increased from 0 to 40 in steps of five. Moreover, it was found that the fault states of \(l=10\), \(\xi=35^{\circ}\) in the case of \(\theta=120^{\circ}\), were most clearly distinguished.