# A Fault-Signal-Based Generalizing Remaining Useful Life Prognostics Method for Wheel Hub Bearings
## 4 Validation
### Analysis of Experimental Results
For the kurtosis feature, the RUL prognostics results are shown in Figure 10 and Table 3. The accuracies of RUL prognostics are 0.4280, 0.6924, 0.8762, and 0.9909 based on 25%, 50%, 75%, and 100% of the accumulative data, as shown in Figure 10a-d. The accuracy also increases as the original data increases. The traditional grey theory can prognosticate the RUL of wheel hub bearings in a way. The accuracy of RUL prognostics is also very poor in the early stage. This also verifies that the traditional grey theory has a poor generalization with the accumulative signal. Figure 10: The RUL prognostics results with kurtosis of the accumulative signal utilizing grey theory: (**a**) prognostics result based on 25% of the accumulative data; (**b**) prognostics result based on 50% of the accumulative data; (**c**) prognostics result based on 75% of the accumulative data; (**d**) prognostics result based on 100% of the accumulative data. Figure 9: The RUL prognostic results with the energy of the accumulative signal utilizing grey theory: (**a**) prognostics result based on 25% of the accumulative data; (**b**) prognostics result based on 50% of the accumulative data; (**c**) prognostics result based on 75% of the accumulative data; (**d**) prognostics result based on 100% of the accumulative data. The RUL of wheel hub bearings is prognosticated utilizing the proposed RUL prognostics method based on the fault signal with the accumulative signal (GG). The original signal is described in Equation (16). The threshold is the maximum time when the damage happens. Here, the time threshold value is taken as \(8.67\times 10^{4}\) h. The \(\alpha_{t}\) in Equation (31) is calculated with Equation (33). Table 2.0  
\(T_{RUL}\) is a constant. Its value only influences the slope of the prognostics curves, but has no influence on the accuracy of RUL. Here, the value is taken as \(8.4\times 10^{4}\). For the energy feature, the RUL prognostics results are shown in Figure 11 and Table 2.1 The accuracies of RUL prognostics are 0.6113, 0.8708, 0.9804, and 0.9997 based on 25%, 50%, 75%, and 100% of the accumulative data, as shown in Figure 11a-d. The accuracy increases as the original data increases, which indicates that the proposed method can prognosticate the RUL of wheel hub bearings with the accumulative signal in a complex and variable working environment. The RUL prognostics have relatively high precision in the initial stage with original data less than 50%. Therefore, the proposed method has a good generalization with the accumulative signal. For the energy feature, the RUL prognostics results are shown in Figure 12 and Table 2.2 The accuracies of RUL prognostics are 0.6160, 0.8788, 0.9880, and 0.9993 based on 25%, 50%, 75%, and 100% of the accumulative data, as shown in Figure 12a-d. The accuracy increases as the original data increases, and the RUL prognostics have relatively high precision in the initial stage. This also verifies that the proposed method has a good generalization with the accumulative signal. For the kurtosis feature, the RUL prognostics results are shown in Figure 13 and Table 2.3 The accuracies of RUL prognostics are 0.6050, 0.8817, 0.9976, and 0.9996 based on 25%, 50%, 75%, and 100% of the accumulative data, as shown in Figure 13a-d. The results show that the proposed method has a good generalization with the accumulative signal. Table 2.4 The RUL prognostics results with amplitude of the accumulative signal utilizing the proposed method: (**a**) prognostics result based on 25% of the accumulative data; (**b**) prognostics result based on 50% of the accumulative data; (**c**) prognostics result based on 75% of the accumulative data; (**d**) prognostics result based on 100% of the accumulative data.