## 4 Comparative Studies  
In this section, we used the test data of the S826 micro-switches to illustrate the practicability of this research result, comparing it with the approaches, the Kalman filter instead of an inverse Kalman filter, and the algorithm of [PERSON] et al. [17] in order to verify the superiority of our method. For the last 80 sampling points, the method with the Kalman filter instead of an inverse Kalman filter was similar with our approach, thus Figure 7 compared the updated parameters obtained by [PERSON] et al. [17] with the method proposed in this paper. For these two approaches, the unknown parameters were obtained by the combination of the Bayesian updating and the EM algorithm. The difference is that the fading factor was added in this paper, thus that the drift coefficient was more sensitive to the change of data. As can be seen from the diagram, the prediction error approaches zero in the approach by [PERSON] et al. [17], resulting in \(\mu_{0}\) being not sensitive to new data, when the micro-switch is about to fail, the degradation rate was obviously accelerated, and our approach could be adjusted better. The literature [17] requires higher precision of initial parameter selection, and it is difficult to set an accurate initial parameter in practical applications, because there does not exist a large number of similar historical information and the accurate time to start data monitoring is unknown. In this paper, we selected a set of relatively inaccurate initial parameters in two methods \(\Theta_{0}\) to verify the ability of our algorithm about updating the initial parameters. It can be seen from the comparison chart (Figure 8) that when the parameters are improperly set, the convergence speed of [PERSON] et al. [17] is slow. Furthermore, the method proposed in this paper has faster convergence speed in the initial few sampling points than the method with Kalman filter instead of an inverse Kalman filter merely. Figure 6: Adaptive estimation process of the model parameters. Figure 7: Compare the last 80 sampling points of the model parameters. Figure 9 reflects the mean square error (MSE) values at different monitoring time points. In the initial phase, degradation data are less, the fluctuation of the method proposed by [PERSON] et al. [17] is the largest and with the smallest fluctuation is our method. This means that the remaining life of the PDF of another two predictive models are sensitive to small changes, and if it is applied for a maintenance decision, it may result in two different monitoring points, which are completely different to the maintenance decisions which increases protection and maintenance costs in turn. As a conclusion, our approach has a higher prediction accuracy. Notice that Figure 9b shows an upward trend of MSE, it is mainly because when the life is about to terminate, the data have fluctuated greatly, and the error has been raised slightly. Figure 10 illustrates the approach proposed by [PERSON] et al. [17], which compares with the one proposed by us regarding the estimation RUL at the last four sampling points. PDF becomes gently sharper and closer to the Z-axis by applying our approach. This means when more data are used to estimate parameters, the uncertainty of the remaining life is decreasing, which agrees with the facts. Figure 8: The comparison chart. Figure 9: Mean square error (MSE) of expectation for all monitoring points. **Remark 4**. : _It can't be ignored to illustrate a superior method between the algorithm proposed by [PERSON] et al. [30] and us. Figure 11 reflects that our method fits the actual degradation path better than [PERSON] et al. [30], especially in the initial several sampling points. It is more obvious in Figure 12, where our PDF is closer to the z-axis than shown by [PERSON] et al. [30]. This means our approach is still very sensitive to the monitoring data in the final phase._  
Figure 11: The comparison chart. Figure 12: The PDF of RUL at the last four different monitoring points.