# Modeling of Distorted Degradation Data Based on Oil Analysis
## 4 Case Studies
It can be seen that the number of oil top-ups is relatively small, and there is a small gap between the observed degradation and the corrected one. Figure 5: Vehicle 1: the relationship between time and degradation. According to the above two examples, our methodology can correct the distortion data and obtain an estimation of the actual degradation curve. The \"uncorrected\" (observed) concentration only indicates that wear is taking place while the \"corrected\" (actual) concentration reflects the degree of wear. Therefore, our methodology can avoid the misdiagnosis of wear condition to some degree. \begin{table}
\begin{tabular}{c c c} \hline
**Serial Number** & **Sampling Time [h]** & **Observed Concentration [ppm]** \\ \hline  
5 & 104.7750 \\ \hline \end{tabular}
\end{table} 
Table 7: The observed data for Vehicle 2. Figure 6: Vehicle 2: the relationship between time and degradation. Furthermore, we compared our methodology with the piecewise linear method [17]. The results shown in Figures 7 and 8 can be summarized as follows:  
1. The estimation of the actual degradation obtained by the piecewise linear method is the minimum among the three methods. This indicates that the possibility of missing alarm is relatively high and the possibility of false alarm is relatively low if the piecewise linear method is used. Therefore, if engineers' goal is to minimize the possibility of false alarms, then the piecewise linear method is a good choice. 2. The estimation of the actual degradation obtained by the non-parametric approach is the maximum among the three methods. This means that the possibility of missing an alarm is relatively low and the possibility of a false alarm is relatively high if the non-parametric approach is used. Consequently, when engineers want to pay more attention on the possibility of missing an alarm, the non-parametric approach should be used. 3. The estimation of the actual degradation obtained by the parametric approach is located in the middle of the three methods. Therefore, if engineers are very certain about the parametric representation of the physical degradation process, it is recommended to use the parametric approach. It should be noted that the piecewise linear method has three drawbacks: Firstly, it uses local observations to piecewisely correct the observed degradation, rather than global observations. Secondly, it uses engineers' subjective determination to identify the disturbed points, thereby lacking objectivity. Thirdly, it assumes that the actual degradation curve is linear. However, the actual degradation is non-linear in many scenarios. Figure 8: The performance comparison for Vehicle 2. Figure 7: The performance comparison for Vehicle 1. In conclusion, compared with the piecewise linear method, our model and the corresponding estimate approaches have some obvious advantages, as follows:  
1. Our model is established based on the global observed data, so it can locate more valuable information in the observed data. 2. Our model can identify the disturbed points automatically, thereby avoiding subjective judgment and improving the objectivity and accuracy. 3. Both the parametric approach and the non-parametric approach can describe various kinds of degradation patterns, whether linear or non-linear. Therefore, our approaches have wider applicability and practicability.