## 3 Fault Diagnosis Method  
### Time-Series Segmentation  
Rail transit rolling bearing data is massive online data, and the overall processing is large. If the data analysis is performed directly on the original time-series, the time and space cost will be too high. In response to this situation, the original sequence is generally segmented first, and then the segmented data is subjected to feature extraction. The cost of analyzing and processing the extracted data features is much lower. We have done some work on time-series segmentation and feature extraction. The proposed SWESSA [29] can quickly and efficiently segment online data, and using local spectrum for feature extraction of rolling bearing faults [30], which can better highlight the local features of the data, clearly has strong anti-noise ability. Time-series segmentation as an important step in time-series mining and time-series representation must meet two basic requirements: streamlining and computational efficiency. Streamlining means that the algorithm must guarantee fewer segments and smaller residual errors; computational efficiency means that the segmentation algorithm can adapt to the online computing environment [31]. For the rolling bearing data applied in this paper, it needs to have a certain anti-interference ability for data noise while being compact and computationally efficient. For time-series segmentation, the practical meaning is time-series dimension reduction. The most important question is how to quickly and accurately detect the split point. The earliest online segmentation algorithms include the classic Sliding Window algorithm (SW), proposed by [PERSON] [32], and Sliding Windows and Bottom-up algorithm (SWAB) [33]. To enhance the approximation effect, we proposed a Sliding Window based on Exponential Smoothing Segmentation Algorithm (SWESSA) [29]. The basic idea is to smooth the sequence and eliminate random errors with the exponential smoothing method and then obtain the main trend of time-series. The adaptive sliding window model based on the short-term prediction ability of the exponential smoothing method and the statistical characteristics of historical data is used to segment the time-series data, obtain the data trend through prediction, and judge the segmentation point by the relationship between the statistical characteristics of the historical data and the prediction error. We have compared the performance of SWESSA, SW, and SWAB from the normal segmentation number (NSN), normal residual error (NRES), and calculation time (NTIME) in the literature [29], as shown in Table 1. The NSN for SW and SWAB and SWESSA is the same. NRES represents the error between the segmentation result and the original data. The smaller the NRES, the better the segmentation effect. The SWESSA is closer to the original sequence than SW and SWAB, and the NRES is the smallest. The NTIME only includes the time to calculate the segmentation point and the residual error. It can be seen from the NTIME that SWESSA is better than SW and SWAB. It is proved by experiments that SWESSA can meet the task of data segmentation with efficient calculation, and it has certain anti-interference ability for data noise, paving the way for the whole fault diagnosis method. The flow chart of SWESSA is shown in Figure 2.  
Where \(s_{t}\) represents a smooth prediction value, \(y_{t}\) represents the true value of the time-series, \(s_{0}\) represents the initial value of the exponential segmentation algorithm, and the calculation method is as follows:  
\[s_{0}=(y_{0}+y_{1}+y_{2})/3 \tag{1}\]  
\(\alpha\) is the weight of the smoothing algorithm, \(\alpha=0.2\). V represents a vector that stores absolute errors, Seg represents the set of stored partition points, and \(Err\) represents the residual error between the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & **SW** & **SWAB** & **SWESSA** \\ \hline NSN & 1 & 0.982 & 1.028 \\ NRES & 1 & 1.052 & 0.978 \\ NTIME & 1 & 2.372 & 0.852 \\ \hline \hline \end{tabular}
\end{table}