## 3 Fault Diagnosis Method
### Improved AdaBoost Algorithm
The red and yellow circles represent, respectively, \(l_{1}\), \(l_{2}\) in the above-described algorithm, i.e., at the farthest distance to the sample set center, the sample point inside the circle is the sample set of this variety while that outside the circle shall be eliminated. The green area is the common share field of the two varieties. According to the original cluster algorithm flow, the sample close to the sample center belongs to that category. To enlarge the differentiation between sample sets, the sample in the green area is to be dropped out. As a result, the two varieties of sample set become more compact, and the differences between the two are more obvious. Second is the problem of excessive sample distribution probability. If a sample is misclassified multiple times, the distribution rate of the sample will be too large, which will interfere with the diversity of the sample data. Therefore, IAA removes samples with a distribution rate greater than \(F(F\) need to be set in advance) from the training set and distributes the distribution rate equally among the remaining samples during the iterative process of the algorithm. Based on this optimization, IAA combines the idea of AdaBoost to learn a series of weak classifiers or weak learners and combines these weak classifiers into one strong classifier, which will improve the classification accuracy greatly. The specific block diagram of the algorithm is shown in Figure 4 (Take two categories as an example). Figure 3: Sample clustering results. After the above analysis, the clustering process, the calculated sample distribution rate, and the AdaBoost algorithm are integrated. The execution steps of the complete IAA fault classification method are shown in Algorithm 1. ```
1: Randomly select a point from the sample set as the cluster center \(c_{1}=(\hat{x}_{1},1)\)
2:for\(i=1\) to \(n\)
3: Calculate the shortest Euclidean distance \(d_{i}\) between the sample point \(x_{i}\) and the current existing cluster center
4:\(sum\leftarrow\)\(-sum+d_{i}^{2},\ i\leftarrow i+1\)
5:endfor
6:for\(i=1\) to \(n\)
7: Calculate the probability \(p_{i}=d_{i}^{2}/sum\) that \(x_{i}\) is selected as the next cluster center
8: Calculate the probability interval of \(x_{i}\)
9:endfor
10: Generate random numbers \"r\" between 0 and 1
11: The sample corresponding to the interval, to which the random number \"r\" belongs, is the second cluster center \(c_{2}=(\hat{x}_{2},2)\)
12: Repeat steps 2\(\sim\)12 to find the third and fourth cluster centers \(c_{3}=(\hat{x}_{3},3)\)-\(c_{K}=(\hat{x}_{K},K)\)
13:for\(i=1\) to \(n\)
14: Calculate the Euclidean distance from \(x_{i}\) for all cluster centers separately and classify \(x_{i}\) into the category corresponding to the cluster center with the smallest distance
15: Update cluster center \(c_{k}\leftarrow\frac{1}{|x_{i}|}\sum\limits_{x\in\hat{x}_{2}}x,k=1,2,\ldots,K\)

Figure 4: The Specific frame of AdaBoost. ## 4 Experimental Results and Analysis

### Experimental Data

The applied sample sets are the original data of rolling bearing experiment platform provided by the National Key Laboratory of Rail Transit Control and Safety under the Beijing Transport University. The main equipment used to collect the simulation data includes rolling bearing fault detection test bench, piezoelectric acceleration sensor, pulsator, data acquisition card, three types of fault rolling bearings, and normal Rolling bearings, as well as service terminals for diagnosing the collected raw data, the specific equipment, and the typical failure of train rolling bearings, as shown in Figure 5. The performance evaluation program is implemented using MATLAB. The experimental system is window10, and the experimental hardware configuration is: CPU: Intel(R) Xeon(R) CPU E5-2643, RAN size: 64 G, memory size: 12 GB \(\times\) 2.