## 3 Fault Diagnosis Method
### Improved AdaBoost Algorithm  
For the bearing fault diagnosis data type, the classification accuracy of general machine learning algorithms, such as BP neural network and standard SVM, can't achieve the desired effect. However, integrated learning algorithms, such as Bagging or Boosting, can effectively improve the classification accuracy of weak classifiers. AdaBoost is a classic iterative integration algorithm in the integrated learning algorithm. It improves classification accuracy by integrating weak classifiers with weak classification. The weak classifier can be any classifier, such as a simple decision tree, a simple linear logistic classifier, a BP algorithm, and so on. The core idea of AdaBoost is to iteratively train the weak learning algorithm for the same data set and integrate them into a strong learning algorithm. The upper limit of the training error decreases with the number of iterations, so there is no over-fitting phenomenon [36]. The strong learning algorithm can greatly improve the accuracy of the weak classifier, which is easy to encode and does not require parameter adjustment with a lower generalized bit error rate, and, at the same time, it is sensitive to outliers or noise [37]. Therefore, the initial condition is to ensure that the classifier uses the sample set data with the least noise. When there are abnormal points or noise in the data, the AdaBoost algorithm does not process it, which will seriously affect the classification result. To enhance the anti-noise ability, this paper improves the AdaBoost algorithm and proposes an improved AdaBoost algorithm (Improved AdaBoost Algorithm, IAA). The main idea of the algorithm is to filter the sample data and eliminate samples with too large sample distribution during the iterative process first, which ensure the diversity of the sample. Then, the data after denoising are classified, during which the classification accuracy is greatly improved. First, for the noisy data, IAA first clusters the sample data to make the sample data of the same category more compact, and the difference between the different categories of sample data is greater through clustering. There are many clustering algorithms, such as Self-organizing Maps and K-means. In this paper, the improved K-means is selected to optimize the clustering process of the K-meansclustering algorithm. The improved K-means eliminate the impact of random initial cluster centers on classification results and improve the discrimination of different categories. The specific optimization details of the clustering process are as follows (Take two categories as an example):  
1. For a given sample data set, \(N=\{(x_{1},y_{1})(x_{2},y_{2}),\ldots,\)\((x_{n},y_{n})\}\), \(x_{i}\in X\), \(y_{i}\in Y=\{1,2\}\), where \(x_{i}\) is the sample data with attributes of \(r\) dimensions, \(y_{i}\) is the category to which the sample belongs. The K-means clustering operation is performed on the two types of samples, and the selection of the initial cluster center is optimized. Finally, the cluster center of the two types of samples, \((\tilde{x}_{1},1)\) and \((\tilde{x}_{2},2)\), is obtained. 2. Traversing all the samples in the sample dataset. All the samples belonging to category \"1\" are required to have a distance to \(\tilde{x}_{1}\) less than \(l_{1}\), and the distance to \(\tilde{x}_{2}\) greater than \(l_{2}\). At the same time, all the samples belonging to category \"2\" are required to have a distance to \(\tilde{x}_{2}\) less than \(l_{2}\), and the distance to \(\tilde{x}_{1}\) greater than \(l_{1}\). Samples that do not meet the requirements are rejected. Then, the new training set is \(N_{1}=\{(x_{1},y_{1})(x_{2},y_{2}),\ldots,\)\((x_{m},y_{m})\}\), \(x_{i}\in X\), \(y_{i}\in Y=\{1,2\}\), and Figure 3 shows the case when the number of clusters is 2 and 2 dimensions in the sample. It is seen from the bipartite classification graph in Figure 3 that the cluster center of category \"1\" is red sample point, whereas that for category \"2\" is yellow.