## 3 Fault Diagnosis Method
### Improved AdaBoost Algorithm
Classification Rate (CR)

CR is applied to measure the classification accuracy for all sample set. This norm reflects the percentage of all accurately classified sample set number occupying total sample set number. The calculation is done as follows:

\[CR=\frac{\text{All accurately classified sample set number}}{\text{Total number of sample set}} \tag{9}\]

In the above listed three indexes, DR and FAR reflect the probability that a certain sample set is correctly or wrongly classified, and it is directed to a single sample set. While CR reflects the entire classification effects of the algorithm. Directed to a certain variety of sample set, if DR is approaching one and FAR is approaching to 0, it means the variety of sample set is classified by higher accuracy. In the case of the entire sample set, if CR is approaching one, it indicates the entire accuracy of the classification algorithm is still higher. ### Result and Analysis of Experiment

The comparison of the classification algorithm in the experiment is the BP neural network, SVM classifier, AdaBoost, and IAA. The same experimental data set is used for the comparison experiments. Due to the stochastic character of the BP neural network, the 8 folds cross method has been adopted to conduct cross verification in this paper for the BP, i.e., the experimental data set is divided into eight equal parts, then turn is taken to have one part as the test data, while the rest seven parts as training data. This procedure is repeated eight times. Finally, the mean value of the results of each index is taken. The standard SVM classifier is applied. Radial Basis Function (RBF) core is taken for core function, where penalty factor parameter c and RBF core function parameter g are extracted with the grid method. In the specific experimental method, \(c=2^{-5},2^{-4},2^{5},\ g=2^{-5},2^{-4},2^{5}\). conduct cross-verification within the scope. On completion of ergodic, the optimum values of c and g are found. If there are existing several groups of \(c\) and \(g\), then the smallest c group is chosen. The reasons are that too high penalty factor would increase the cross-verified data accuracy rate, but possibly make the whole classifier dropped in over learning state that would lead the classifiers inferior. AdaBoost and the IAA's weak classifier are all applied in the BP neural network, and the number of weak classifiers is 10. The input vector of each classifier is the feature vector of the training sample, and the results of the classification experiment are compared by the evaluation index mentioned above. The specific experimental flow is shown in Figure 8.

Classification and comparison experiments are conducted according to the experimental flow chart. The results of each algorithm based on the vibration data set at 4 r/s and the standard data set are taken as an example. Table 7 shows the performance of the DR; Table 8 shows the performance of the FAR, and Table 9 shows the performance of the CR. Figure 8: Classification experiment flow chart. Table 7 shows that in the entire manifestation, the IAA is slightly higher than the rest few algorithms, the next is AdaBoost, then is the SVM, the last one is the BP algorithm. Each algorithm in a single data set manifests differently. In the inner fault detection rate at rotation velocity 4 r/s of the rolling bearing in the running department of rail train, the detection rate of the BP algorithm is better than the other algorithms. This means a different classification algorithm should be tried in the different data set. The good average performance does not necessarily confirm all data set. The solution is to be taken according to the specific situation. It can be seen from Table 8 that the FAR of BP is the highest, the FAR of IAA is the lowest, and the FAR of the SVM algorithm is slightly higher than AdaBoost. This proves the shortcomings of the BP algorithm, that is, it is easily dropped in local optimum, to obtain the most satisfactory result.