## 5 Internal Leakage Fault Diagnosis
### Robustness Verification of the Proposed Fault Features  
In order to further verify the robustness of the proposed features for the internal leakage diagnosis, more diagnostic methods and datasets were introduced. Firstly, the widely used SVM and BP neural network were introduced for comparison. Support vector machine (SVM) is a binary classification model, which maps the samples to a high-dimensional space by introducing a kernel function, so as to find a suitable hyperplane for classification [39]. Back Propagation (BP) neural network is a multi-layer feedforward neural network, which uses back-propagation algorithm to train the weights and biases in the network, so as to achieve accurate prediction or classification [40]. The SVM uses the Radial Basis Function (RBF) with penalty parameter c = 1.8 and kernel function parameter g = 16. BP algorithm has three layers of network structure, and seven neurons are used in the hidden layer. The final diagnosis result is shown in the Figure 15. Specifically, the diagnostic results based on the Data 2 and Data 3 are listed, and the results based on Data 1 are all accurate and are not listed. It is clear that the detection accuracy of the three internal leakage diagnosis methods based on the proposed five features exceeds that of methods based on the existing three energy features.  
Moreover, 30 samples, 60 samples, and 120 samples were randomly selected from the 120 sample sets, which consists of 30 healthy datasets, 30 minor leakage datasets, 30 medium leakage datasets and 30 serious leakage datasets. Then, the three data sets were divided into the training set and the test set with the proportion of 70% and 30%, respectively.  
Figure 14: The accuracy of T\({}^{2}\) statistics and SPE statistics based on three features and five features under different training sets: (**a**) Accuracy of T\({}^{2}\) statistics in different data sets; (**b**) Accuracy of SPE statistics in different data sets.  
In addition to the above mentioned SVM and BP neural network, two machine learning algorithms, random forest and AdaBoost, were used. Random forest is an integrated learning method, which improves the accuracy and stability of the model by constructing multiple decision trees and synthesizing their prediction results [41]. AdaBoost algorithm is an iterative algorithm that trains a new weak classifier at each iteration step and updates sample weights based on its classification performance to obtain the final strong classifier [42]. These methods based on the proposed five features were used for the internal leakage diagnosis, and the average accuracy was calculated. The parameter settings of these methods are shown in Table 3. Figure 16 presents average accuracies for different methods under the three sample sets. The accuracy of all methods is more than 97% in different sample sets, except for AdaBoost, which achieved an accuracy of 75%. Therefore, the internal leakage fault diagnosis based on the proposed five features is robust.  
Figure 16: The average accuracy of different methods with different sample sets.  
Figure 15: The accuracy of three features and five features based on three diagnosis methods under different training sets: (**a**) Accuracy of different methods obtained with Data 2; (**b**) Accuracy of different methods obtained with Data 3.