## 4 The Application of the ACCLN to Power Cable Fault
### Performance of the IPSO-SVM Algorithm  
In order to test performance of the IPSO-SVM algorithm, Figure 7 shows the training result of IPSO-SVM method. Figure 8 shows the test result of IPSO-SVM method. Figure 7 shows the training result the by IPSO-SVM method via 32 training data in Table 1. Figure 8 shows the test result the by IPSO-SVM method via 22 test data in Table 1. The cable fault features have different degrees of difference. However, it is not easy to distinguish the similar cable fault. So the ACCLN method is proposed to solve the problem. short circuit, three phase short circuit, and normal condition, respectively. A total of 54 sample data are used in the experiment. The ACCLN consists of a neuron array \(54\times 1\) in the input layer and three neuron nodes in the output layer. The transient state \(u_{x;j}\) and the internal state \(v_{x;j}\) are \(54\times 3\) array. Each testing point of phase entropy and amplitude entropy are composed of an input vector, and normalized in the input layer. The phase entropy and amplitude entropy are normalized as follow. For example, for each phase entropy and amplitude entropy, the normalized value is shown as Equations (20) and (21):  
\[p_{norm;j}=\left(p_{i}-p_{\min}\right)/\left(p_{\max}-p_{\min}\right) \tag{20}\]  
\[a_{norm;j}=\left(a_{i}-a_{\min}\right)/\left(a_{\max}-a_{\min}\right) \tag{21}\]  
and an input vector \(z_{i}\) is shown:  
\[z_{i}=\left[p_{norm;i}\ a_{norm;j}\right] \tag{22}\]  
Where \(p_{i}\) indicates the \(i\)-th phase entropy, \(p_{\min}\) and \(p_{\max}\) is the minima and maxima of the 54 phase values, respectively. \(p_{norm;i}\) is the \(i\)-th normalized phase value. The process of normalizing amplitude entropy is the same as phase entropy. \(z_{i}\) is the \(i\)-th input vector, composing the normalized phase value \(p_{norm;i}\) and the normalized amplitude value \(a_{norm;i}\). The flow chart of ACCLN algorithm is shown in Figure 9. The step of ACCLN algorithm for power cable fault classification is shown as follow:  
Step 1: Preprocess the input phase entropy and amplitude entropy for each test point using Equations (20-22). Step 2: Set the cluster-center \(w_{j}\) (\(j\)=1,2,3...) randomly for interphase short circuit, three phase short circuit, and normal condition. Step 3: Initialize self-feedback connection \(T(0)\), internal states and transient state for all interconnection strengths. Step 4: Calculate the energy function (14). Step 5: Update internal states and transient state for all interconnection strengths using Equations (15) and (16). Step 6: Update the cluster-centers by a small learning-rate parameter using Equations (17) and (19). Step 7: Decrease the self-feedback connection weight \(T(t)\) using Equation (18). Step 8: If the network does not converge then goes to Step 4; otherwise stop. Figure 10 shows the experimental sample data distribution. There are 6 category data, interphase short circuit of training data and test data, three phase short circuit of training data and test data, respectively. The recognition accuracy was 87.0% with the SVM method and 90.7% with the IPSO-SVM method in [16]. Figure 10: Experimental sample data distribution. X axis indicates amplitude entropy; Y axis indicates phase entropy. Figure 9: Flow chart of annealed chaotic competitive neural network (ACCLN). Figure 11 shows the experimental result of ACCLN. There are 54 sample data. Those samples are divided into three classifications. The green \">\" indicates normal condition of power cable, 25 samples. The blue \">\" indicates the power cable of three-phase short circuit, 13 samples. The red \"<#\" indicates the power cable of interphase short fault, 16 samples. The different colors \">\" corresponds to each cluster-center. Table 2 shows the recognition accuracy of SVM, IPSO-SVM, and ACCLN. The recognition accuracy of ACCLN, IPSO-SVM and SVM is 96.2%, 90.7%, 87.0%, respectively. The training times are 0.032, 0.0523, 0.0575, respectively.