# Intelligent Fault Diagnosis of Rotating Machinery Using Hierarchical Lempel-Ziv Complexity
## 4 Experimental Validations
### Experiment 2  
Experiment 2 aimed to investigate the performance of HLZC in compound fault diagnosis of rotating machinery. Experiment 2 was composed of five compound fault types: health condition (Normal), broken tooth in the driving tooth with inner race fault (BI), missing tooth in the driving tooth with inner race fault (MI), health tooth in the driving tooth with inner race fault (NI), and pitting in the driving tooth with inner race fault (PI). There were 100 samples in each class and 500 samples in total. In addition, the data length was 2048 points. The waveforms under five working types are shown in Figure 15. The detailed information of five compound fault conditions is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Experiments**} & \multicolumn{3}{c}{**HLZC**} & \multicolumn{3}{c}{**MLZC**} & \multicolumn{3}{c}{**LZC**} \\ \cline{2-10}  & \multicolumn{3}{c}{**Accuracy (\%)**} & \multicolumn{3}{c}{**Accuracy (\%)**} & \multicolumn{3}{c}{**Accuracy (\%)**} \\ \cline{2-10}  & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** \\ \hline
1 & 95.67 & 91.33 & 94.30 & 93.67 & 89.33 & 91.72 & 66.33 & 61.67 & 63.47 \\
2 & 97.20 & 92 & 94.72 & 90 & 84.80 & 87.82 & 45.20 & 36 & 41.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed classification accuracy of the experimental datasets in Experiment 1 and Experiment 2. Figure 14: Diagnosis results of 20 trials using three methods in Experiment 1. Figure 13: Confusion matrix using the proposed HLZC method for Experiment 1. Like Experiment 1, the proposed HLZC-SVM method was also utilized for fault type identification of rotating machinery. Figure 16 shows the classification results. From Figure 16, we can see that there were a total of 10 samples misclassified with an accuracy of 96%. For comparison, the LZC and MLZC methods were also tested. The testing accuracies of the four methods are listed in Table 2 and Figure 17. As can be seen, the LZC-SVM was not effective, with an average classification accuracy of 41.22%. Second, combined with multi-scale analysis, the diagnosing performance of the MLZC-SVM method was enhanced with the average classification accuracy of 87.82%. Lastly, the proposed HLZC-SVM method had the highest average classification accuracy of 94.72%. To better evaluate the classifier performance, we calculated the receiver operating characteristic (ROC) curves of HLZC-SVM, MLZC-SVM, and LZC-SVM methods using the experimental data. Here, we ran each method 20 times. The average ROC curve chart and AUC mean value of five health conditions of rotating machinery using three methods are shown in Figure 18. It can be observed from Figure 18a that our proposed HLZC-SVM method had the best performance with the highest AUC value for five health conditions (Normal with 1, BI with 1, MI with 0.99, NI with 0.99, and PI with 0.99). In contrast, the AUC values of MLZC-SVM and LZC-SVM for five health conditions showed a decreasing trend, as shown in Figure 18b,c, respectively. Among the three methods, the LZC-SVM method performed worst, in which the AUC values of five health conditions were only 0.5, 0.93, 0.53, 0.50, and 0.86. The comparison results further demonstrate that our proposed HLZC-SVM method had the best classification ability compared with the other two methods. Moreover, random forest (RF) classifier was also applied for pattern identification for comparison. The ROC curve chart and AUC value were used to evaluate classification performance. Figure 19 shows average ROC curve chart and AUC mean value after running 20 times. As can be seen, the SVM classifier obtained a larger AUC value of 0.99 compared with RF classifier (AUC with 0.97), which meant the SVM had a better classification performance in recognizing various fault types of rotating machinery.