# Intelligent Fault Diagnosis of Rotating Machinery Using Hierarchical Lempel-Ziv Complexity
## 4 Experimental Validations
### Experiment 1  
Experiment 1 consisted of one healthy condition and five single fault conditions, including inner race fault (IRF), ball fault (BF), grooving in the inner race (GIR), grooving in the outer race (GOR),  
Figure 11: Faulty gears and bearings: (**a**) pitting in the driving tooth, (**b**) broken tooth in the driving tooth, (**c**) missing tooth in the driving tooth, (**d**) ball fault, (**e**) inner race fault, (**f**) outer race fault, (**g**) grooving in the inner race, (**h**) grooving in the outer race.  
Figure 10: The experimental platform and its schematic diagram.  
and outer race fault (ORF). There were 100 samples in each class and 600 samples in total. Meanwhile, the data length was 2048 points. The waveforms under six healthy conditions are shown in Figure 12. Table 1 gives the detailed information of six healthy conditions, including class label, damage diameter, and the numbers of training and testing data.  
Following the steps in Section 3, we firstly utilized the proposed HLZC method to extract the fault features. Then, the obtained features were fed into SVM for classification. The obtained results are shown in Figure 13. It can be seen from 0 that 16 samples were misclassified and the final accuracy was 94.67%. For comparison, the MLZC and LZC were also tested. To avoid randomness, we carried out 20 trials. Figure 14 and Table 2 illustrate the detailed recognition results using three methods. First, the proposed HLZC method achieved the highest average classification accuracy of 94.3% (ranging from 91.33% to 95.67%). This can be attributed to the high frequency components considered in the HLZC method, which can contribute more information in the high frequency to generate a more accurate estimation of complexity. Second, the MLZC method obtained the second-highest average classification accuracy of 91.72% (ranging from 89.33% to 93.67%). Third, the LZC method had the lowest classification accuracy of 63.47% (ranging from 61.67% to 66.33%) due to the ineffectiveness of single analysis. It is indicated that HLZC had the best performance in extracting fault features among the three methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Class** & **Class Label** & **Damage Diameter (mm)** & \
\begin{tabular}{c} **Number of** \\ **Training Samples** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Testing Samples** \\ \end{tabular} \\ \hline Normal & 1 & 0 & 50 & 50 \\ Ball fault & 2 & 0.01 & 50 & 50 \\ Inner race fault & 3 & 0.01 & 50 & 50 \\ Outer race fault & 4 & 0.01 & 50 & 50 \\ Grooving in the inner race & 5 & 0.2 & 50 & 50 \\ Grooving in the outer race & 6 & 0.2 & 50 & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed information of six conditions in Experiment 1.  
Figure 12: The time domain waveforms of rotating machinery under six healthy conditions in Experiment 1: (**a**) health condition (Normal), (**b**) ball fault (BF), (**c**) inner race fault (IRF), (**d**) outer race fault (ORF), (**e**) grooving in the inner race (GIR), (**f**) grooving in the outer race (GOR).