# Intelligent Fault Diagnosis of Rotating Machinery Using Hierarchical Lempel-Ziv Complexity
## 4 Experimental Validations
### Experiment 2
To gain a clear sense of the cluster ability of the extracted features using HLZC and MLZC methods, we used two-dimensional projection for visualization with PCA, as drawn in Figure 20. In 0a, it can be observed that the HLZC features of the five health conditions had a clear boundary and each cluster was individually separate. However, for the MLZC method, a few features were mixed,  
Figure 17: Diagnosis results of 20 trials using three methods in Experiment 2. Figure 18: Performance comparison between three methods: (**a**) HLZC-support vector machine (SVM), (**b**) MLZC-SVM, and (**c**) LZC-SVM. resulting in difficulty for classification. This phenomenon indicated that the fault features extracted using HLZC had more cluster ability than the MLZC method. We also tested the performance of our proposed HLZC method using different percentages of samples for training (the remaining samples will be considered as testing samples). Eight percentages were tested: 10% to 80%. To reduce randomness, 20 trials were conducted for each percentage. The averaging of training and testing accuracies were calculated and their corresponding standard deviations are illustrated in Figure 21. When the percentage increased to 50%, it achieved the highest classification accuracy at 94.72%. Therefore, we selected 50% of samples for training to demonstrate the advantage of our proposed HLZC method. In order to discuss the influence of layer \(k\), we applied the data of Experiment 2 for validation. Figure 22 shows the obtained classification accuracies using different layer \(k\). As can be seen, when the layer \(k<4\), the classification accuracy will be significantly enhanced as the layer \(k\) rises. However, a larger layer \(k\) will greatly enhance the central processing unit (CPU) time. We observed that when the layer \(k=4\) increased to 5, the obtained classification accuracy was only improved by 0.08% from 94.72% (layer \(k=4\)) to 94.80% (layer \(k=5\)). However, the CPU time for layer \(k=5\) was 2116 s, which was almost double that of layer \(k=4\) at 1095 s.  
Moreover, there was one extremely useful byproduct of RF--variable importance measures [33]--which was calculated to show the contribution of different components for the final classification accuracy, as shown in Figure 23. Note that a lager importance value indicated that  
Figure 14:0 Performance comparison for different random forest (RF) and SVM. Figure 14:1 Projections of two-dimensional visualization of the obtained features in Experiment 2: (a) our proposed HLZC method, (b) traditional MLZC method. the component had a greater influence on final predictions. It can be seen that \(X_{50}\) generated by layer \(k=5\) had a lower feature importance compared with that of component \(X_{40}\) generated by layer \(k=4\). This phenomenon further indicated that the additional features generated by HLZC with \(k=5\) had a small contribution on the final classification accuracy, which was well consistent with the classification results in Figure 14:2 Considering both the classification accuracy and CPU time, we selected the layer \(k=4\) for HLZC in this study. Figure 14:3 The classification results of the proposed method using training by different percentages of samples. Figure 14:4 The importance of each component for the HLZC method. Figure 14:5 The mean classification accuracy and computation time using HLZC with different \(k\).