# An Intelligent Condition Monitoring Approach for
## 4 Application and Results
### Results and Discussions
#### 4.2.3 Comparative Analysis Results  
To verify the enhancement of the HMM-ANN prediction accuracy, two more comparison experiments were carried out. An isolated HMM model and an isolated ANN model were established.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c c} \hline \hline
**States** & **State No.** & \multicolumn{11}{c}{**Predicted Values**} \\ \hline Normal & 1 & & 3 & 3 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & - & - \\ Fault 2 & 2 & & 2 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & - & - & - & - \\ Fault 3 & 3 & & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 4 & 3 & 3 & 3 & 4 & 3 \\ Fault 4 & 4 & & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & - & - & - & - & - & - \\ \hline \hline \end{tabular}  
Total samples for validation: 68, correct predictions: 62, accuracy rate: 91.18%.  
\end{table}
Table 6: Comparisons of health states and HMM-ANN outputs.  
\begin{table}
\begin{tabular}{l c c} \hline
**Training Rule** & **Neurons in Hidden Layer** & **Training Error (mse)** & **R** \\ \hline trainlm & 10 & \(3.10\times 10^{-10}\) & \(1\) \\ traingdx & 10 & \(5.00\times 10^{-2}\) & 0.85633 \\ trainrp & 10 & \(4.62\times 10^{-2}\) & 0.86827 \\ trainscg & 10 & \(1.44\times 10^{-2}\) & 0.96095 \\ trainlm & 5 & \(2.26\times 10^{-3}\) & 0.99397 \\ trainlm & 8 & \(3.40\times 10^{-5}\) & 0.99991 \\ trainlm & 12 & \(7.12\times 10^{-9}\) & \(1\) \\ trainlm & 14 & \(2.22\times 10^{-8}\) & \(1\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The performance of ANN for different settings.  
For comparison purposes, the isolated HMM and ANN model used the same parameter settings and initial values (or initialization method) as for the hybrid HMM-ANN model. Furthermore, the same training and testing sample sets were applied, and the same three-level WPT method was used for feature extraction. The extracted energy feature vectors of the training samples (known state categories) were fed to train the isolated HMM. In addition, the input/target vector pairs (the input vectors were the extracted energy feature vectors, target vectors were constructed by the above mentioned method) are fed to train the isolated ANN. Then, the feature vectors of the testing samples were fed to the trained HMM and ANN. The results are shown in Tables 7 and 8.  
Comparing Table 6 with Tables 7 and 8 shows that some prediction errors in the isolated HMM or ANN model were correctly predicted in the hybrid HMM-ANN model. As seen from Figure 17, for Faults 1 and 3, the hybrid model gave better results than the isolated HMM, while, for Faults 2 and 4, they had the same accuracy rates. By contrast, for each health state, the hybrid model gave better results than the isolated ANN model. Furthermore, the total accuracy of the hybrid HMM-ANN model was significantly higher than that of the isolated HMM or ANN model.  
Note that accuracy of the proposed approach strictly depends on the availability of the complete (e.g., in each health state) condition monitoring data. Hence, to avoid accuracy reduction in fault diagnostics, the proposed approach should be validated with the complete data samples.