# Fault-Diagnosis Method for Rotating Machinery Based on SVMD Entropy and Machine Learning
## 4 Experimental Analysis
### Analytical Comparison  
The energy entropy and fuzzy entropy of each component were obtained by decomposing the bearing- and gear-vibration signals through VMD and SVMD. Each of them was constructed into an energy-entropy sample set and a fuzzy-entropy sample set. A machine-learning [32; 33] classification model was established to perform intelligent diagnosis of faults. Firstly, the gear data of two working conditions of the SEU dataset were be studied, and the data length of each class of gear was 1,048,560. This paper took the length of 4096 as a data sample, which could be divided into 255 in total, and then used the VMD and SVMD methods for mode decomposition of each data sample. When computing energy entropy and fuzzy entropy as feature vectors, it is generally sufficient to take the first six components. The disadvantage of choosing more or fewer components is that choosing more components can increase the computation burden and may lead to overfitting problems, where the model performs well on training data but poorly on unknown data. Additionally, too many components can increase the complexity of the model, making it harder to interpret and understand. Choosing fewer components may result in the loss of important information and a decrease in model accuracy. Therefore, selecting an appropriate number of components, specifically the first six orders, can ensure model accuracy while avoiding issues of excessive complexity and computational burden. Therefore, in this paper, we sought the energy-entropy value and fuzzy-entropy value \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operation** & **Dataset** & **Data Length** & **Fault Type** \\ \hline \multirow{4}{*}{I} & Chipped\_20\_0 & 1,048,560 & Broken-tooth failure \\  & Health\_20\_0 & 1,048,560 & Normal condition \\  & Miss\_20\_0 & 1,048,560 & Missing-tooth failure \\  & Root\_20\_0 & 1,048,560 & Tooth-root failure \\  & Surface\_20\_0 & 1,048,560 & Tooth-surface failure \\ \hline \multirow{4}{*}{II} & Chipped\_30\_2 & 1,048,560 & Broken-tooth failure \\  & Health\_30\_2 & 1,048,560 & Normal condition \\ \cline{1-1}  & Miss\_30\_2 & 1,048,560 & Missing-tooth failure \\ \cline{1-1}  & Root\_30\_2 & 1,048,560 & Tooth-root failure \\ \cline{1-1}  & Surface\_30\_2 & 1,048,560 & Tooth-surface failure \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Planetary-gear dataset of SEU. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operation** & **Dataset** & **Data Length** & **Fault Type** \\ \hline \multirow{4}{*}{I} & Ball\_20\_0 & 1,048,560 & Rolling-body failure \\  & Comb\_20\_0 & 1,048,560 & Inner-ring and outer-ring mixed failure \\  & Health\_20\_0 & 1,048,560 & Normal condition \\  & Inner\_20\_0 & 1,048,560 & Inner-ring failure \\  & Outer\_20\_0 & 1,048,560 & Outer-ring failure \\ \hline \multirow{4}{*}{II} & Ball\_30\_2 & 1,048,560 & Rolling-body failure \\  & Comb\_30\_2 & 1,048,560 & Inner-ring and outer-ring mixed failure \\ \cline{1-1}  & Health\_30\_2 & 1,048,560 & Normal condition \\ \cline{1-1}  & Inner\_30\_2 & 1,048,560 & Inner-ring failure \\ \cline{1-1}  & Outer\_30\_2 & 1,048,560 & Outer-ring failure \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data set of rolling bearings of SEU. of the first six components. There were five types of gears. The final composition of the energy-entropy and fuzzy-entropy sample-set size was 1275 \(\times\) 6 (the former represents rows and the latter represents columns, except for labeled columns). In this paper, there were no training datasets, and all data were used for testing. Then, a machine-learning classification model was built for pattern recognition. Figures 12 and 13 show the diagnostic effect of the support-vector machine (SVM) [34] in the form of a confusion matrix for the sample set of energy entropy and fuzzy entropy of the SEU gearwork data. The parameters of the two classification models were derived in the form of a grid search. In the SVM model, the penalty factor was [0.01, 0.1, 1, 10, 100] and the kernel-function parameter was [0.01, 0.1, 1, 10, 100].