# A Fault Diagnosis Method of Mine Hoist Disc Brake System Based on Machine Learning
## 4 Decision Tree Classification Method  
The commonly used decision tree classification algorithms are the ID3 and C4.5 algorithms. The ID3 algorithm uses the information gain criterion when selecting feature attributes and constructs the decision tree layer by layer. C4.5 is improved based on ID3. Besides the function of ID3 algorithm, C4.5 has the following advantages [21]: (1) using information gain rate as the basis for dividing attributes, the classification is more reasonable in the face of a few sample subsets; (2) it can process training samples containing both discrete and continuous data and training samples with attribute missing values; (3) multiple pruning methods are used to avoid redundant rules; (4) rules are easier to interpret and more accurate. Therefore, this study focuses on the in-depth analysis of the C4.5 algorithm. The core idea of C4.5 is to set the training dataset \(T\). When constructing the decision tree with dataset \(T\), the attribute with the largest information gain rate is selected as the dividing node, and the data set \(T\) is divided into \(n\) subsets according to the current attribute partitioning standard. If one subset \(T_{i}\) contains the same element class, the node is used as the leaf node and the partition is stopped. If the subset still contains different elements, it continues to divide according to the above division \begin{table}
\begin{tabular}{c c c} \hline \hline
**Source** & **Dependent Variable** & **Significant** \\ \hline \multirow{3}{*}{Correction model} & Hydraulic station oil temperature & 0.059 \\ \cline{2-3}  & Hydraulic station oil pressure & 0.073 \\ \cline{2-3}  & Lifting velocity & 0.697 \\ \hline \multirow{3}{*}{Intercept} & Hydraulic station oil temperature & 0.000 \\ \cline{2-3}  & Hydraulic station oil pressure & 0.000 \\ \cline{2-3}  & Lifting velocity & 0.000 \\ \hline \multirow{3}{*}{Brake shoe clearance} & Hydraulic station oil temperature & 0.059 \\ \cline{2-3}  & Hydraulic station oil pressure & 0.073 \\ \cline{1-1} \cline{2-3}  & Lifting velocity & 0.697 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inter-subjective effect test results. method recursively until all the elements of the subset belong to the same category. At last, nodes are no longer divided and are generated into trees instantly [22; 23; 24]. The specific process is:  
Let \(D\) be the training dataset and \(|D|\) denote the size of the sample. Set \(K\) to be a natural number, for all \(k=1,2,\cdots,K\), \(C_{k}\) is a class. Assume that \(|C_{k}|\) is the number of samples which belong to the class \(C_{k}\) and \(\sum\limits_{k=1}^{K}|C_{k}|=|D|\). Suppose characteristic \(A\) has different values \(\{a_{1},a_{2},\ldots,a_{n}\}\). According to the value of the characteristic \(A\), \(D\) can be divided into \(n\) subsets \(D_{1},D_{2},\cdots,D_{n}\), where, for each \(i=1,2,\cdots,n\), \(|D_{i}|\) is the sample size of \(D_{i}\), and \(\sum\limits_{i=1}^{n}|D_{i}|=|D|\). Denote the set of samples belonging to class \(C_{k}\) in subset \(D_{ik}\), namely \(D_{ik}=D_{i}\cap C_{k}\). Here, \(|D_{ik}|\) is the sample size of \(D_{ik}\). Step 1: Calculate the empirical entropy \(H(D)\)  
\[H(D)=-\sum\limits_{k=1}^{K}\frac{|C_{k}|}{|D|}\log_{2}\frac{|C_{k}|}{|D|}, \tag{1}\]  
Step 2: Calculate the empirical conditional entropy \(H(D|A)\)  
\[H(D|A)=\sum\limits_{i=1}^{n}\frac{|D_{i}|}{|D|}H(D_{i})=-\sum\limits_{i=1}^{n} \frac{|D_{i}|}{|D|}\sum\limits_{k=1}^{K}\frac{|D_{ik}|}{|D_{i}|}\log_{2}\frac{ |D_{ik}|}{|D_{i}|}, \tag{2}\]  
Step 3: Calculate the information gain  
\[g(D,A)=H(D)-H(D|A), \tag{3}\]  
Step 4: Calculate the information gain rate  
\[g_{R}(D,A)=\frac{g(D,A)}{H_{A}(D)}, \tag{4}\]  
where  
\[H_{A}(D)=-\sum\limits_{i=1}^{n}\frac{|D_{i}|}{|D|}\log_{2}\frac{|D_{i}|}{|D|}, \tag{5}\]  
and \(n\) is the number of characteristic \(A\) values. **5. C4.5 Algorithm Improvement**  
The structure of the hoist brake system is complex and the cause of the failure is often not single, so the various failure factors should be taken into consideration.