## 2 Data Collection and Processing
### Data Processing  
#### 2.2.1 Outlier Handling  
Analysis of the data collected at the blast furnace site reveals that there may be many unreasonable outliers in the collected data due to the influence of uncontrollable factors such as the equipment and environment, which must be combined with appropriate data cleaning and rejection methods. Therefore, to handle outliers in the blast furnace data, the following approach was employed:  
1. [label=(0)]
2. Outlier detection. There are many ways to detect data outliers. Common methods include 3\(\sigma\) criterion (Lajda criterion) distribution and box plots. The 3\(\sigma\) criterion distribution [12] is a method based on the calculation of the standard deviation, which results in limited processing of the data collected at the blast furnace site, because the data must satisfy a normal distribution. A box plot [13] is essentially a statistical graph used to show the dispersion of data, but it may not provide an accurate assessment of the skewness and tail weight of the data distribution. In addition, for datasets that contain relatively large batches of data, box plots reflect more ambiguous information. Therefore, in this study, an isolated forest algorithm was utilized for detecting anomalies in the blast furnace site data. Isolated forest [14] is a nonparametric machine-learning method that does not require a specific mathematical model to model or label anomalous data, allowing for unsupervised anomaly detection. Its schematic structure is shown in Figure 1.  
The isolated forest algorithm is used to randomly divide the data interval of the blast furnace site to construct a binary tree. Each leaf node represents a data node. The path length from the leaf node to the root node reflects the degree of dispersion of the data node. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial** & **key Parameters** & **Serial** & **Key Parameters** & **Serial** & **Key Parameters** \\
**Number** & **key Parameters** & **Number** & **Key Parameters** & **Number** & **Key Parameters** \\ \hline
1 & \begin{tabular}{c} Breathability index \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \\ 9 \\ \end{tabular}  & \begin{tabular}{c} 10 \\ 2 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 17 \\ 18 \\ 19 \\ \end{tabular}  & \begin{tabular}{c} Gas CO2 volume fraction \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 17 \\ 18 \\ 19 \\ \end{tabular}  & \begin{tabular}{c} 19 \\ 20 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 17 \\ 18 \\ 19 \\ \end{tabular}  & \begin{tabular}{c} 19 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ \end{tabular}  & \begin{tabular}{c} 19 \\ 20 \\ 20 \\ 21 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ \end{tabular}  & \begin{tabular}{c} 19 \\ 20 \\ 20 \\ 21 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ \end{tabular}  & \begin{tabular}{c} 19 \\ 20 \\ 20 \\ 21 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ \end{tabular}  & \ \begin{tabular}{c} 19 \\ 20 \\ 20 \\ 21 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 28 \\ 29 \\ 20 \\ 25 \\ 25 \\ 25 \\ 25 \\ 25 \\ 25 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ \end{tabular}  &
\begin{tabular}{c} 19 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 28 \\ 29 \\ 29 \\ 28 \\ 29 \\ 29 \\ 20 \\ 20 \\ 21 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 28 \\ 29 \\ 29 \\ 29 \\ 29 \\ 29 \\ 20 \\ 20 \\ 21 \\ 22 \\ 2 The isolated forest is constructed, and the key is calculated. For the fraction of outliers in the parameters, the specific calculation method is shown in Equations (1)-(3):  
\[s(x,n)=2^{-\frac{E(h(x))}{c(n)}} \tag{1}\]  
\[c(n)= \begin{cases}2H(n-1)-\frac{2(n-1)}{n},&n>2\\ 1,&n=2\\ 0,&n<2\end{cases}  \tag{2}\]  
\[H(i)=ln(i)+0.5772156649 \tag{3}\]  
where: \(E(h(x))\) denotes the mean value of the path length of the data in the forest; \(s(x,n)\) is the anomaly score of node \(x\); \(c(n)\) is defined as the mean path length of the search failure in the binomial search tree; \(H(i)\) is the number of matching levels, and 0.5772156649 is the Euler constant.