## 2 Theoretical Background of Applied Method
### Observations and Targets in BOS
The values of variable \(ys_{i}\) can be extracted from the static database  
Tensor (2) is created for each target variable individually. In this paper, only two points of each melting are regarded (i.e., initial and endpoint, so \(r=2\)). Four input observations and two targets are regarded in this study as basic, and it is possible to consider adding other relevant observations to investigate the performance of the models. Two large melting datasets were created to fit machine models of BOS, i.e., the datasets for the temperature model and the dataset for the carbon model. These sets were made in data mining by pairing static and dynamic data. The corresponding start and endpoint data (i.e., CO, CO\({}_{2}\), waste gas temperature) from the dynamic data database were assigned for each start and end measured melt temperature from the static dataset. Information on the accumulated amount of inflated oxygen was taken from the static data database. This \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Observations** & **Ranges** & **Units** & **Targets** & **Ranges** & **Units** \\ \hline \(x_{1}\)–Concentation of CO in waste gas & 0–85 & (\%) & Melt temperature & 1580–1720 & (\({}^{\circ}\)C) \\ \(x_{2}\)–Concentation of CO\({}_{2}\) in waste gas & 0–35 & (\%) & Carbon concentration in melt & 0.02–0.08 & (\%) \\ \(x_{3}\)–Temperature of waste gas & 80–1000 & (\({}^{\circ}\)C) & & & \\ \(x_{4}\)–Accumbulated amount of blown oxygen & 0–8500 & (Nm\({}^{3}\)) & & & \\
**Optional**: & & & & \\ Concentration of O\({}_{2}\) in waste gas & 0–23 & (\%) & & & \\ Concentration of H\({}_{2}\) in waste gas & 0–12 & (\%) & & & \\ Volume flow of waste gas & 80,000–100,000 & (m\({}^{3}\)/h) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dynamic observations and targets with measurement ranges. pairing was done for each melting. Similarly, the corresponding data from the dynamic dataset were assigned for each initial and final actually measured melt carbon concentration from the static dataset. Then the prediction from the learned model can be realized in an inverse way, where from the test or online dynamic data (i.e., CO, CO\({}_{2}\), waste gas temperature, and blown oxygen flow rate), the melt temperature or carbon concentration can be calculated by the model. Meltings with missing dynamic data or no-valid melting has been removed in big datasets. In this way, the datasets of filtered meltings have been obtained. The obtained datasets of merged data can be subsequently divided into training and testing sets (i.e., in offline testing). Based on this principle, a data-driven soft-sensor can be built to continually adapt the selected machine model with new melts, thus improving the prediction (see Figure 2). Finally, the principle of creating big datasets by merging static and dynamic data is illustrated in Figure 3. The flowchart demonstrates the sequence of steps applied for machine learning and making predictions in offline or online mode. Figure 3: Merging static and dynamic data. Figure 2: Idea scheme of modeling and prediction in steelmaking based on machine learning. Soft sensors based on dynamic steelmaking data enable real-time estimating process variables without a hardware device (e.g., thermocouple or pyrometer). As a result, they can provide less expensive and quicker process data than slow and costly hardware devices.