Online Self-Learning-Based Raw Material Proportioning for Rotary Hearth Furnace and Intelligent Batching System Development

Abstract

With the increasing awareness of environmental protection, the rotary hearth furnace system has emerged as a key technology that facilitates a win-win situation for both environmental protection and enterprise economic benefits. This is attributed to its high flexibility in raw material utilization, capability of directly supplying blast furnaces, low energy consumption, and high zinc removal rate. However, the complexity of the raw material proportioning process coupled with the rotary hearth furnace system’s reliance on human labor results in a time-consuming and inefficient process. This paper innovatively introduces an intelligent formula method for proportioning raw materials based on online clustering algorithms and develops an intelligent batching system for rotary hearth furnaces. Firstly, the ingredients of raw materials undergo data preprocessing, which involves using the local outlier factor (LOF) method to detect any abnormal values, using Kalman filtering to smooth the data, and performing one-hot encoding to represent the different kinds of raw materials. Afterwards, the affinity propagation (AP) clustering method is used to evaluate past data on the ingredients of raw materials and their ratios. This analysis aims to extract information based on human experience with ratios and create a library of machine learning formulas. The incremental AP clustering algorithm is utilized to learn new ratio data and continuously update the machine learning formula library. To ensure that the formula meets the actual production performance requirements of the rotary hearth furnace, the machine learning formula is fine-tuned based on expert experience. The integration of machine learning and expert experience demonstrates good flexibility and satisfactory performance in the practical application of intelligent formulas for rotary hearth furnaces. An intelligent batching system is developed and executed at a steel plant in China. It shows an excellent user interface and significantly enhances batching efficiency and product quality.

1. Introduction

The metallurgical dust and sludge generated during the steel smelting process account for approximately 5–10% of crude steel production [1]. The iron content in this dust and mud is generally between 30% and 60%, and these substancescontain valuable metals such as calcium, magnesium, and zinc, which have high recovery value [2]. Rotary hearth furnace technology has the advantages of high output, low energy consumption, stable product quality, and no specific requirements for raw materials. It also shows excellent performance in zinc removal efficiency and environmental protection and has been widely recognized in the metallurgical industry [3].

In the rotary hearth furnace system, batching is a crucial preliminary process and the foundation for ensuring product quality. Due to the direct relationship between raw material ratios and the efficiency of resource conversion, which affects the type, concentration, and quantity of emissions and has a critical impact on subsequent production processes, engineers have spent a lot of time on the batching process. Therefore, achieving automatic batching and releasing labor is the key to improving the efficiency of the rotary hearth furnace system.

Raw material batching is the mixing of various dust materials such as electric furnace ash and blast furnace ash in a certain proportion, preparing for a series of subsequent processes such as ball forming and reduction reactions [4]. In many steel plants, the formula plans are manually calculated by engineers based on their long-term experience and professional knowledge accumulated in frontline work [5,6,7].

The program for preparing production plans is as follows: (1) Experts in the relevant field use Excel files to complete calculations. (2) A group of two or three experts in the relevant field discuss and revise the plan. (3) The expert group produces the final production plan. However, the results have some errors, so the experts must solve these errors by using a trial-and-error method, and they go through a long process to obtain a feasible solution. In this process, experts need to consider not only the capacity limit of the warehouse and the type of materials but also uncertainty factors such as the differences in element contents in the same material. The trial-and-error method cannot comprehensively consider all relevant factors and takes a long time [8,9,10].

As the rotary hearth furnace is a new technology, its raw material proportioning method has not yet found a similar mature and referential case. Experience and methods can be learned from relevant raw material proportioning fields, such as the copper strip loading process, zircon brick raw material proportioning, raw coal proportioning, the production ratio of blast furnaces, ore proportioning, and other fields, to try to solve the problem of satisfying the proportioning of rotary hearth furnace raw materials. For example, Zhang et al. [11] proposed a hybrid multiobjective artificial bee colony algorithm for the batching process of copper strip production. By normalizing the sum of target values and selecting the corresponding dominant sorting method based on diversity, the smelting process element proportioning scheme for copper strip was achieved. However, its adaptability was insufficient, convergence speed was slow, and algorithm complexity was high. To achieve greater precision and efficiency in determining the satisfactory raw material ratio for zircon bricks, Liang et al. [12] employed a support vector machine (SVM) to develop a model correlating zircon brick density with the raw material ratio. Subsequently, they utilized an adaptive particle swarm algorithm to refine the model and derive the best possible raw material ratio.

As for raw coal blending, Lei et al. [13] introduced a method based on interval programming. By utilizing interval numbers to depict the variability ranges of ash and sulfur contents across different density levels of raw coal, they developed a prediction model for the quantity and quality of dense medium cyclone separator products and established a mixed-integer nonlinear programming model.

For blast furnaces, the prevailing approach involves modeling blast furnace ironmaking based on the principles of ironmaking and material balance. Cui and Chen [14] enhanced the genetic algorithm and penalty function via leveraging the principles of blast furnace ironmaking and material balance and developed an intelligent system for the burden structure across the entire sintering and blast furnace ironmaking process. Huang  et al. [15] proposed a two-stage decision-making method for burden distribution parameters based on recognizing the conditions. Zhai et al. [16] employed the GA-SVR method to identify the five most informative features for fuel ratio adjustment during blast furnace ironmaking, enabling operators to proactively adjust input parameters. Feng et al. [17] introduced an automatic sintering ore-blending model to quickly configure the sintering of raw materials according to the requirements of the production line. Li et al. [18] developed A GA-RNN quality prediction model with raw material composition as input parameters and physical and metallurgical properties of sinter as output.

Wu et al. [19] proposed an intelligent integrated batching system for the field of ore batching. By understanding the chemical and physical properties of batching, the requirements for batching were determined. Firstly, a proportioning scheme was established, and then a cascaded integrated quality prediction model was designed. The model used the prediction indicators as feedback for the proportioning scheme, thereby determining the satisfactory proportioning scheme. However, the results of these studies still require human involvement and cannot be updated online, or they have not been truly implemented.

As a new industry, the raw material composition for rotary hearth furnaces is complex and frequently changes, so the batching process is more complex. As far as we know, a rotary hearth furnace intelligent batching system is rarely used in the world. In this study, an intelligent batching system with self-learning ability for rotary hearth furnaces is proposed, which consists of four parts: data preprocessing, AP offline formula learning, AP online formula updating, and expert experience-based formula fine adjustment:

• In the first part, outliers of the ingredient composition in historical ratio data are found via the local factor algorithm [20], and measurement noise is filtered by Kalman filtering [21]; the one-hot method [22] encodes the types of raw materials to form data sets with the contents of raw material ingredients and ratio of raw materials.
• In the second part, AP clustering analysis is used to obtain many clustering groups from the above data sets and generate a machine learning formula library. Each cluster group represents a type of raw material’s composition characteristics, which corresponds to a type of ratio. Through unsupervised machine learning of historical data, valuable human formula experience is mined.
• In the third part, the incremental AP clustering algorithm is used to update clustering groups during the continuous operation of the system and consequently to update the machine learning formula library. On the basis of the existing cluster grouping, if the new formula data are similar to a cluster, they belong to this cluster grouping; if the new formula data are not similar to all existing clustering groups, a new clustering group will be created. This method effectively inherits the previous clustering results and realizes dynamic updating of formula data.
• In the fourth part, learning from experts’ experience, the formula generated by machine learning is finely adjusted to make the mixture of raw materials meet the requirements in C, $Zn$, $Cl$, and $C/O$ performance. The reason is that the machine learning formula learns the human experience formula, while the human experience formula does not fully consider the requirements of rotary hearth furnaces for C, $Zn$, $Cl$, and $C/O$ performance.

The developed intelligent batching system has good interactivity and a user-friendly interface. Users can easily modify configuration parameters to meet different needs and conditions.

The remaining part of this paper is organized as follows. In Section 2, the different types of raw materials and their elements in the rotary hearth furnace batching system are mainly introduced. Section 3 provides a detailed introduction to the intelligent batching approach based on online clustering. Section 4 mainly introduces an application example of a rotary hearth furnace system. The conclusion is given in Section 5.

2. Types of Raw Materials and Their Element Analyses

When designing the batching system of a rotary hearth furnace, it is necessary to comprehensively consider the load capacity of the production equipment, and at the same time, it is necessary to conduct a comprehensive analysis based on the actual situation on-site and the limiting conditions of element content in the batching. Taking a steel plant in China as an example, the data analysis of its batching process mainly involves two core aspects: the types of raw materials involved and the types of elements contained in these raw materials.

It includes six different types of raw materials, as shown in

Table 1. Raw material types.

Number	$x_1$	$x_2$	$x_3$
Raw material	Environmental ash	CDQ	Ash from an iron casting plant
Number	$x_4$	$x_5$	$x_6$
Raw material	Cold-rolled mud	Secondary ash from a blast furnace	Mixed ash

. $x_1$ is environmental ash, mainly derived from raw materials dispersed during system operation. $x_2$ is coke dry quenching dust (CDQ). Its main component is “C” element, and its element content is as high as 84.4%. $x_3$ is the ash from an iron casting plant, with C content of about 5% and $Zn$ content of about 0.1%. $x_4$ is cold-rolled mud, with C content of about 3%, $Cl$ content of about 0.3%, and $Zn$ content of about 14%. $x_5$ is the secondary ash from the blast furnace, with C content of about 16%, $Zn$ content of about 2.4%, and $Cl$ content of about 5%. $x_6$ is mixed ash, which is composed of electric furnace ash, LT ash, OG sludge, etc. Electric furnace ash is produced from the dust removal ash from electric furnace smelting in a steel plant, while OG sludge and LT ash are both produced from the converter steelmaking process in a steel plant. OG sludge is the sludge produced by a converter gas wet recovery system, and LT ash is the dry dust removal ash of the converter. The C content in electric furnace ash is generally around 1.7%, $Zn$ content is around 7.9%, and $Cl$ content is around 0.6%. C content in LT ash is generally around 2%, and $Zn$ content is generally around 4%; C content in OG mud is generally around 2%, and $Zn$ content is generally around 3%. In addition, during the operation of the rotary hearth furnace, due to the mixing, ball pressing, screening, high-temperature treatment, and other processes of raw materials, a certain quantity of returned materials may be generated due to ball fracture, equipment performance, and other reasons. The returned material $FMQ$ is a mixture of various raw materials. The content of each element in the returned material and $x_1$ are approximately considered as the average of various raw material components.

Considering the production process requirements, special attention needs to be paid to the elemental contents of C, $Zn$, and $Cl$ in the mixture as well as to the $C/O$ ratio. The contents and proportions of these elements in the formula may have a significant impact on the performance and quality of the final product. Therefore, when constructing a formula model, it is necessary to ensure accurate monitoring and control of the content of these elements to meet process requirements and achieve satisfactory production results.

3. Online Clustering-Based Intelligent Batching Method

In this section, we propose a raw material proportioning method for rotary hearth furnaces based on online clustering algorithms. The structure of the proposed online clustering proportioning method is shown in Figure 1. First, we use the LOF algorithm and Kalman filtering algorithm to process the historical data of raw material components. Next, the principle of the AP clustering algorithm is described in detail, and it is used for offline learning of preprocessed data to generate a machine learning formula library. Then, the online AP clustering algorithm is used to effectively cluster the current data and historical data to update the machine learning formula library. According to the current raw material composition, a preliminary formula is recommended based on the updated machine learning formula library. Finally, using the expert experience-based formula fine-tuning module, the preliminary formula is adjusted to ensure that the final formula meets the performance requirements of the rotary hearth furnace.

3.1. Data Preprocessing

During the continuous operation of the rotary hearth furnace system, some new data are generated. These data mainly include the ratio and its corresponding content of raw materials. The elemental composition of these raw materials mainly includes carbon (C), zinc ($Zn$), and iron ($Fe$). Iron oxide ($FeO$) is the material component of most concern. The differences in the sources of raw materials may lead to differences in the composition content, for example, iron ore from different regions or suppliers may contain different impurities or element contents. In addition, seasonal fluctuations, such as weather changes, may also affect the composition of raw materials, as they may affect the humidity and temperature during mining or transportation, thereby affecting the properties of raw materials. Furthermore, laboratory errors may also cause data fluctuations, as different laboratories or testing methods may yield different measurement results. In view of these factors, it is particularly important to process the raw material composition data.

Firstly, the element content data of the raw material components are preprocessed. Anomaly detection methods based on statistics usually need to assume that the data follow a specific probability distribution. Clustering-based anomaly detection methods, such as DBSCAN, only provide binary judgment of whether or not an anomaly exists, cannot quantify the extent of the anomaly, and use the same parameters to process all data. In contrast, the LOF (local outlier factor) algorithm is more intuitive and flexible, as it does not require strong assumptions about data distribution and quantifies the degree of anomaly of each data point [23]. In industrial applications, sliding filtering and Kalman filtering are two commonly used filtering methods. Sliding filtering is suitable for simple interference scenarios, but its effect on pulse interference is poor. Kalman filtering performs better in dealing with signals containing noise or bias. By combining estimated or measured values, it provides more accurate observations and has stronger adaptability [24]. Therefore, the local outlier factor (LOF) algorithm and Kalman filtering are chosen for data preprocessing.

Specifically, the LOF algorithm is used to identify outliers, and a linear interpolation method is used to complete the missing values. Kalman filtering technology is employed to filter out measurement noise. Additionally, it is necessary to remove inferior formulas from historical data.

In order to facilitate readers’ understanding of the effectiveness of LOF outlier detection, we take three elements (C, $Fe$, $Zn$) in the secondary ash from a blast furnace as an example to visualize the detection results, as shown in Figure 2, where the circular data represent normal data and the pentagonal represent the anomaly values detected by the algorithm.

In order to demonstrate the effectiveness of the filtering algorithm in data preprocessing, we take the C element in blast furnace secondary ash as an example, as shown in Figure 3. From Figure 3, it can be seen that the filtering algorithm can greatly alleviate the steepness of the data, making them smoother.

In industrial environments, if the raw material proportioning scheme can be used for more than h (h > 0) hours, it is considered an excellent scheme, and vice versa. In addition, the sum of the percentage of raw materials (excluding environmental ash) must meet the condition in Equation (2), otherwise it is also considered an inferior formula and should be removed. 

$$\begin{array}{cc}\hfill FMQ+IMQ+OMQ& =TMQ\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill \sum _{i=2}^6{w}_i& =100\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill w_{FMQ}+w_{IMQ}+w_{OMQ}& =100\hfill \end{array}$$

(3)

where $FMQ$ represents the return material quantity; $IMQ$ represents the total quantity of raw materials exclusive of environmental ash; $OMQ$ stands for the environmental ash raw material quantity; $TMQ$ indicates the total set material quantity; $w_i$ represents the material percentage of $x_i$ in $IMQ$; $w_{FMQ}$ denotes the material percentage of $FMQ$ in $TMQ$; $w_{IMQ}$ indicates the material percentage of $IMQ$ in $TMQ$; and $w_{OMQ}$ represents the material percentage of $OMQ$ in $TMQ$.

After data preprocessing, a data set set about $[x_1,x_2,x_3,x_4,x_5,x_6,C,Cl,Zn,Fe,FeO]$ is constructed that includes information on ratio and ingredient content, where $x_1$, $x_2$, $x_3$, $x_4$, $x_5$, $x_6$ are the corresponding proportions of the mixture $x_i$; C is a row vector, specifically represented as C = [$c_1$, $c_2$, $c_3$, $c_4$, $c_5$, $c_6$], where $c_i$ is the element content of C in the material; $Cl$ is a row vector, specifically represented as $Cl$ = [$c{l}_1$, $c{l}_2$, $c{l}_3$, $c{l}_4$, $c{l}_5$, $c{l}_6$], where $c{l}_i$ is the content of $Cl$ element in material $x_i$; and $Zn$ is a row vector, specifically represented as $Zn$ = [$z{n}_1$, $z{n}_2$, $z{n}_3$, $z{n}_4$, $z{n}_5$, $z{n}_6$], where $z{n}_i$ is the element content of $Zn$ in material $x_i$; $i=1,2,3,4,5,6$.

3.2. AP Offline Formula Learning

Historical data hide the valuable operational wisdom of engineers. By using the AP clustering algorithm, we can extract empirical knowledge of human formulas from these historical data. At present, the main clustering methods include K-means, DBSCAN, hierarchical clustering, etc. However, the dynamic characteristics of real-time data put forward higher requirements for the traditional clustering algorithm. The algorithm needs to quickly process and summarize a large number of continuously arriving data while at the same time adapting to the changes of data distribution, detecting new clusters, and merging old clusters. In order to meet the needs of rapid processing, many dynamic data clustering methods are incremental algorithms, such as incremental K-means, incremental DBSCAN, and incremental AP clustering algorithms. Incremental K-means needs to preset the number of clusters K. If the appropriate number cannot be determined, it may need to try many times. The incremental DBSCAN algorithm is computationally complex and needs to deal with a large number of center points and boundary points each time [25,26,27]. In contrast, incremental the AP clustering algorithm does not need to preset a K value and has fewer parameter settings. Therefore, the AP clustering algorithm is used for the machine learning of formulas.

The basic idea of the AP clustering algorithm is to treat the element content corresponding to N historical ratio data as nodes in the network and then calculate the clustering centers of each sample through the messages passing from each edge in the network. During the clustering process, there are two types of messages passing between nodes, namely, attractiveness $r(i,k)$ and belonging $a(i,k)$. $R={\left[r(i,k)\right]}_{N\times N}$ is the attractiveness matrix, and $A={\left[a(i,k)\right]}_{N\times N}$ is the belonging matrix. The AP clustering algorithm continuously updates the attractiveness and membership values of each point through an iterative process until n high-quality cluster centers (Exemplar) are generated, where $n\in N$. At the same time, the remaining ratios are assigned to the corresponding clusters, and R and A can be obtained.

The iterative equations for attractiveness and belonging are as follows:

$$r_{t+1}(i,k)=\left\{\begin{array}{c}s(i,k)-\underset{j\ne k}{max}\left\{a_t(i,j)+r_t(i,j)\right\},i\ne k\hfill \\ s(i,k)-\underset{j\ne k}{max}\left\{S(i,j)\right\},i=k\hfill \end{array}\right.$$

(4)

$$a_{t+1}(i,k)=\left\{\begin{array}{c}min\left\{0,r_{t+1}(k,k)+\sum _{j\ne i,k}max\left\{r_{t+1}(j,k),0\right\}\right\}i\ne k\hfill \\ \sum _{j\ne k}max\left\{r_{t+1}(j,k),0\right\},j=k\hfill \end{array}\right.$$

(5)

where $r(i,j)$ is the degree of attraction, which is used to describe the suitability of the element content of ratio j as the clustering center of the element content of ratio i; $a(i,j)$ is is the attribution degree, which is used to describe the appropriate degree of selecting the element content of ratio j as its clustering center of the element content of ratio i; and $s(i,k)$ is the similarity, which represents the ability of the element content of ratio k to serve as the clustering center for the element content of ratio i.

Generally, negative Euclidean distance is used, so the larger the $s(i,k)$, the closer the two points are. In order to avoid oscillations during the iteration process, a soft update strategy is adopted, and the update equations are as follows:

$$\left\{\begin{array}{c}{r}_{t+1}(i,k)=\lambda \ast r_t(i,k)+(1-\lambda )\ast r_{t+1}(i,k)\hfill \\ a_{t+1}(i,k)=\lambda \ast a_t(i,k)+(1-\lambda )\ast a_{t+1}(i,k)\hfill \end{array}\right.$$

(6)

where $\lambda$ is the parameter damping factor, $\lambda \in (0,1)$. The damping factor is introduced to prevent data oscillations during the information propagation process. A higher $\lambda$ limits the magnitude of updates during iterations, thus enhancing algorithm stability but slowing convergence. Conversely, a lower $\lambda$ accelerates convergence but may lead to more oscillations. Based on expert experience, common settings for $\lambda$ are 0.5 or 0.9. In this study, a damping factor of 0.5 is used.

After the AP offline formula learning is completed, the formula data can be divided into n clusters based on the mapping of ingredient content to the ratio data. The centers of the clusters are denoted as $(K1,K2,K3,\dots ,Kn)$, where $n\in [1,N]$. The system will record the key information of these clusters, including cluster centers, similarity matrices, and attraction matrices. These pieces of information form the foundation of the machine learning formula library, providing a basis for adjusting future formulas.

3.3. AP Online Formula Updating

In practical rotary hearth furnace systems, data are constantly updated. To tackle these issues related to data updates, there are primarily two operations: reclustering and incremental clustering. During the continuous operation of the rotary hearth furnace system, the data are increasing. If the amount of data is big, the cost of reclustering is great, which will lead to time-consuming and inefficient calculation. On the contrary, incremental clustering can solve the above problems.

In this study, incremental AP clustering [28] is realized by using affinity propagation clustering combined with nearest neighbor technology. The nearest neighbor is used to establish a connection between the newly added formula data and the existing clustered data sets.

Nearest neighbor techniques mean that the informational content of newly added formula data is configured based on its closest formulas. The strategy is based on the following consideration: if two formulas have similar compositions, their ratios are similar, implying that the data formulas should belong to the same class with identical information. If the newly added formula data do not resemble any of the known clustered groups, a new clustering group will be created.

Given an $N_{t-1}\times N_{t-1}$-dimensional data set, where the similarity matrix is $S_{t-1}$ and the corresponding matrices for membership and attractiveness are $R_{t-1}$ and $A_{t-1}$, respectively, the membership and attractiveness values for the newly added formula are expanded according to Equation (7).

$$r_t(i,j)=\left\{\begin{array}{c}{r}_{t-1}(i,j),i\le N_{t-1},j\le N_{t-1}\hfill \\ r_{t-1}(i^{\prime },j),i>N_{t-1},j\le N_{t-1}\hfill \\ r_{t-1}(i,j^{\prime }),i\le N_{t-1},j>N_{t-1}\hfill \\ 0,i>N_{t-1},j>N_{t-1}\hfill \end{array}\right.$$

(7)

The above $N_{t-1}$ represents the initial number of formulas, where $i^{\prime }$ = $arg{max}_{i,i^{\prime }\le M_n}\left\{s\left(i,i^{\prime }\right)\right\}$, and similar memberships are expanded according to Equation (8).

$$a_t(i,j)=\left\{\begin{array}{cc}{a}_{t-1}(i,j),& i\le N_{t-1},j\le N_{t-1}\\ a_{t-1}(i^{\prime },j),& i>N_{t-1},j\le N_{t-1}\\ a_{t-1}(i,j^{\prime }),& i\le N_{t-1},j>N_{t-1}\\ 0,& i>N_{t-1},j>N_{t-1}\end{array}\right.$$

(8)

Using the AP online formula learning, the element contents in the current formula data and the historical formula data will be clustered to form $n_1$ clusters. The centers of the clusters are then rerecorded as $(c{1}^{\prime },c{2}^{\prime },c{3}^{\prime },\dots ,c{n}_1^{\prime })$, where $n_1\in [1,N+1]$. The system will store information about these clusters, including the cluster center, similarity matrix, and attraction matrix, to construct a machine learning formula library. In the machine learning formula library, the recommended formula will be the one corresponding to the cluster center of the current formula data cluster.

For the convenience of readers’ understanding, the process of online AP clustering is shown in Figure 4 and Figure 5.

Figure 4 illustrates the distribution of formulation data points. The hollow circles and solid circles represent distinct formulation data points, while the connecting lines indicate that the hollow circle data points cluster around the solid circles. After time t, the right diagram shows that the newly added red formulation data point has emerged as the new clustering center. In online AP clustering, the newly added data are the recommended formula.

In Figure 5, the hollow circles and solid circles represent the data points of the formula, and the connecting lines illustrate how the hollow circles form clusters around the solid circles. After time t, the right figure shows that the new red formula data point has not become a new cluster center. The center of the cluster where the newly added formulation data are situated is the recommended formula.

3.4. Expert Experience-Based Formula Fine Adjustment

Through cluster analysis, a machine learning formula library can be constructed. The recommended formula is based on the formula represented by the cluster center of the current formula cluster. This formula usually adapts well to the operating habits and actual production conditions of workers. However, it may not fully meet the performance requirements of the rotary hearth furnace. To ensure that the formula meets all performance requirements, it is necessary to introduce a formula fine adjustment module based on expert experience. This module meticulously adjusts the recommended formula to meet performance requirements. Firstly, as shown in

Table 2. Symbol table.

Symbol	Meaning
$TMQ$	Total set material quantity (t/h)
$OMQ$	Total amount of environmental ash raw materials (t/h)
$IMQ$	Total raw material amount excluding environmental dust (t/h)
$FMQ$	Return material (t/h)
$w_{OMQ}$	Percentage of $OMQ$ in $TMQ$ composition (%)
$w_{x_1}$	Percentage of $x_1$ in $TMQ$ composition (%)
$C_{x_1}$	Mass percentage of carbon in $x_1$ (%)
$C{l}_{x_1}$	Mass percentage of chlorine in $x_1$ (%)
$Z{n}_{x_1}$	Mass percentage of zinc in $x_1$ (%)
$F{e}_{x_1}$	Mass percentage of iron in $x_1$ (%)
$Fe{O}_{x_1}$	Mass percentage of ferrous oxide in $x_1$ (%)
$O_{Fe{O}_{x_1}}$	$O_{Fe{O}_{x_1}}$ is the mass percentage of oxygen in $Fe{O}_{x_1}$ (%)
$F{e}_2{O}_{3_{x_1}}$	The mass percentage of ferric oxide in $x_1$ (%)
$O_{F{e}_2{O}_{3_{x_1}}}$	The mass percentage of oxygen in ferric oxide (%)
$O_{Z{n}_{x_1}}$	The mass percentage of oxygen in zinc oxide within $x_1$ (%)
$O_{x_1}$	The mass percentage of oxygen in zinc oxide within $x_1$ (%)
$w_{FMQ}$	The percentage composition of $FMQ$ in $TMQ$ (%)
$C_{FMQ}$	The mass percentage of carbon in $FMQ$ (%)
$C{l}_{FMQ}$	The mass percentage of chlorine in $FMQ$ (%)
$Z{n}_{FMQ}$	The mass percentage of zinc in $FMQ$ (%)
$O_{FMQ}$	The mass percentage of oxygen in $FMQ$ (%)
$F{e}_{FMQ}$	The mass percentage of ferrous oxide in $FMQ$ (%)
$Fe{O}_{FMQ}$	The mass percentage of ferrous oxide in $FMQ$ (%)
$O_{Fe{O}_{FMQ}}$	The mass percentage of oxygen in $Fe{O}_{FMQ}$ (%)
$F{e}_2{O}_{3_{FMQ}}$	The mass percentage of $ferricoxide$ in $FMQ$ (%)
$O_{F{e}_2{O}_{3_{FMQ}}}$	The mass percentage of oxygen in $ferricoxide$ (%)
$O_{Z{n}_{FMQ}}$	The mass percentage of oxygen in zinc oxide within $FMQ$ (%)
$w_{IMQ}$	Percentage composition of $IMQ$ in $TMQ$ (%)
$w_i$	Percentage of material $x_i$ in $IMQ$ (%)
$C_{IMQ}$	Mass percentage of carbon in $IMQ$ (%)
$w_{C_i}$	Mass percentage of carbon in $x_i$ (%)
$C{l}_{IMQ}$	Mass percentage of chlorine in $IMQ$ (%)
$w_{C{l}_i}$	Mass percentage of chlorine in $x_i$ (%)
$Z{n}_{IMQ}$	Mass percentage of zinc in $IMQ$ (%)
$w_{Z{n}_i}$	Mass percentage of zinc in $x_i$ (%)
$F{e}_{IMQ}$	Mass percentage of iron in $IMQ$ (%)
$w_{F{e}_i}$	Mass percentage of iron in $IMQ$ (%)
$O_{Fe{O}_{IMQ}}$	Mass percentage of oxygen in $Fe$ within $IMQ$ (%)
$w_{Fe{O}_{IMQ}}$	Mass percentage of ferrous oxide in $IMQ$ (%)
$O_{F{e}_2{O}_{3_{IMQ}}}$	Percentage mass of oxygen in $F{e}_2{O}_{3_{IMQ}}$ within $IMQ$ (%)
$w_{F{e}_2{O}_{3_{IMQ}}}$	Mass percentage of $F{e}_2{O}_{3_{IMQ}}$ in $IMQ$ (%)
$O_{Z{n}_{IMQ}}$	The mass percentage of the oxygen in zinc oxide (%)
$O_{IMQ}$	Total mass percentage of oxygen in $IMQ$ (%)
$C_{sum}$	Total dry basis mass percentage of carbon (%)
$C{l}_{sum}$	Total dry basis mass percentage of chlorine (%)
$Z{n}_{sum}$	Total dry basis mass percentage of zinc (%)
$C/O_{sum}$	Mass percentage ratio of total carbon to oxygen (%)
$\overline{C}$,$\underline{C}$	The upper and lower bounds of carbon content (%)
$\overline{Cl}$,$\underline{Cl}$	The upper and lower bounds of chlorine content (%)
$\overline{Zn}$,$\underline{Zn}$	The upper and lower bounds of zinc content (%)
$\overline{C/O}$	The upper bound of the carbon to oxygen ratio (%)

, we provide the following parameters.

Due to the lack of separate assay values for $OMQ$ and returned materials, we use the average value of the total raw material quantity “$IMQ$” (excluding environmental ash) of its composition for calculation.

The dry basis composition of each element in $IMQ$ is calculated according to the following Equations (9) and (10):

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{C}_{IMQ}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(C_i\right)\ast w_i}{100}}\hfill \\ C{l}_{IMQ}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(C{l}_i\right)\ast w_i}{100}}\hfill \\ Z{n}_{IMQ}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(Z{n}_i\right)\ast w_i}{100}}\hfill \\ F{e}_{IMQ}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(F{e}_i\right)\ast w_i}{100}}\hfill \end{array}\right.\end{array}$$

(9)

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{O}_{Fe{O}_{IMQ}}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left({\left(FeO\right)}_i\right)\ast w_i\ast \frac{16}{72}}{100}}\hfill \\ O_{F{e}_2{O}_{3_{IMQ}}}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(F{e}_i\right)-w\left({\left(FeO\right)}_i\right)\ast \frac{56}{72})\ast w_i\ast \frac{48}{112}}{100}}\hfill \\ O_{Z{n}_{IMQ}}={\displaystyle \frac{{\sum }_{i=2}^{6}w\left(Z{n}_i\right)\ast w_i\ast \frac{16}{65}}{100}}\hfill \\ O_{IMQ}=O_{{\left(FeO\right)}_{IMQ}}+O_{F{e}_2{O}_{3_{IMQ}}}+O_{Z{n}_{IMQ}}\hfill \end{array}\right.\end{array}$$

(10)

where $E_{1_{IMQ}}$ represents the mass percentage of $E_1$ in $IMQ$, $E_4$ in $FMQ$, and $E_1$ = (C, $Cl$, $Zn$, $Fe$, $FeO$, $F{e}_2{O}_3$, O), and $w_i$ represents the mass percentage of material $x_i$. $w\left(E_{2_i}\right)$ represents the mass percentage of $E_2$ in material $x_i$, where $E_2=(C,Cl,Zn,Fe,FeO)$. $O_{Fe{O}_{IMQ}}$ represents the mass percentage of oxygen in $Fe{O}_{IMQ}$, $F{e}_2{O}_{3_{IMQ}}$ denotes $F{e}_2{O}_3$ in $IMQ$ and $O_{F{e}_2{O}_{3_{IMQ}}}$ represents the mass percentage of oxygen in $F{e}_2{O}_{3_{IMQ}}$.

The dry basis composition of each element in $OMQ$ is calculated according to the following Equation (11):

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{E}_{3_{OMQ}}={\displaystyle \frac{100\ast E{1}_{IMQ}}{{\sum }_{i=2}^6{w}_i}}\hfill \\ O_{OMQ}=O_{{\left(FeO\right)}_{OMQ}}+O_{F{e}_2{O}_{3_{OMQ}}}+O_{Z{n}_{OMQ}}\hfill \end{array}\right.\end{array}$$

(11)

where $E_{3_{IMQ}}$ represents the mass percentage of $E_3$ in $IMQ$, $E_3$ in $FMQ$, $E_3$ = (C, $Cl$, $Zn$, $Fe$, $FeO$, $F{e}_2{O}_3$, O), $O_{Fe{O}_{OMQ}}$ represents the mass percentage of oxygen in $Fe{O}_{OMQ}$. $F{e}_2{O}_{3_{OMQ}}$ represents $F{e}_2{O}_3$ in $OMQ$, and $O_{F{e}_2{O}_{3_{OMQ}}}$ represents the mass percentage of oxygen in $F{e}_2{O}_{3_{OMQ}}$.

The dry basis components of each element in returned material $FMQ$ are calculated as shown in the following Equation (12):

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{E}_{4_{FMQ}}={\displaystyle \frac{100\ast E{1}_{IMQ}}{{\sum }_{i=2}^6{w}_i}}\hfill \\ O_{FMQ}=O_{Fe{O}_{FMQ}}+O_{F{e}_2{O}_{3_{FMQ}}}+O_{Z{n}_{FMQ}}\hfill \end{array}\right.\end{array}$$

(12)

where $E_{4_{FMQ}}$ represents the mass percentage of $E_4$ in $FMQ$, $E_4$ = (C, $Cl$, $Zn$, $Fe$, $FeO$, $F{e}_2{O}_3$, O), and $O_{Fe{O}_{FMQ}}$ represents the mass percentage of oxygen in $Fe{O}_{FMQ}$. $F{e}_2{O}_{3_{FMQ}}$ represents $F{e}_2{O}_3$ in $FMQ$, and $O_{F{e}_2{O}_{3_{FMQ}}}$ represents the mass percentage of oxygen in $F{e}_2{O}_{3_{FMQ}}$.

Combining Equations (9)–(12), we obtain the contents of C, $Cl$, $Zn$, and O in the overall mixture: 

$$\left\{\begin{array}{c}{E}_{5_{sum}}=\sum _{Mt=IMQ,IMQ,FMQ}\left({\displaystyle \frac{E_{5_{Mt}}\ast W_{Mt}}{100\ast 100}}\right)\hfill \\ C/O_{sum}={\displaystyle \frac{C_{sum}}{O_{sum}}}\hfill \end{array}\right.$$

(13)

where $E_{5_{sum}}$ denotes the content of elements C, $Cl$, $Zn$, and O in the overall mixture, represented as $E_5=(C,Cl,Zn,O)$. $C_{sum}$ is the mass percentage of total dry basis carbon, $O_{sum}$ is the mass percentage of total dry basis oxygen, and $C/O_{sum}$ is the total $C/O$ ratio.

However, due to practical on-site operations and product manufacturing requirements, certain elemental contents need to meet specific upper and lower limits:

$$\begin{array}{c}\hfill \left\{\begin{array}{c}\underline{C}\le C_{sum}\le \overline{C}\hfill \\ Z{n}_{sum}\le \overline{Zn}\hfill \\ C{l}_{sum}\le \overline{Cl}\hfill \\ C/O_{sum}\le \overline{C/O}\hfill \end{array}\right.\end{array}$$

(14)

In the equation, $\underline{C},\overline{C}$ represent the lower and upper bounds of the mass percentage of carbon, respectively, $\overline{Zn}$ is the upper bound of the mass percentage of zinc, $\overline{Cl}$ is the upper bound of the mass percentage of chlorine, and $\overline{C/O}$ is the upper bound of the mass percentage of the $C/O$ ratio.

The purpose of the intelligent formula of a rotary hearth furnace in this paper is to mine the human experience formula from a large number of historical data by using a machine learning method to form an automatic formula method. Since the performances of C, $Cl$, and $Zn$ in the mixture are not considered in the human experience formula and the machine learning formula learns from the human experience formula, therefore the performances of C, $Cl$, and $Zn$ in the mixture are also not considered in the machine learning formula. However, as a formula automation, the actual site needs the mixture to meet the performances of C, $Cl$, and $Zn$. Therefore, we added the function of fine-tuning the formula based on expert experience after machine learning so that the formula can meet the performance with slight adjustments.

According to the experience of experts, the carbon content of CDQ is the highest, usually reaching 84.4%, followed by the secondary ash from a blast furnace, in which the content of “C” is generally 20% and the content of “$Cl$” is 5%. Therefore, in practice, the proportion of these two materials is mainly adjusted to meet the production constraints. In order to meet the requirements of actual production operation, the proportion of materials changed each time is $ϵ$. Generally, a smaller adjustment leads to greater accuracy. However, depending on the specific site and the experience level of workers, $ϵ$ is typically set at either 0.1% or 1%. In this study, we chose $ϵ$ as 0.1%. The fine adjustment process is illustrated in Figure 6.

When the mixture of raw materials derived from the machine learning formula cannot meet the requirements in C, $Zn$, $Cl$, and $C/O$ performance, the machine learning formula needs to be adjusted through a formula fine-tuning module based on expert experience, as in Figure 6.

First, the module determines whether the sum of the internal ratios is equal to 100. If the internal ratios are not equal to 100, they will be adjusted according to the current proportion and expanded to 100. If the internal ratios are equal to 100, calculate the $C/O$ ratio of the formula and determine whether it is within the specified range:

(1)

If the $C/O$ ratio is below the range, prioritize increasing the CDQ content to improve the $C/O$ ratio. Rejudge whether the sum of internal ratios is equal to 100, and repeat the above logic until the final formula is output.

(2)

If the $C/O$ ratio is higher than the range, priority should be given to reducing the content of secondary ash from a blast furnace. If the content of secondary ash from the blast furnace is insufficient, the CDQ content should be further reduced. Rejudge whether the sum of internal ratios is equal to 100, and repeat the above logic until the final formula is output.

(3)

If the $C/O$ ratio is within the specified range, calculate the contents of C, $Zn$, and $Cl$ separately:

(a)

If C, $Zn$, and $Cl$ are within the specified range, the current formula is output as the final formula.

(b)

If C, $Zn$, and $Cl$ are not within the specified range, consider the following:

• If the C content is too high, reduce CDQ; if it is too low, increase the amount of secondary ash from the blast furnace. Rejudge whether the sum of internal ratios is equal to 100, and repeat the above logic until the final formula is output.
• If the $Zn$ content is too high, reduce the content of cold-rolled mud; if the content of cold-rolled mud is insufficient, reduce the content of LT-OG mud. Rejudge whether the sum of internal ratios is equal to 100, and repeat the above logic until the final formula is output.
• If the $Cl$ content is too high, reduce the content of secondary ash from the blast furnace. Rejudge whether the sum of internal ratios is equal to 100, and repeat the above logic until the final formula is output.

4. Applications

This section mainly introduces the intelligent batching system and its practical application in a steel plant in China. The environmental protection department of the steel plant uses a trial-and-error method to make the production plan of the raw material ratio of the rotary hearth furnace. There are two problems: the first problem is that different methods need to be formulated for different materials, and the the thinking process is complex. The second problem is that this method is time-consuming. The intelligent batching system solves these two problems.

4.1. System Development Technology

The overall development framework of the intelligent batching system is illustrated in Figure 7. The intelligent batching system is composed of a data server, control server, human machine interface, intelligent batching model, and database. The system employs C# for web development, MATLAB for the core algorithmic logic and models, and SQL Server for backend database management. It also utilizes PLC for effective on-site communication, as illustrated in Figure 7.

4.2. Implementation Method

First, the intelligent batching system retrieves raw data from the database and preprocesses them to create a new data table. According to different kinds of raw material combinations, the system uses the AP offline clustering algorithm for clustering analysis and determines the corresponding clustering center of this kind of raw material combination. At the same time, the key attraction matrix and similarity matrix are retained to form a machine learning formula library, which provides the basis for the adjustment of subsequent formulas. Next, the system reads the current formula data and determines which group they belongs to according to the combination of raw material types. Then, according to the content of elements and compounds (C, $Cl$, $Zn$, $Fe$, $FeO$) in the current raw materials, the machine learning formula library recommends the ratio according to the clustering center. This recommended ratio may not fully meet the product production standards, so it is also necessary to make minor adjustments to the recommended ratio through the ratio fine-tuning module based on expert experience to form the final intelligent ratio and output the ratio. The online AP clustering algorithm is implemented to read the newly generated formula data, update the clustering center, attraction matrix, and similarity matrix, and then update the machine learning formula library.

4.3. Human Machine Interface

The system provides a friendly human machine interface. After logging in with a password, users can access the interface for the entire batching process directly and can adjust system parameters, such as the type of ash in the batching warehouse, the weight limits of materials, etc. The upper and lower limits for elements C, $Zn$, and $Cl$ can be configured. The main interface of the intelligent batching system of the rotary hearth furnace in a steel plant in China is depicted in Figure 8. Clicking on “System Parameters” takes users to the system’s parameter settings. The system parameter interface is illustrated in Figure 9. The types of raw materials are customizable, and the weight limits for each warehouse and the ratio limits for each material can be adjusted. The availability of each warehouse can be configured using a button. Within the main interface of the batching system shown in Figure 9, one can also individually view the fundamental parameters of the batching algorithm, as shown in Figure 10. Settings for the batching constraints, the algorithm’s automatic warehouses switching mode, and the periodic retrieval of inspection and testing data are configurable.

4.4. Analysis and Comparison of Batching Results

Taking a rotary hearth furnace in a steel plant in China as an example, it has 12 warehouses: the first warehouse for environmental ash; the second warehouse for CDQ; the third, fifth, sixth, seventh, and eighth warehouses for mixed ash; the fourth warehouse for ash from an iron casting plant; the ninth warehouse for secondary ash from a blast furnace; the tenth warehouse for cold-rolled mud; the eleventh warehouse for the FMQ (controlled by workers, no need to consider); and the twelfth warehouse for binder, which is not a raw material, so it does not need to be considered. To align with actual production needs, the parameter settings are as follows: $h=1.5$, $\overline{C}=10$, $\underline{C}=8$, $\overline{Zn}=4.3$, $\underline{Zn}=0$, $\overline{Cl}=0.8$, $\underline{Cl}=0$, and $\overline{C/O}=1.5$. The $OMQ$ ratio ($Rati{o}_{OMQ}$) is given based on expert experience from the plant as in (15):

$${\mathrm{Ratio}}_{\mathrm{OMQ}}=\left\{\begin{array}{cc}10\hfill & 40<\mathrm{TMQ}\le 100\hfill \\ 8\hfill & 20<\mathrm{TMQ}\le 30\hfill \\ 5\hfill & \mathrm{TMQ}\le 20\hfill \end{array}\right.$$

(15)

Later, the on-site experimental data will be analyzed and discussed for two cases. In Case 1, the formula at the present moment meets the production requirements; in Case 2, the formula at the present moment does not meet the production requirements. The intelligent batching system adopts different processing strategies for these two situations. Since the performances of C, $Cl$, and $Zn$ of the mixture are not considered in the human experience formula and the machine learning formula learns from the human experience formula, therefore the performances of C, $Cl$, and $Zn$ of the mixture are also not considered in the machine learning formula. The following experiments illustrate the necessity of expert experience-based formula fine adjustment.

4.4.1. Case 1: When the Formula at the Present Moment Meets the Production Requirements

Scenario 1: In the previous moment, the formula became the cluster center.

As shown in

Table 3. At the previous moment, the formula became the cluster center (Case 1, Scenario 1).

Warehouse Number	Ratio One	C	Cl	Zn	Fe	FeO
1	5	8.1707	0.1783	3.2892	40.2301	32.2100
2	6	84.4	0	0	0	0
3	0	0	0	0	0	0
4	0	5.8133	0.016	0.1338	63.9333	11.8774
5	32	3.7800	0.2000	3.6903	45.1367	36.1384
6	0	3.7800	0.2000	3.6903	45.1367	36.1384
7	31	3.7800	0.2000	3.6903	45.1367	36.1384
8	31	3.7800	0.2000	3.6903	45.1367	36.1384
9	0	19.435	5.2200	3.7277	41.5333	3.7069
10	0	3.4295	0.3200	14.1331	38.7285	13.3310
11	100	8.1707	0.1783	3.2892	40.2301	32.2100
12	3.5	0	0	0	0	0

, the table details the formula labeled as “Ratio One” from 1 July 2023 at 13:11:23 with TMQ = 18, which lists the elemental content of the current formula and its ingredients. After activating the intelligent formula system, users can access the recommended formulas, as shown in Scenario 1 of

Table 4. Formula comparison. WN represents warehouse number, H is the human formula, A is the formula clustered by online AP, and I is the final formula after fine-tuning.

WN	Case 1						Case 2
	Scenario 1			Scenario 2			H	A	I
	H	A	I	H	A	I
1	5	5	5	5	5	5	5	5	5
2	6	6	6	5	5	5	3	3	1.1
3	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	25	25	26.3
5	32	32	32	29	33	33	24	20	21
6	0	0	0	0	0	0	0	0	0
7	31	31	31	28	15	15	0	0	0
8	31	31	31	28	37	37	33	37	38
9	0	0	0	10	10	10	15	15	12.7
10	0	0	0	0	0	0	0	0	0
11	100	100	100	100	100	100	100	100	100
12	3.5	3.5	3.5	3.5	3.5	3.5	3	3	3

and

Table 5. Performance comparison. WN represents warehouse number, H is the human formula, A is the formula clustered by online AP, and I is the final formula after fine-tuning.

WN	Case 1						Case 2
	Scenario 1			Scenario 2			H	A	I
	H	A	I	H	A	I
C	8.0277	8.0277	8.0277	8.6278	8.7710	8.7710	10.6223	10.5120	9.7656
Cl	0.1751	0.1751	0.1751	0.4050	0.4510	0.4510	0.8423	0.8333	0.7820
Zn	3.2316	3.2316	3.2316	3.2377	3.2381	3.2381	2.6890	2.6604	2.6941
C/O	0.7528	0.7528	0.7528	0.8026	0.8148	0.8148	0.8549	0.8555	0.7872

. It can be seen that H is the human formula from the previous time, A is the formula after online AP clustering, and I is the final formula after fine-tuning. It can be observed that the data in columns H, A, and I are the same, indicating that the formula became the center of the formula cluster after online AP clustering during the previous time. Furthermore, it can be seen from Scenario 1 in Table 5 that the center of the formula cluster meets production requirements and does not require fine-tuning, so H, A, and I are all the same. The intelligent ingredient system will recommend using the current formula.

Scenario 2: At the previous moment, the formula did not become the cluster center.

As shown in

Table 6. When the current formula does not meet production requirements (Case 1, Scenario 2).

Warehouse Number	Ratio Two	C	Cl	Zn	Fe	FeO
1	5	8.6761	0.1769	3.2642	39.9253	31.9659
2	5	84.4	0	0	0	0
3	0	0	0	0	0	0
4	0	5.8133	0.016	0.1338	63.9333	11.8774
5	29	3.7800	0.2000	3.6903	45.1367	36.1384
6	0	3.7800	0.2000	3.6903	45.1367	36.1384
7	28	3.7800	0.2000	3.6903	45.1367	36.1384
8	28	3.7800	0.2000	3.6903	45.1367	36.1384
9	10	19.435	5.2200	3.7277	41.5333	3.7069
10	0	3.4295	0.3200	14.1331	38.7285	13.3310
11	100	8.6761	0.1769	3.2642	39.9253	31.9659
12	3.5	0	0	0	0	0

, the formula labeled as “Ratio Two” from 2 July 2023 09:21:42 has a TMQ of 18. The table details the current formula and the elemental content of each ingredient. After activating the intelligent formula system, users can access the recommended formulas, as shown in Scenario 2 of Table 4 and Table 5. It can be seen that H is the human formula from the previous time, A is the formula clustered by online AP, and I is the final formula after fine-tuning. It can be observed that the elemental content of H meets the production standards, but it can be found that the data in columns A and I are different from those in H. From Scenario 2 in Table 4, it can be seen that the previous formula did not become the center of the formula cluster after online AP clustering. Furthermore, from Scenario 2 in Table 5, it can be observed that although the previous formula met the production standards, the system selected the center of the cluster where the formula is located as the recommended formula. The final recommended formula I meets the production requirements, so A and I are the same. The intelligent ingredient system recommends using this recommended formula to ensure compliance with production standards.

4.4.2. Case 2: When the Formula at the Present Moment Does Not Meet the Production Requirements

As shown in

Table 7. When the formula at the present moment does not meet the production requirements (Case 2).

Warehouse Number	Ratio Three	C	Cl	Zn	Fe	FeO
1	5	11.10011508	0.8557	2.7473	41.8985	21.1786
2	3	84.4	0	0	0	0
3	0	0	0	0	0	0
4	25	5.04181	0.016	0.1281	64.2987	12.4034
5	24	8.49444	0.2	4.35355	42.4917	33.2209
6	0	8.49444	0.2	4.35355	42.4917	33.2209
7	0	8.49444	0.2	4.35355	42.4917	33.2209
8	33	8.49444	0.2	4.35355	42.4917	33.2209
9	15	15.9483	5.22	2.30592	44.4709	3.87191
10	0	3.31824	0.32	14.5748	38.7635	14.1481
11	100	11.1001	0.8557	2.7473	41.8985	21.1786
12	3	0	0	0	0	0

, the table includes a formula labeled as “Ratio Three” from 10 July 2023 18:23:12, where TMQ = 18. The table details the current formula and the elemental content of each ingredient. After activating the intelligent formula system, users can access the recommended formulas, as shown in Case 2 of Table 4 and Table 5. It can be seen that H is the human formula from the previous time, A is the formula clustered by online AP, and I is the final formula after fine-tuning. It can be observed that the data in columns A, H, and I are all different. Comparing Table 5, it can be seen that the contents of C and $Cl$ elements in H do not meet the production standards. The element content obtained through online AP clustering formula is shown in A. In Table 5, it can be found that the formula obtained through online AP clustering still does not meet the production standards, so it needs to be finely tuned. It can be found that the element content in column I meets the production standards. Therefore, the intelligent ingredient system will recommend using the fine-tuned formula.

5. Conclusions

To meet the challenges of efficiency and precision in the rotary hearth furnace batching process, this study successfully developed and deployed an innovative intelligent batching system. The system utilizes a online clustering algorithm framework, seamlessly integrating data preprocessing techniques with both offline and online AP clustering algorithms. Additionally, incorporating an expert-driven formula fine-tuning module, the system adeptly processes historical formula data and dynamically updates batching plans. The application of these advanced technologies allows the system to accurately identify and handle outliers and missing values in the data, efficiently perform online clustering based on new data, avoid redundant computations, and significantly enhance processing efficiency and batching precision. The system design also considers user interactivity, featuring a user-friendly interface and flexible parameter configuration, further enhancing its practicality and adaptability. The successful development and implementation of this system not only achieved an automatic batching process and improved product quality and efficiency, it also introduced a new intelligent solution for the bottom furnace batching industry, which has important theoretical significance and practical value. Its application at a Chinese steel plant demonstrated the system’s efficiency and practicality.

The method of a machine learning formula based on AP clustering has some limitations. Before using the system, it is necessary to accumulate certain experience data. When one or more new materials are added, because the previous historical data do not contain the new materials, it is necessary to accumulate experience data for a period of time. In addition, the AP clustering algorithm has insufficient processing capacity for large-scale data. In the future, we will study an online AP clustering method based on limited time windows to extend the AP method to scenariosthat can handle large-scale data.