Review of Intelligent Modeling for Sintering Process Under Variable Operating Conditions

Abstract

The steel industry serves as a cornerstone of a nation’s industrial system, with sintering playing a pivotal role in the steelmaking process. In an effort to enhance the intelligence of the sintering process and improve production efficiency, numerous scholars have carried out extensive research on data analysis and intelligent modeling techniques. These studies have made significant contributions to expanding production capacity, optimizing cost efficiency, and enhancing the quality of products, and supporting the sustainable development of the steel industry. This paper begins with an analysis of the sintering production process, explores the distinctive characteristics of the sintering process, and discusses the methods for identifying the operating conditions of sintering. It also provides an overview of the current state of research on both mechanism modeling and data-driven modeling approaches for the sintering process. Finally, the paper summarizes the existing challenges in sintering process modeling and offers perspectives on the future direction of research in this field.

1. Introduction

The steel industry is a cornerstone sector in a nation’s industrial system, with profound implications for a country’s economy, society, and national defense. Its robust development is directly linked to the overall development level and competitiveness of the country. The steel production process encompasses several key stages, including the coking process, sintering process, ironmaking process, steelmaking process, and rolling process. Among these, sintering plays a crucial role as a heat-induced agglomeration process that mixes iron ore powder, recycled ironmaking products, fluxes, slagging agents, and solid fuels, contributing significantly to the steelmaking process [1].

However, due to the complexity of the sintering system and technical limitations in industrial settings, many key parameters are difficult to measure directly or exhibit significant measurement delays [2]. For instance, accurate prediction of the sintering endpoint is critical for the quality of sintered [3]; the composition and drum strength of the sintered ore directly affect the quality of downstream smelting [4]; and dynamic monitoring of sintering flue gas composition is central to achieving green production and emission control [5]. To address the challenges posed by these hard-to-measure parameters, sintering modeling has become a key research tool for solving such problems [6]. By constructing mathematical models or leveraging data-driven techniques, sintering modeling can accurately predict difficult-to-measure or delayed parameters, providing real-time guidance for the production process.

Currently, mainstream modeling approaches are primarily classified into two distinct categories: mechanism modeling and data-driven modeling [7]. Mechanism modeling, based on a deep understanding of thermodynamics, fluid mechanics, and chemical reaction kinetics, can accurately describe the physical and chemical phenomena during the sintering process and provide logically sound explanations of the effects of parameter variations [8]. In contrast, data-driven modeling relies on historical data and statistical patterns, using methods like machine learning to capture nonlinear relationships between inputs and outputs. This approach has shown considerable effectiveness in parameter prediction and model training speed.

This paper seeks to offer a comprehensive review of the advancements in research within the field of sintering modeling, with a focus on analyzing the current status, application scenarios, advantages, and limitations of mechanistic and data-driven modeling. By summarizing the characteristics and recent developments of different modeling methods, this paper seeks to offer insights and references for both theoretical research and industrial practices in sintering modeling. Section 2 provides an overview of the sintering process and its defining characteristics; Section 3 discusses the methods for identifying operating conditions in the sintering process; Section 4 reviews both mechanistic and data-driven modeling approaches for the sintering process; and Section 5 presents a comprehensive summary and outlook on existing modeling methods.

2. Analysis of Sintering Process

Sintering is a metal smelting process widely applied in the steel manufacturing sector [9,10]. The primary objective of this process is to agglomerate fine ore particles into larger masses, forming sintered ore suitable for blast furnace smelting [11]. The process involves complex production procedures and inherent characteristics, making it essential to conduct a thorough analysis of the process and its features before undertaking sintering process modeling studies.

2.1. Description of Iron Ore Sintering Process

Modern sintering methods typically place greater emphasis on improving energy efficiency, reducing environmental impact, and manufacturing precision components. In response to the high demand for steel, the most commonly used method in steel production is the belt-type, forced-air sintering process. Beneath the sintering machine, there are two rows of wind boxes. The exhaust fans below these wind boxes continuously extract air from within, allowing air to flow into the material layer above and ultimately exit through the wind boxes. This process provides sufficient oxygen for the combustion of fuel within the mixed charge, ensuring stable operation of the sintering process. Currently, most sintering plants use sintering machines with a functional area of 360 m². The process flow diagram of the sintering process is shown in Figure 1.

The sintering process mainly consists of several steps, including mixing and granulation, ignition, sintering, and cooling. Generally, the sintering process takes approximately 120 min. The batching process involves mixing iron ore powder with fuel (coke powder), return fines, and fluxes (limestone and dolomite) to form the raw material mixture. Water is added to the raw mix, which is then subjected to both primary and secondary mixing and granulation to form uniform particles with appropriate moisture content and particle size distribution. The optimal particle size of sinter charged into the blast furnace is typically between 5 and 20 mm. The proper distribution of these particles is crucial for improving the permeability of the material layer. During secondary mixing, the raw mix undergoes steam preheating, which helps raise the initial temperature of the mix. The water-mixed granules are then transported by a conveyor belt to the charging bin. The primary goal of the first mixing stage is to achieve uniformity and moisture adjustment. During this stage, various raw materials are evenly mixed to ensure that different components, such as iron ore powder, fluxing agents, fuel, and return fines, are fully blended into a homogeneous mixture. The second mixing stage, in addition to further homogenization and fine-tuning of moisture content, primarily aims to create a sinter mix with a specific particle size distribution and appropriate moisture levels. This mixture has sufficient permeability, facilitating efficient airflow during the sintering process. To prevent smaller granules from being carried away by the wind boxes, the granules are distributed on the sintering grate in a manner where the particle size gradually increases from top to bottom. This is achieved through a nine-roll spreading machine. Additionally, to protect the sintering grate from high temperatures, a layer of coarse sinter is typically spread on the grate as a bed material before charging. In normal sintering production, the material layer has a thickness of approximately 700 mm, and the solid fuel on the surface of the raw mix is initiated beneath the ignition chamber. During the sintering ignition process, key factors include ignition temperature, oxygen supply, particle size, and the chemical composition of the material. In ironmaking plants, operators primarily determine whether sintering has achieved complete combustion by measuring the temperature in the flue gas duct of the sintering process using thermocouples, in combination with their professional judgment and operational experience. The sintering grate is equipped with 24 wind boxes that initiate ventilation for sintering. As the sintering machine advances, the raw mixture undergoes melting and combustion in a top-to-bottom progression. This process culminates in the formation of sintered ore with specific strength characteristics at the burn-through point ($BTP$).

The fully mixed raw mix burns within the material layer, generating high temperatures of approximately 1300 °C. Proper temperature promotes the reaction of minerals in the sinter, resulting in the formation of sinter with good mechanical strength. However, excessively high temperatures may cause over-melting of the minerals, which negatively affects the strength and structure of the sinter, increasing its brittleness and, consequently, its fragility. This high-temperature environment induces physical changes and chemical reactions in the sintering mixture, leading to the formation of distinct layers within the material bed. The material layer can be divided into several zones from bottom to top, including the raw material layer, the over-wet layer, the preheating and drying layer, the combustion zone, and the sintered ore layer. The combustion zone represents the area with the highest temperature and the most intense reaction activity. As the combustion zone moves downward, high-temperature molten material agglomerates into blocks, forming the molten layer. The introduction of cooling air causes the sintered ore to cool and form the sintered layer.The preheating and drying layer is in direct proximity to the combustion zone and is exposed to the high-temperature exhaust gases produced therein. The free moisture in the material layer quickly evaporates, and the evaporated water vapor comes into contact with the colder material layer below, forming the over-wet layer. From the layering phenomenon of the sintering bed described above, it can be concluded that the combustion of carbon is integral to the quality and yield of the sintered ore.

Sintering production generally occurs in a high-alkalinity environment. The addition of fluxes such as limestone and quicklime to the sintering mixture ensures the alkaline conditions necessary for the sintering process. Because of the substantial presence of calcium oxide ($CaO$), a series of chemical reactions take place with the raw mixture, leading to the formation of diverse minerals. The main minerals formed include magnetite ($F{e}_3$$O_4$), dicalcium silicate ($2CaO$·$Si{O}_2$), calcium ferrite ($CaO$·$F{e}_3$$O_2$), calcium ferrite ($2CaO$·$F{e}_2$$O_3$), and tricalcium silicate ($3CaO$·$Si{O}_2$). The properties of these minerals are summarized in

Table 1. Main mineral properties in sintered ore.

Components	Melting Point/(°C)	Compressive Strength/(Mpa)	Reductability/(%)
$F{e}_3$$O_4$	1590	3.69	26.7
$CaO$·$F{e}_3$$O_2$	1216	3.76	40.1
$2CaO$·$F{e}_3$$O_2$	1436	1.42	28.5
$2CaO$·$Si{O}_2$	2130	-	-
$3CaO$·$Si{O}_2$	1410	0.67	-

.

The primary mineral in sintered ore is calcium ferrite ($CaO$·$F{e}_2$$O_3$). As shown in Table 1, ($CaO$·$F{e}_2$$O_3$) exhibits the highest compressive strength, the best reducibility, and the point of minimum melting temperature. The higher the content of $CaO$·$F{e}_2$$O_3$, the more favorable it is for producing high-quality molten iron during the ironmaking process. These stable minerals enhance the mechanical strength of the sinter. Additionally, limestone improves the flowability of the ore, reduces ore fines during the sintering process, and minimizes the formation of small particles. Therefore, it is essential to produce a sufficient amount of $CaO$·$F{e}_2$$O_3$ during the sintering process to ensure better steelmaking performance.

2.2. Analysis of Sintering Characteristics

The sintering process is characterized by strong nonlinearity and significant time delays, with many factors within the process exhibiting strong interdependencies. An examination of the sintering process identifies the following key characteristics:

• Multiple types of parameters. Raw material parameters: coke powder ratio, return fines, and the contents of $CaO$, $Si{O}_2$, $MgO$, total iron ($TFe$). Operational parameters: Grate speed and material layer thickness. State parameters: Wind box negative pressure, $BTP$, $BTP$ temperature, average vertical combustion rate, sintering rise point position, and sintering rise point temperature.
• Nonlinearity. The sintering process involves numerous physical and chemical reactions, encompassing the evaporation and decomposition of water, redox reactions, and solid-phase reactions of sintering materials. Various factors affect the comprehensive coke ratio, such as the chemical composition of the raw mix, its permeability, and the sintering endpoint position. These parameters display time-dependent and uncertain behaviors, with many of them being unmeasurable in real-time, resulting in significant nonlinearity among the sintering variables. Consequently, developing accurate mathematical models for the sintering process proves to be a difficult task.
• Time delay. There is a time delay between the detection of raw material composition and the subsequent production of sintered ore. The production rate of sintered ore is a key factor influencing the comprehensive coke ratio. Delays in detecting sintered ore production affect the coke ratio, which complicates the selection of suitable data for use as inputs in time-series predictions. Nevertheless, this delay is primarily attributed to sensor detection, with measurement intervals generally remaining fixed. This challenge can be mitigated by shifting the input and output data either forward or backward to account for the delay prior to making model predictions.
• Strong coupling between parameters. The sintering process is governed by numerous parameters, primarily encompassing raw material, state, and operational factors. Raw material and operational parameters exert an indirect influence on the target parameters by altering the state parameters. These parameters are highly interdependent, such that a variation in one parameter induces simultaneous changes across multiple others.
• Multiple operating modes. In actual sintering production, various types of charge recipes are used to guide production, with each recipe representing a distinct operating mode. When predicting indicators such as carbon efficiency, a single integrated predictive model is inadequate for comprehensively forecasting carbon efficiency under different operating modes.

3. Identification Methods for Sintering Process Conditions

The sintering process is a continuous and extended-duration manufacturing procedure characterized by complex material and energy conversion and transfer mechanisms, with variable operating conditions that exhibit intricate operational features [12]. Production data under different operating conditions exhibit distinct characteristics, and relying on a single model to describe the sintering process may lead to inaccurate results, thereby affecting the prediction of key parameters [13]. Therefore, in sintering process modeling research, it is essential to first conduct effective identification of the variable operating conditions, and then propose appropriate modeling methods based on this identification.

Cluster analysis is frequently employed in industrial processes to categorize operational conditions based on industrial data [14,15]. As a multivariate statistical technique, cluster analysis classifies data into distinct operational states, ensuring that data within the same state share similar attributes. For instance, reference [16] utilized the fuzzy c-means clustering algorithm to classify distinct operational conditions in the nylon polymerization process, while reference [17] proposed a hierarchical clustering method based on the Ward algorithm for automatic classification of various operational conditions in photovoltaic power plants. In the identification of sintering process conditions, reference [18] employed the K-means clustering algorithm to distinguish various operational states within the sintering process. Changes in operational conditions lead to variations in the comprehensive coke ratio, which was used to validate the effectiveness of the K-means algorithm. However, this method is hindered by the high number of computational steps and long processing times, making it unsuitable for real-time application in sintering operations. The fuzzy clustering algorithm can address some of these limitations. reference [19] applied the fuzzy C-Means clustering algorithm, and reference [20] proposed a weighted kernel fuzzy C-Means clustering algorithm to identify multiple operational states in the sintering process. However, these methods require the pre-definition of the quantity of clusters (i.e., the count of operational conditions). This poses a challenge, as the number of operational conditions in the sintering process cannot be predetermined. To overcome this, reference [21] introduced a quantification error modeling approach [22], and subsequently proposed a fuzzy C-Means clustering algorithm based on the quantification error model for the automatic identification of multiple operational conditions in sintering. In reference [23], a multi-dimensional characterization method for sintering conditions was proposed, based on polycrystalline indicators. This method integrates polycrystalline indicators with radar charts to define and calculate performance and balance indicators for sintering conditions, providing a comprehensive and accurate assessment of operational states. In reference [24], the affinity propagation clustering algorithm was applied to effectively classify different operational conditions, and support vector machine were used to recognize these conditions. Fuzzy C-Means clustering methods enable the accurate classification of production data under stable and smooth sintering production modes, particularly in cases where the number of process parameters is relatively small. However, most of these methods do not consider the real-time status information of actual sintering operations, which may limit their applicability in practical engineering settings.

Most methods for identifying operational conditions in the sintering process are limited to considering either production status information or the classification of operational conditions based on different production data characteristics. These approaches lack a comprehensive method that simultaneously accounts for both production status information and the varied characteristics of different production data for intelligent recognition of operational conditions. Images of the rear section of the sintering machine can reflect the actual production status and contain rich information about the sintering operational conditions. These images also carry production-related data such as yield, quality, and energy consumption. Timely and effective acquisition of the tail section images of the sintering machine is therefore a crucial prerequisite for the accurate and efficient recognition of sintering operational conditions. Thus, in practical sintering production, a deep analysis of the tail section images and the distinct characteristics of production data is essential. Research into intelligent recognition methods that consider both production status and the different characteristics of production data is beneficial for accurately describing the dynamic changes in the sintering production state. This approach will also provide a foundation for developing high-precision dynamic prediction models for carbon consumption in the sintering process.

4. Modeling Methods for the Sintering Process

During real-world sintering processes, it is essential to measure and monitor several critical parameters in real-time to maintain production safety, operational stability, and energy efficiency. However, due to limitations such as the high cost of sensors and the challenging industrial conditions, accurate measurement of most parameters is difficult and time-consuming. Therefore, modeling the sintering process and predicting certain key parameters is of significant importance for the monitoring, optimization and regulation of the sintering production process.

4.1. Mechanism Modeling

The sintering process involves several complex steps, including raw material mixing, segregation, ignition, and sintering, accompanied by intricate physicochemical changes. This process is characterized by numerous process parameters, such as temperature, pressure, flow rate, and velocity, along with extensive material and energy exchanges and transfers. Mechanism-based models are primarily derived from the physicochemical characteristics of the material strata involved in the process [25], as well as the laws of energy conservation and mass balance [26]. These models can clearly and accurately describe the interrelationships between various parameters of the sintering process.

In mechanism modeling research, many scholars have proposed corresponding analytical models, summarizing valuable theoretical findings with practical applications. For instance, focusing on individual mixed particles, reference [25] proposed a mechanism-based model to characterize the rate of combustion of solid coke during the sintering process, both under single-addition or distributed addition conditions. Additionally, a fuel particle model was established, with the combustion process and heat transfer identified as key factors influencing sintering productivity. Reference [27] proposed a transient heat and mass transfer model, which explains temperature changes within the material layer after ignition during sintering. A further model [28] describes the combustion behavior of solid fuel layers during sintering. Based on the local non-equilibrium thermodynamic relationships in the sintering process, another model [29] was developed to describe heat transfer, subject to five specific assumptions to ensure accurate heat transfer effects. Reference [30] established an unsteady-state, two-dimensional mechanism model, based on the analysis of key chemical reactions and physical processes involved in iron ore sintering, using reasonable assumptions. Additionally, a thermal reaction mechanism model, grounded in the principles of energy conservation, was developed to forecast the ignition temperature during the sintering process [26]. Reference [31] introduced a mechanism model to provide a detailed description of coke particle combustion in the sintering process. Reference [32] reflected the impact of liquid-phase formation during coke combustion on the sintering temperature field. Reference [9] outlined the direct influence of coke particle combustion behavior and gas flow velocity on the temperature, width, and velocity of the flame front within the sintering bed. It incorporated a granulation model into the thermal treatment framework to characterize coke combustion, and integrated two endothermic reactions, thereby enhancing the accuracy of temperature change predictions within the sintering bed.

While these mechanism-based models are theoretically rigorous and effectively reveal the inherent relationships between parameters in the sintering process, they require precise measurement of process parameters for the various materials involved, and their development relies on numerous assumptions. However, the sintering process represents a complex industrial system governed by numerous parameters, time delays, varying operating conditions, and nonlinearity. Some critical process parameters cannot be measured directly, limiting the application of mechanism-based modeling methods in characterizing the dynamics of these complex industrial systems. As a result, these models face significant challenges when applied to real-world industrial settings.

4.2. Data-Driven Modeling

With the advancement of database technology and artificial intelligence, scholars both domestically and internationally have begun to explore data-driven predictive models to address the challenges that mechanism models face in predicting complex industrial process parameters. Data-driven modeling methods involve studying the implicit mathematical relationships between production data, thus avoiding the complexities of mechanism analysis [33]. These models utilize actual production data to compute the relationships between various process parameters. These models are especially effective for complex and dynamic industrial processes, facilitating the creation of data-driven models that are customized to meet the specific requirements of industrial operations. Commonly used data-driven models include support vector machines (SVM) [34,35], feedforward neural networks [36,37], deep belief networks (DBN) [38], autoencoders [39], recurrent neural networks (RNN) [40], and convolutional neural networks (CNN) [41]. In the context of sintering, data-driven models primarily focus on predicting certain key parameters, which can then serve as the basis for process control or optimization. Sintering parameter prediction mainly targets parameters that cannot be directly measured or those for which measurement involves time delays, such as sintering endpoints, sintered product composition indicators, sintering flue gas composition, and sintering ore drum index, among others.

4.2.1. FeO Prediction Method

In the sintering process, the ferrous oxide ($FeO$) content refers to the mass fraction of $FeO$ in the sintered ore. It is one of the key indicators used to evaluate the quality of the sintered ore, directly reflecting the extent of reduction reactions and fuel consumption efficiency during the sintering process. The optimal range for $FeO$ content is typically closely related to the actual requirements of blast furnace smelting. During sintering, the $FeO$ content cannot be quantified in real-time through online sensors and is usually determined through laboratory chemical analysis. Given the inherent time lag in measurement, it is challenging to adjust process parameters promptly to optimize production. Therefore, the ability to accurately predict and control the $FeO$ content in sintered ore is crucial for optimizing the sintering process and improving smelting efficiency.

Reference [42] introduces a data-driven approach for forecasting the $FeO$ content in sintered ore, utilizing multi-source data and $LSTM$. This approach incorporates multi-source features, including image data, vibration, and temperature parameters, to effectively reflect the $FeO$ content in the sintered ore. Reference [43] introduced an innovative framework for dynamic time feature expansion and extraction, utilizing recursive neural network regression to forecast critical quality variables, such as $FeO$, for sintered ore quality prediction. Reference [24] proposed a multi-model ensemble framework for predicting $FeO$ content in the iron ore sintering process, utilizing affinity propagation clustering to effectively classify different operating conditions and employing support vector machine ($SVM$) algorithms to identify these conditions. Reference [44] developed a method for predicting $FeO$ content, integrating heat transfer mechanisms with a data-driven model, in which sintered ore is classified into three categories based on the peak temperature. Three variants of Long Short-Term Memory ($LSTM$) models, known for their robust adaptability to dynamic and nonlinear data across varying conditions, are utilized to forecast the $FeO$ content during the sintering process. Reference [45] introduced the use of a restricted Boltzmann machine ($RBM$) to design a supervised $RBM$ ($SRBM$), integrating quality variables into the visible layer to direct the model’s learning of quality-relevant features. A stack of multiple $SRBMs$ is used to form a supervised $DBN$, which facilitates the prediction of $FeO$ content by progressively learning quality-related features across layers. Reference [46] introduced an online measurement approach for $FeO$ content, utilizing infrared images of the sinter machine’s rear section in conjunction with $CNN$. Reference [47] through the compression of observed images, image features are combined with numerical data corresponding to sampling time. A multi-source information fusion model, MIF-Autoformer, which integrates deep convolutional neural networks with $Autoformer$, is proposed for soft sensing-based modeling of sintering quality. Finally, reference [48] proposed an online composition monitoring model utilizing deep neural networks ($DNN$) alongside an advanced component prediction model based on $LSTM$, designed to support field operators in real-time management of variations in sintered ore composition. Reference [49] proposed a novel semi-supervised dynamic feature extraction framework based on sequence pre-training and fine-tuning to predict the FeO content in sintered ore. Reference [50] presented an implicit subspace identification regression neural network based on orthogonal basis decomposition and reconstruction, this approach employs a recursive Fourier transform-like encoding block to extract features that capture long-term memory through orthogonal basis decomposition. Subsequently, a stochastic gradient-based identification algorithm is used to approximate the true system and model the $FeO$ content.

4.2.2. BTP Prediction Method

$BTP$ denotes the specific location or time point in the sintered ore bed where the temperature required for combustion reactions and melting is reached. During the sintering process, the $BTP$ marks the completion of the combustion of fuel and thermal energy transfer within the material bed, making it one of the critical process parameters in sintering. Predicting the $BTP$ can help optimize the bed height, sintering speed, and fuel ratio, thereby improving production efficiency and product quality. However, the $BTP$ is difficult to measure directly, typically relying on manual experience, thermocouple monitoring, or offline experimental methods. These approaches face challenges such as measurement delays, insufficient accuracy, or operational complexity, preventing real-time adjustment of process parameters. By predicting the location and time point of the sintering end, dynamic control of the sintering process can be achieved, providing a basis for enhancing process stability. Reference [51] proposed a probabilistic spatiotemporal perception network named $BTPNet$. Within the encoder network, a multi-channel temporal convolution network ($MTCN$) is employed to extract temporal features. Additionally, a novel architecture unit, called the variable interaction awareness module ($VIAM$), is introduced to capture spatial features, thereby enabling accurate multi-step prediction of the $BTP$. In reference [52], an integration of process expertise and multiple feature selection techniques is used to identify key feature variables associated with $BTP$. A forecasting model for $BTP$ and burn through temperature ($BTT$) is established using a gradient boosting decision tree ($GBDT$) algorithm. Grid search and cross-validation methods are employed to fine-tune the parameters of the ensemble algorithm, and a system model based on training data is developed. Moreover, a decision model is incorporated into the result generated by the predictive model, enhancing the system’s prediction accuracy. Reference [53] developed a multi-step prediction model known as the denoising spatiotemporal Encoder-Decoder, which forecasts $BTP$ in advance. Mechanistic analysis is conducted to identify the key $BTP$ variables, and formulate $BTP$ prediction as a sequence-to-sequence modeling task. Reference [54] utilized mechanistic and mutual information analyses to identify key process variables that are directly associated with $BTP$. The weighted kernel just-in-time learning ($WKJITL$) method is subsequently employed to extract historical production data analogous to the $BTP$ query data, facilitating local learning-based modeling. Additionally, a fuzzy broad learning system ($FBLS$) is introduced as an effective approach for $BTP$ soft sensor prediction. Finally, reference [55] proposed a decomposition-driven encoder-decoder model that leverages a self-attention mechanism to capture long-range dependencies between variables, and is applied for multi-step $BTP$ prediction in the sintering process. Reference [56] proposed a 3-D convolution-based multi-step $BTP$ prediction model that captures spatiotemporal features, resolved the spatial interdependencies among process variables, while addressing the limitations inherent in existing loss functions, which primarily rely on Euclidean distance and fail to capture the dynamic information in multi-step prediction sequences.

4.2.3. Carbon Efficiency Prediction Method

Carbon efficiency denotes the efficiency with which carbon energy is utilized during the sintering process. Commonly used indicators for carbon efficiency include the comprehensive coke ratio ($CCR$) and the ratio of carbon monoxide ($CO$) to carbon dioxide ($C{O}_2$), denoted as $CO/C{O}_2$. $CCR$ serves as an indicator of carbon utilization efficiency, representing the amount of carbon consumed to produce one ton of sintered ore. A lower $CCR$ indicates a reduced carbon consumption per ton of sintered ore, implying higher carbon energy utilization efficiency. The $CO/C{O}_2$ ratio reflects the completeness of carbon combustion; a higher CO/CO₂ ratio indicates lower combustion efficiency, with a higher proportion of $CO$ in the exhaust gases. Conversely, a lower ratio signifies a reduced $CO$ content in the exhaust, indicating higher combustion efficiency. Both of these indicators are challenging to measure simply and stably using sensors, and they can only be assessed after the entire sintering process is completed. Therefore, if these indicators are to be used for optimizing or scheduling sintering production, it is necessary to predict them before the completion of the sintering process.

Reference [57] asserted that the primary energy consumption process in sintering is the combustion of carbon, and it predicts carbon efficiency. This study uses the $CCR$ as the indicator for measuring carbon efficiency and proposes a prediction model based on a particle swarm optimization ($PSO$) algorithm combined with a backpropagation ($BP$) neural network to analyze carbon efficiency. Reference [58] investigated the multi-time-scale characteristics of carbon efficiency by developing a model that integrates intelligent multi-time-scale techniques and neural networks. This model is capable of optimizing process variables across both short-term and long-term time frames. It uses $CCR$ and the ratio of $CO$ to $C{O}_2$ in the exhaust gases as indicators of carbon efficiency, establishing prediction models for state variables using both a single neural network and a linear combination of neural networks. The study indicates that the carbon efficiency prediction method has practical significance. Reference [18] selected $CCR$ as the indicator for carbon efficiency and designs a method for modeling and optimization that is grounded in operational modes. This study utilizes the K-means clustering technique to identify distinct operational modes within the sintering process. For each identified mode, a $CCR$ prediction model is developed, incorporating two $BP$ neural networks. The model predicts the optimal operating mode based on $CCR$, reducing the $CCR$ problem to a two-step optimization problem, which is solved using $PSO$. The method is validated using real industrial data, demonstrating the predictive performance of the model.Reference [59] proposed a carbon efficiency prediction model combining Elman and recurrent neural networks.

Over the past few years, a flexible and efficient modeling approach, known as the width learning model [60], has gained attention in the industrial sector. Reference [20], Grounded in the principles of the sintering process, this approach identifies the key sintering parameters that affect carbon efficiency and proposes a weighted fuzzy C-means clustering algorithm to recognize various operating conditions. Subsequently, a width learning model is developed for each operating condition. Finally, the nearest-neighbor criterion is employed to determine the optimal width learning model for predicting the carbon efficiency time series. Reference [61] introduced a specialized kernel-based fuzzy C-means clustering algorithm to classify real operational data under multiple conditions, which is then utilized to model the iron ore sintering process. Additionally, the width learning model’s broad network structure is used to model carbon efficiency predictions under different operating conditions. Reference [54] developed a soft sensor model for sintering endpoint prediction based on a weighted kernel instant learning and fuzzy width learning system. The method involves using the weighted kernel instant learning approach to gather historical production data comparable to the sintering endpoint query data for local learning-based modeling and adopts the fuzzy width learning system as an effective approach for predicting sintering endpoint soft measurements. Reference [62] designed a dynamic carbon consumption prediction model for sintering, where broad learning models are developed for different operating conditions. Reference [63] proposed a novel adaptive weighted broad echo state learning system ($AWBESLS$) for dynamic carbon consumption prediction in the sintering process, which adaptively assigned weights to production data to mitigate the influence of outliers and used an echo state network ($ESN$) to capture the dynamic states of the process.

Moreover, many scholars have applied $SVM$ [64] to model the sintering process. Reference [21] develops a multi-level carbon efficiency prediction model based on mechanism analysis, identifying the sintering process parameters that influence the comprehensive coke ratio. For different operating conditions, the least squares support vector machine (LS-SVM) is used, and a differential evolution algorithm is proposed to optimize the parameters and weights of the LS-SVM sub-models to improve their generalization ability. The results indicate that the prediction accuracy is within acceptable limits and meets the demands of real-world sintering production” or “the practical requirements of sintering production. Reference [65] constructed an optimization model to minimize blending costs, constrained by the best granulation and mineralization performance of the mixture, and uses an LS-SVM-based prediction model along with the basic properties of raw materials to predict the fuel consumption, drum strength, and productivity of sintered ore. This model comprehensively considers sintering performance, optimizes raw material costs, and achieves low-carbon, low-cost sintering. Reference [66] proposed a $CO/C{O}_2$ soft measurement model based on a hybrid kernel relevance vector machine for incomplete output data through data augmentation. Reference [67] proposed a sintering energy consumption prediction model using extreme learning machine and support vector regression.

4.2.4. Other Parameters and Summary

Reference [68] developed a quality prediction model for the tumbler strength in the sintering process using a $BP$ neural network algorithm with momentum and variable learning rates. Reference [59] taking into account the unique characteristics of the process, a real-time dynamic forecasting model for the $CCR$, which reflects carbon efficiency, was developed. This model leverages predictive error information and is grounded in the principles of generalized learning to enhance accuracy and adaptability. Reference [69] applied linear regression and artificial neural network ($ANN$) algorithms to predict the productivity of the sintering machine and the composition of input materials. In reference [70], a hybrid ensemble model was proposed to predict key operational parameters, including solid fuel consumption, gas fuel consumption, $BTP$, and tumbler index ($TI$). This model integrates the extreme learning machine with an enhanced AdaBoost. RT algorithm, leveraging their complementary strengths to achieve higher predictive accuracy and robustness. Reference [71] developed a novel fusion network by integrating the local feature extraction capabilities of $CNN$, the sequential data processing strengths of $LSTM$, and the adaptive focus provided by the attention mechanism. This attention-augmented CNN-LSTM fusion network demonstrated substantial improvements in the accuracy of ignition temperature predictions, highlighting its effectiveness in capturing both spatial and temporal dependencies within the data. Reference [72] combined a local thermal non-equilibrium model and proposed a data-driven Tumble strength prediction approach. Reference [73] proposed a knowledge-data dual-driven graph neural network ($KDGNN$) to address the limitation of data-driven models that neglect domain knowledge, and was applied for end-to-end prediction of tumbler strength. Reference [74] constructed a data-driven prediction model with multiple time scales to predict the iron grade of sintered ore.

In summary, data-driven modeling methods do not require precise mechanistic knowledge or comprehensive expert knowledge. Instead, these methods build models using large amounts of data and continuously refine model parameters to improve their ability to fit real-world processes, ultimately establishing a data-driven model. The advantages of data-driven modeling methods include strong adaptability in handling highly coupled, nonlinear, and time-varying complex sintering reaction processes. However, their limitations include model accuracy being constrained by sample data and algorithms, with a heavy reliance on empirical data. Compared to mechanistic models, data-driven approaches are better at describing nonlinear, complex industrial processes, are more efficient, and have greater versatility. As a result, they have gradually become the preferred modeling method for sintering process modeling.

4.2.5. Summary of Data-Driven Models

The limitations of data-driven methods in the context of the sintering process can be discussed as follows: First, the composition of raw materials, operating conditions, and environmental factors in industrial processes are often highly complex and variable. Changes in the composition, moisture, and particle size of the raw materials during the sintering process can lead to diverse and complicated sintering production data. Relying solely on data-driven methods to build models may struggle to capture all the complex relationships between features and variables. Second, many industrial processes, such as sintering, may not have sufficient historical data, or the quality of available data may be poor. Missing data, noise, or incorrect labeling can affect the accuracy and robustness of models. In the iron ore sintering process, if there is insufficient data from various raw material compositions or operating conditions, the model may fail to fully learn the complex characteristics of the sintering process, resulting in inaccurate predictions or overfitting. Third, many data-driven methods, particularly deep learning, are “black box” models, meaning that they are difficult to interpret and understand. In industrial applications, engineers typically want to understand and control the decision-making process of the model. In the sintering process, data-driven models may not provide sufficient transparency, making it challenging to integrate them with traditional engineering expertise, thus reducing the model’s operability. Fourth, in practical production, raw materials and operating conditions frequently change. A model trained under specific raw materials and operating conditions may perform poorly when faced with new raw materials or conditions. In the sintering process, variations in ore composition, particle size, or moisture content can cause data-driven models to make biased predictions regarding sintering outcomes, especially if the training data does not cover all possible raw material combinations.

To address these challenges and enable data-driven methods to adapt to a broader range of industrial applications, the following strategies can be employed: First, perform in-depth feature engineering by selecting features closely related to the sintering process, such as ore composition, particle size distribution, heating rate, and moisture content, and use them as input features for the model. Through data analysis and domain knowledge, key features that significantly influence the sintering process can be identified and extracted. Second, increase the number of sensors and monitoring devices to improve the frequency and accuracy of data collection. Installing real-time monitoring equipment, such as temperature, humidity, and gas composition sensors, during the sintering process will provide more high-quality training data. Data cleaning and preprocessing can be used to remove or correct anomalous data, while data augmentation techniques can simulate and generate new data to compensate for the lack of data in actual production, thereby enhancing the model’s ability to adapt to different operating conditions and raw materials. Third, choose machine learning algorithms with a certain level of interpretability, such as decision trees or random forests, which can provide a visual representation of the decision-making process. This helps engineers understand the model’s behavior and facilitates the integration of the model with practical operational experience. By combining data-driven models with expert knowledge, operational rules or optimization strategies that meet industrial needs can be derived, allowing for a better integration of data-driven predictions with traditional engineering expertise to support decision-making. Fourth, through incremental learning, the model can continuously receive new data and update itself during production, adapting to changes in raw material proportions and operating conditions. Transfer learning can be applied by leveraging pre-trained models developed for specific scenarios, enabling rapid adjustments to new environments or conditions. This approach allows for fine-tuning existing models based on different raw materials and operating conditions, reducing the need for extensive training data.

5. Summary and Prospect

In recent years, substantial advancements have been achieved in the modeling and prediction of the sintering process, particularly in improving process efficiency, optimizing energy utilization, and achieving green production. The research has primarily focused on the prediction of sinter ore composition, $BTP$ forecasting, carbon efficiency optimization, and the modeling of key performance parameters, resulting in a variety of innovative methods and technological applications. Overall, the research on sintering process modeling and prediction has evolved from data fusion and feature extraction to dynamic optimization, gradually achieving an integrated approach that combines machine learning with industrial mechanisms. Through dynamic operational condition classification, model optimization, and soft-sensing modeling, these studies have provided crucial technical support for the intelligent control of the sintering process, energy utilization optimization, and low-carbon production.

5.1. Problems

Currently, the modeling of the sintering process primarily adopts a data-driven approach. The typical workflow involves obtaining actual production data from the sintering plant, followed by data preprocessing such as anomaly detection and correction. Afterward, feature engineering is performed, and models are selected either based on operational condition identification or through direct modeling. Below are some potential issues that may arise:

• Data limitations affecting prediction accuracy. One of the key challenges of data-driven modeling methods lies in the necessity of having sufficient training data to train the model. In turn, machine learning techniques based on data-driven approaches are used to construct and design the prediction model’s structure and parameters. While data-driven models perform well in predicting the sintering process, when labeled data is difficult to obtain, traditional supervised data-driven models fail to achieve the desired prediction accuracy.
• Insufficient consideration of real-world sintering conditions. Existing models for the sintering process often fail to adequately account for the multi-parameter, nonlinear, time delay, strong coupling, and multi-condition characteristics of the sintering process. These complexities make it difficult to develop accurate models. Additionally, a single modeling approach may not yield high-precision prediction models for all indicators, highlighting the limitations of conventional methods in capturing the full complexity of the process.
• Time asymmetry between process influencing factors impacting model accuracy. The sintering process is a continuous, long-duration industrial production process, where iron ore powder undergoes steps such as mixing, granulation, distribution, and sintering, taking approximately one hour to complete. The parameters that need to be predicted during the sintering process are closely related to prior process parameters. For example, in the prediction of carbon efficiency, factors like carbon ratio and moisture content influence the carbon combustion trajectory in subsequent sintering materials, which in turn affects the composition of the exhaust gases. As process parameters are detected simultaneously in the sintering process, but there is a time difference-referred to as time asymmetry-between the various parameters influencing the sintering process at any given moment, this creates modeling challenges and negatively impacts the accuracy of the computational models.

5.2. Prospects

The modeling technology for the sintering process has advanced to a new level, achieving some successes in practical applications. However, several challenges remain, such as the complexity of process coupling and the difficulty of calculation, the inability to fully incorporate all characteristic evaluation factors into the model, incomplete data for model updates, and the inability of simulation calculations for specific problems to meet actual research needs. With the continuous upgrade of computer networks and industrial information technologies, big data and intelligent sintering production have become crucial components of future innovations in intelligent manufacturing. The following points may serve as directions for improvement in steel sintering process modeling:

• Incorporating more methods into data-driven models. In recent years, large models have been rapidly developed. By leveraging the powerful data pattern discovery capabilities of these models, it may be possible to predict certain parameters that are difficult to measure or forecast.
• Fully considering the actual conditions of sintering production. Most studies on energy consumption modeling in the sintering process have treated various process parameters at different time scales as inputs to energy consumption models. However, these studies have not adequately accounted for the diverse operating conditions and time delays characteristic of the sintering process. A single modeling approach cannot achieve high-precision prediction models for all indicators. Therefore, research on hybrid modeling methods, combining multiple models, multi-level structures, and intelligent modeling techniques across different time scales, is needed. This represents a new approach to achieving high-precision prediction of sintering energy consumption.
• Considering multiple objectives in operational parameter settings. In actual sintering production, operational parameters must not only meet the demands of a single objective but also ensure smooth production and guarantee the quality and yield of sintered ore. With the flourishing development of multi-objective optimization algorithms, the next step will be to consider both the constraints of smooth production and the uncertainty of state parameters under multi-level and multi-objective conditions. Research will focus on intelligent optimization techniques for the global carbon efficiency optimization of the sintering process, as well as the optimization of raw material parameters and operational settings, based on advanced multi-objective optimization algorithms.
• Integrating the model into the real-time control system can significantly enhance operational efficiency. By combining the hybrid model with the real-time control system, it is possible to predict key parameters such as carbon consumption and gas emissions at various stages of the sintering process. These predictions can then be used to adjust operational parameters of the sintering equipment in real time, such as temperature, airflow rate, and raw material proportions. This predictive feedback control approach effectively prevents energy waste and improves the overall efficiency of the sintering process. Moreover, integrating the data-driven hybrid model with an expert system enables adaptive adjustments to complex operating conditions, enhancing the intelligence of the system while building upon traditional control systems.