Development of a Self-Updating System for the Prediction of Steel Mechanical Properties in a Steel Company by Machine Learning Procedures

Abstract

This study is focused on the implementation of statistical learning methods for the prediction of the mechanical properties of steel products from the chemical profile of the raw material and the process parameters. The integration of this model into the production process allows a large-scale steel industry to predict steel properties with heightened accuracy, optimizing the manufacturing process for minimal waste and improved consistency. A workflow for process data analysis has been developed, based on the use of machine learning algorithms to build an interface for data treatment to be directly used online. The proposed approach has a comprehensive connotation, starting from data pre-treatment and cleaning, to model building and prediction. Different machine learning algorithms are compared (Polynomial Regression, LASSO, Random Forests and Gradient Boosting, ANN, SVM, and k-NN), to provide the best predictive ability, also exploiting human reinforcement. The results proved to be very promising for all the types of steel investigated, with very good RMSE and R² values both in fitting and in prediction. The application here presented is being integrated into Total Quality Tutor (TQT) software, developed in-house in C# language, for predicting the mechanical properties of steel.

1. Introduction

In the flat rolled steel industry, addressing the costs of scrapping non-compliant material and losing competitiveness due to quality or process issues is a key challenge. When a material does not meet required standards, the economic consequences can be substantial. Material rejection involves not only the direct loss of product, but also of all investments in terms of energy and labor used. Furthermore, the need to manage rejected materials, both through disposal and recycling, introduces additional logistics and treatment costs.

Reducing production efficiency is another critical aspect. Any interruption in the production process due to non-compliant material implies downtime, which translates into a decrease in the operational efficiency of the production line. This downtime not only slows down production, but can also cause delays in deliveries to customers, damaging the company’s image in the market. Customers look for reliable suppliers who guarantee consistent quality products. Furthermore, the need to repeat production processes to replace discarded materials implies consumption of resources and time, increasing the overall cost of the finished product.

Machine learning (ML) is revolutionizing the steel industry, leading to significant improvements in efficiency, product quality, and environmental sustainability, one of the most impactful uses being improving steel quality. Through predictive analytics, ML models are able to predict imperfections in the finished product by analyzing data collected during the production process [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. This allows corrections to be made in real time, reducing waste and improving the product quality. In addition, machine learning plays a crucial role in optimizing production processes [18,19,20,21,22,23,24,25]. By analyzing huge datasets, models can identify patterns and correlations, allowing various parameters (e.g., temperature and cooling rate) to be optimized [18,19,20,21,22,23,24,25]. This not only improves energy efficiency but also helps to reduce the production costs. Predictive maintenance is another area where machine learning finds application in the steel industry [26,27,28]: analyzing data collected from sensors installed along the process, ML models can predict failures or malfunctions before they occur. On the front of sustainability, modeling the data on energy consumption and CO₂ emissions, it is possible to suggest changes to production processes that reduce the carbon footprint [29,30]. Finally, through advanced analytics, the recycling of steel and waste materials can be optimized [31,32], reducing dependence on raw materials and promoting a more sustainable production model.

Offline mathematical analyses and computational simulations are traditionally used to predict many types of steel properties, but it is generally difficult to convert them to online applications unless a simplification of the models is performed, thus compromising accuracy [33]. Moreover, they fail in the processing of large and complex datasets, like the ones coming from modern industrial production processes [34]. On the other hand, machine learning methods are able to establish connections between performance and patterns, capturing effective information from the input data and finding nonlinear relationships between those and the output(s) [33,35,36], even in case of complex and highly dimensional datasets, by also offering proper optimization techniques which allow to maximize the prediction performance and, at the same time, find the best hyper-parameters’ values of, and the number of, original variables to use to train it [33].

The present study was conducted at the Acciaierie d’Italia facility in Novi Ligure (Italy). In pursuit of enhanced efficiency and quality in steel production, the industry is increasingly adopting predictive modeling techniques. The aim of the study is the implementation of statistical learning methods, to analyze historical process data, and to identify patterns indicative of the mechanical characteristics of steel. The integration of this model into the production process allows a large-scale steel industry to predict steel properties with heightened accuracy, optimizing the manufacturing process for minimal waste and improved consistency. Designed to process extensive industrial datasets, the proposed workflow applies different statistical models to forecast key steel properties like tensile strength, ductility, and hardness. These predictions are vital for producing steel that meets rigorous requirements across various applications, from construction to automotive. The paper delves into the algorithm’s design specifics, including feature selection, model training on historical data, and validation of its predictive accuracy. Additionally, it discusses the practical implications of implementing this algorithm in an industrial setting, underscoring the potential for enhanced product quality, cost savings, and increased competitiveness in the steel industry.

The manuscript outlines the goal of developing a machine learning model for steel property prediction. It highlights not only the ability to predict mechanical characteristics, but also its proactive application in optimizing manufacturing parameters. Unlike existing industry standards, which mainly focus on real-time monitoring or post-production assessment, the model aims to innovate by providing actionable insights before production begins. This approach improves process control, allowing manufacturers to adjust parameters such as annealing temperatures to prevent non-conformances.

2. Materials and Methods

2.1. Steel Production Plant and Data Storage

This work was carried out in the Acciaierie d’Italia (A.d.I., Italy), arranged in different production units located in Italy, in particular in Taranto, Genova, Novi Ligure, Racconigi, and Marghera. The present study was conducted in the plants located in Taranto, where the hot rolled coils are produced, and in Novi Ligure, devoted to the finishing of the product.

The production cycle begins with the extraction of iron ore, which is crushed, ground, and finally cleaned of impurities through magnetic or gravitational separation, flotation, screening, and thermal processes such as drying, calcination, and roasting. These processes prepare the ores for smelting in blast furnaces, where pig iron is produced with a carbon content ranging from 2.06% to 4%.

At the Taranto plant, the blast furnaces operate through a charging system with alternating layers of ore, metallurgical coke, and limestone, introducing high-temperature air produced by cowpers, i.e., heaters that recover the heat from the blast furnace gasses. The hot coke reduces the iron ore producing liquid pig iron, which is collected in the blast furnace crucible. These melting and tapping cycles, which last over six hours, allow a continuous process to be maintained until the refractory lining of the blast furnace needs to be replaced.

The liquid pig iron, with a still high carbon percentage (usually >4%), is transferred to the converters where decarburization occurs. In this phase, carbon reacts with oxygen to form carbon dioxide, in a process that reaches temperatures close to 1750 °C and is self-sustaining thanks to the exothermic nature of the oxidation reactions of carbon, manganese, and silicon. The liquid steel then follows a path to the steel mill for secondary treatments such as desulfurization and enrichment with elements such as Mn, Cu, Cr, and Ti, as well as removal of inclusions.

Subsequently, the liquid steel is transported in ladles lined with refractory material, poured through refractory tubes into a copper ingot mold cooled with demineralized water, where solidification begins. Solidification continues through secondary cooling, which shapes the steel into the desired final products, which are then processed through a series of hot rollers to give specific shape and dimensions.

Finally, the coils produced are prepared for further cold processing at the Novi Ligure facility, i.e., a cold rolling mill (Figure S1 in Supplementary Information). The existing equipment produces coils of various dimension, thicknesses, and types of coating, which allows for considerable operational and commercial versatility according to the market needs. The hot rolled produced in Taranto are all subjected to thickness reduction at the “Cold rolling plant” stage, a tandem pickling and cold rolling line. Depending on the type of final product, they are directed to different annealing, galvanizing, electro-galvanizing, or aluminizing plants. The coils produced by the plants are then packed and finally shipped throughout Italy and Europe, primarily to customers in the automotive market.

All the production phases are recorded by means of a sequence of numbers as unique identifiers, with coil identifiers for both the input and output stages: steel casting is also recorded. Customer information is provided through codes and names, assuring the customization of the process/product according to the customer’s requirements. Quality and material specifications are carefully noted, including thickness before and after treatment, and width. These data are crucial to ensure that the finished product meets the dimensional requirements. Special attention is given to the mechanical properties of the material, such as Yield Strength and tensile strength: minimum and maximum values are recorded and used to ensure that the material remains within the tolerances. Elongation, anisotropy, and work hardening values are also recorded, highlighting the ductility and structural quality of the steel. The chemical composition (as mass %) of the steel is controlled by the measurement of several elements (C, Si, Mn, N, Ti, Al, Cu, V, Nb, and P), which are critical in determining the final product characteristics (strength and ductility). Critical parameters of the thermal process (heating phase and temperature maintenance) are monitored, indicating accurate control over this critical step that can significantly affect the microstructure of the material. Process speed and force, applied during rolling, are also recorded to optimize the process and ensure uniformity of the finished product. Finally, thickness reduction and speed for each rolling group are tracked to ensure that each step in the process correctly contributes to the final desired shape and technical grade for the material. Taken all together, these data provide a complete view of the rolling process and are vital to maintaining high production standards and making continuous improvements to the process.

2.2. Steel Products

The work involved different types of steel products:

• -. Interstitial Free (IF) steels, characterized by the almost complete absence of carbon and nitrogen (<0.005 ppm) in a solid solution. This is achieved by the addition of Ti or Nb that bind with C and N. The absence of these interstitial elements makes the steel extremely ductile and easy to work with, and particularly suitable for deep drawing or bending. IF steels are often used in the automotive industry for components that require good cold formability.

• -. High Strength Low Alloy (HSLA) steels, designed to offer high mechanical strength and greater resilience. This is achieved through the precise addition of small amounts of various alloying elements such as V, Nb, Ti, and Mo, which improve the strength and toughness of the steel without significantly increasing its weight. HSLA steels are used in a variety of structural applications, including building construction, bridges, oil and gas pipelines, and in the automotive and marine industries.

• -. Low Carbon Steels (LC), contain a low percentage of carbon (typically <0.1%), which makes them softer and more ductile than high-carbon steels. They are easily worked with and welded, and they are suitable for a wide range of applications, including metal fabrication, automotive components, tubing, and generally where bending, forming, and welding is required. Although they offer good formability, they have lower mechanical strength, which can be increased by hardening processes (e.g., quenching and tempering).

These types of steels are regulated under different UNI EN standards, which may include, but are not limited to, UNI EN 10130 [37], UNI EN 10268 [38], and UNI EN 10346 [39].

2.3. Modeling Strategies

Figure 1 represents the workflow for modeling and predicting the mechanical properties of the final material adopted in this study. The workflow can be described in different steps:

• (1). Data collection. All process data are collected using automation systems and continuous online monitoring. These data are produced on a production basis, for each coil, and by collecting measurements like every 10, 100, or 500 m of produced coils. The Quality Laboratory therefore determines the mechanical properties of the products (Yield Strength, tensile strength, and elongation). During this phase, the chemical analysis of the input steel casts from the Taranto plant are also carried out. Data from the Taranto and the Novi Ligure plants are therefore synchronized to form a global database.

• (2). TQT development. An online platform (Total Quality Tutor—TQT) is developed and complemented by a series of multivariate methods, from exploratory data analysis to predictive model calculation and production management. The TQT system is developed as a modular interface able to manage all the different steps of data analysis in an automatic way.

• (3). Data pre-processing. The data collected first undergo a pre-processing including data verification and clean-up, involving the identification and elimination of possible duplicates and outliers. The number of records is in the range of 5000/10,000 units. A preliminary exploratory data analysis is carried out by Principal Component Analysis (PCA) [40]. In the case outliers are detected, classification methods are applied to identify the reasons. Data are then split into training, test, and production sets: genetic algorithms are applied at this level for samples and variables selection, to increase the subsequent model’s reliability.

• (4). Predictive models. Models are trained for predicting the quality of the final product from the input features (chemical composition) and the process parameters; several modeling procedures are compared: Support Vector Machine (SVM), LASSO Regression, Random Forest, Gradient Boosting Machine (GBM), k-Nearest Neighbors (k-NN), Polynomial Regression, and Neural Networks. The modeling method providing the best results in prediction is selected.

• (5). New productions: prevision of mechanical properties and process parameters. The best model is then used for predicting the mechanical properties of new productions and, by inverse prevision, for predicting the optimal process settings to achieve target mechanical properties.

• (6). TQT update and human reinforcement. Once a new coil is produced, its experimental mechanical properties, together with its input-material chemical profile and the process parameters used for its production are fed back to the TQT system to enrich the database. In this phase, human reinforcement is also applied to improve the model’s performances.

• (7). New productions: prevision of the intended use. Raw coils are delivered from the Taranto plant accompanied by their final intended use, but this often is not the most proper use since the characteristics of the different final commercial products usually overlap. A procedure is therefore applied to identify the best commercial intended use for each coil, based on classification approaches.

Figure 1

General strategy with input/output variables.

[Figure omitted. See PDF]

The input data X (light green block in Figure 1) are listed hereafter (the labels used in tables and graphical representations are given in parentheses together with the unit of measure).

X variables include data from the casting process analysis, in particular the chemical composition, based on:

• -. Content, expressed as mass %, of: C, Si, Mn, P, S, Cr, Nb, Al, Ti, Cu, V, N, Ni, and Mo.

• -. Carbon equivalent calculated as according to the International Institute of Welding (IIW) and to the Ito–Bessyo formula (C_IIW, C_IBF).

• -. Ti content: Ti equivalent (TI_EQ) and free Ti % (TI_FR).

• -. Ratios and sums of specific elements: Ti/Al (TiAl), C + N (CN), Mn/S (MnS), and B/N (BN).

X variables also include process measurements along the lines of cold rolling and hot galvanizing:

• -. Measurement of thickness, width and their reduction, at different stages along the line (all expressed as mm): thickness reduction (TR), black and exit thickness (BLT, EXT), strip width (SWI), reduction % at stands G0–G4 (RG0, RG1, RG2, RG3, RG4), entry thickness at stand G0 (ENTG0), thickness reduction between stands (TRG01, TRG12, TRG23, TRG34), and exit thickness at stand G4 (EXTG4).

• -. Measurement of speeds: line speed (LS, m/s), speed at stands G0-G4 (SG0, SG1, SG2, SG3, SG4, m/min), process speed (PROC_SPD, m/min).

• -. Forces (expressed in N if not otherwise specified): slip force (SF, kg/m²), rolling force at stands G0–G4 (FORCE_G0, FORCE_G1, FORCE_G2, FORCE_G3, FORCE_G4, kN), entry pull between different stands (PULL_ENT_G0, PULL_G0_G1, PULL_G1_G2, PULL_G2_G3, PULL_G3_G4, PULL_EXIT_G4), hot bridle tension (HOTBRIDLE, -), force at skin pass (SKP_FORCE), total skin pass effect (SKP_ALL, -), total tension leveler effect (TLV_ALL, -), pull at dansroll (DANS_PULL), pull at heating zone (HEAT_PULL), pull at soaking zone (SOAK_PULL), pull at tunnel zone (TUNN_PULL), entry and exit pull at skin pass (ENT_SKP_PULL, EXIT_SKP_PULL), and entry and exit pull at tension leveler (ENT_TLV_PULL, EXIT_TLV_PULL).

• -. Bending, positions, roll diameters: bending at stands G0-G4 (BEND_G0, BEND_G1, BEND_G2, BEND_G3, BEND_G4, %), roll position at stands G0-G4 (POS_G0, POS_G1, POS_G2, POS_G3, POS_G4, mm), and work roll diameter at stands G0-G4 (WR_DIA_G0, WR_DIA_G1, WR_DIA_G2, WR_DIA_G3, WR_DIA_G4, mm).

• -. Saturation degree at stand G0–G4 (DOS_G0, DOS_G1, DOS_G2, DOS_G3, DOS_G4, -).

• -. Temperatures (expressed as °C if not otherwise specified): annealing, heating and soaking temperatures (AT, HEAT, SOAK), and total furnace effect (FURN_ALL, -).

The output data Y (light blue block in Figure 1) are the mechanical properties of the material:

• -. Tensile strength (Rm, MPa), i.e., the maximum stress a material can withstand before breaking during a tensile test. This parameter is crucial to understanding the ability of a material to withstand extreme stresses and is used to select materials suitable for specific structural applications, where high mechanical strength is required.

• -. Yield Strength (Rp02, MPa): It indicates the stress below which a material elastically deforms. This value is critical in determining the safe operating limit of a material in engineering applications, ensuring that in-service stresses remain below this threshold to avoid permanent deformation.

• -. Percentage of elongation at break (ALL): It measures the plastic deformation undergone by the material before failure. It provides valuable insight into the ductility of a material, that is, its ability to undergo significant plastic deformation before fracturing.

The data collected from both the casting analysis and the manufacturing process measurements are aggregated into a dataset, including both historical (last 2 years) and current data, used to train and test the models. The database on which the study was carried out comprised 8275 records (samples) described by 82 X-block variables and 3 Y variables.

2.4. Online and Offline Measurements

2.4.1. Sensors and Online Data Acquisition

Sensors, placed in different points of the rolling mill, provide the continuous measurement of different properties: thickness, width, tension, temperature, and others. Thickness sensors (X-ray based IMS 578_OS sensors) continuously measure the thickness of the laminates as they pass through the rollers. Similarly, width sensors ensure that the width of the material remains within specified tolerances set for the different types of steel. The measurement of the strain of the material during the rolling process is crucial to prevent deformation or breakage, while the measurement of the temperature is important for maintaining desired mechanical properties.

Once collected, data are transmitted in real time to the rolling mill control systems that automatically adjust the process parameters (roller pressure, rolling speed, and temperature), ensuring the maintenance of specified properties of the material and reducing the risk of defects. Data are also stored for future quality control purposes, and for the continuous improvement of the rolling process, allowing the identification of areas of inefficiency or potential innovation.

2.4.2. Determination of the Elements in the Iron Alloy

C and S in steels are determined by thermo combustion [41]. The steel sample is burned in a HF-400 furnace of a LECO CS-444 system (Leco s.r.l., Milan, Italy) at 1500 °C, in the presence of pure oxygen, to transform C and S into CO₂ and SO₂, respectively. The gases are then transferred to the IR detector by O₂ at 35 PSI. For the determination of other alloying elements (Si, P, Mn, Ni, Cr, Cu, Mo, V, Ti, B, Nb, Al, N), a spark quantometer ARL 360 (Thermo Scientific, Milan, Italy) is used.

2.4.3. Tensile Tests

The tensile tests are performed in accordance with UNI EN ISO 6892-1:2020 [42]. This test allows the evaluation of tensile strength, Yield Strength (Rp02), elongation after failure, and area reduction. Steel samples are cut in rectangular cross-sections of 20 × 20 mm. The tensile tests are carried out on a V5T9 system (Galdabini, Italy), applying an axial tensile force of 100 kN until the sample breaks. A tension–strain diagram is recorded from which the different parameters are calculated. During the test, the load is increased gradually as defined in UNI EN ISO 6892-1 2020.

2.5. Workflow

The workflow adopted in TQT for data analysis and model building was developed in R-code [43] and is reported in Figure 2. The single phases are described in detail in the next paragraphs and are usually applied using the samples of each class separately.

The heart of the procedure is represented by a variable selection procedure based on genetic algorithms [44], coupled to different modeling strategies, ranging from linear models to complex procedures such as artificial neural networks and Random Forests, each with unique strengths in modeling data relationships. This ensemble approach enhances prediction accuracy and provides model uncertainty, crucial for steel production risk assessment and decision-making. Genetic algorithms excel at identifying influential factors affecting steel properties and their iterative evolution balances model complexity and predictive accuracy. Employing diverse modeling approaches instead allows one to capture the multifaceted structure of the data.

The modeling step is preceded by a first step of data filtering and mining aimed at: (i) identifying and eliminating outliers; (ii) investigating data distribution; (iii) evaluating the correlation between the variables; and (iv) performing pattern recognition. Hereafter, each step is described in detail.

2.5.1. Step 1: Dataset Loading and Outlier Removal

Outliers are removed exploiting the Median Absolute Deviation (MAD) method [45] (details in Section 2.6.1), with a 3.5 threshold. The function calculates an outlier score for each entry of the dataset and for each X-block variable and identifies rows that are considered outliers for at least three X variables contemporarily; the outliers are then removed and stored in a separate dataset called “Data-out”, while the non-outlier samples are contained in the “Data-in” dataset.

A Linear Discriminant Analysis (LDA) [40] is then used as a classification method to investigate the causes for data exclusion from the dataset. The Data-out dataset is investigated to provide a list of X-block variables affected by values exceeding the threshold and their corresponding occurrences. Then, a number of non-outlier samples, equal to the number of detected outliers, is randomly sampled from the Data-in, to ensure a balanced comparison. For both outlier and non-outlier groups, summary statistics are calculated for each variable (average, median, and standard deviation) to allow a first investigation. The results provided by LDA, in particular the weight of each X variable on the first one or two discriminant functions, are recorded for further investigation. In the case where the number of identified outliers is less than half the number of X variables, LDA is not computed and the comparison between outliers and non-outliers is made just through basic statistics.

The subsequent steps are calculated on the Data-in dataset only.

2.5.2. Step 2: Exploratory Data Analysis

The distribution of each response variable (Y) is examined by means of a histogram and the correlation matrix considering both the Y and the X-block variables is also generated. A Principal Component Analysis (PCA) is performed on the dataset, after autoscaling, including the X-block variables only. PCA is used for data visualization and pattern recognition, i.e., the identification of groups of samples and/or variables.

2.5.3. Step 3: Dataset Splitting and Use of Genetic Algorithms

The Data-in dataset is randomly divided into three parts: training set (Data-tr, 70% of Data-in), test set (Data-ts, 15% of Data-in), and production set (Data-pr, 15% of Data-in). Z-score normalization is applied, using the average and standard deviation calculated on the training set.

Genetic algorithms [44] are used to further select samples and variables (features) in the training set. Since the ranges of acceptance of steel are quite wide, the selection of the best sample set for model building is fundamental to obtain models trained on the most reliable productions. The selection of variables is necessary because each type of steel and each process influences them differently. For example, IF steel is very sensitive to variations in carbon content and annealing temperature, unlike low C steel, which is less affected by changes in these two parameters. Therefore, it is essential to create models under the best possible conditions, including variables that truly impact the final result.

The first genetic algorithm is aimed at the selection of the samples: in this case the population size is set to 100, indicating the number of potential solutions evaluated per generation, each solution being a group of nBits selected samples, where each solution is represented as a binary vector of length nBits, with each bit indicating the inclusion (1) or exclusion (0) of a specific sample from the dataset. The length of the vector, nBits, is determined by the number of rows in Data-tr, which represents the number of samples used in the selection process. The first GA was trained with a crossover probability of 0.7 and a mutation probability of 0.3. The algorithm stops after 500 iterations or earlier upon convergence, monitored through a custom function, designed to track whether the GA is improving its fitness values over successive iterations: GA stops if the fitness value has not improved (decreased) for ten consecutive iterations. The fitness values are based on the mean squared error (MSE), calculated in 5-fold cross-validation, of a linear model containing all the X-block variables. A check is present on the number of selected samples: no more than 20% of the samples can be eliminated.

The second genetic algorithm focuses on variable selection, using the same parameters as the first one (population = 100, crossover probability = 0.7, mutation probability = 0.3, 500 maximum iterations) and a fitness score based on the mean squared error (MSE) in 5-fold cross-validation that has to be minimized. In this case, each chromosome consists of nBits genes where each gene represents the presence (=1) or absence (=0) of each variable in the model; therefore, nBits has length equal to the number of X-block variables.

2.5.4. Step 4: Models Training and Best Model Selection

Several modeling strategies are compared and each type of model is optimized independently. The modeling strategies selected in the study were aimed at covering different approaches, mainly belonging to three main groups: regression models, coupled or not to penalty strategies (Polynomial Regression, LASSO, SVM, and K-NN), methods based on decision trees (Random Forests, Gradient Boosting), and soft computing (artificial neural networks). The three types of strategies differ in the computational effort they require and in the complexity of the models they provide, and of the situations they can model. Regression models with or without penalty strategies allow us to obtain models that can be interpreted through the coefficients of the parameters included in the models and represent less time-demanding strategies, however they can be lacking from the point of view of modeling the experimental reality if it is characterized by a high complexity. Soft computing systems such as artificial neural networks can effectively model complex and nonlinear realities; on the other hand, they are difficult to interpret and require large amounts of data and computational effort. Methods that instead rely on decision trees can be placed in between: they provide information that can be interpreted by the operator but at the same time they can model complex situations and are also time demanding.

Hereafter, details about each modeling strategy are provided, while the theoretical aspects are described in Section 2.6. For each modeling strategy, the parameters affecting the final results have been optimized; where more than one parameter has to be optimized, different levels are selected for each and all possible combinations of the parameters have been tested to identify the best settings. The ranges of each parameter have been selected to guarantee a good compromise between exploration of the combinations and the computational effort. Hereafter, details of each modeling strategy are provided:

• -. Back-propagation artificial neural networks (ANN) [46]. The number of hidden layers was studied at three levels (between 1 and 3) and the number of neurons in each hidden layer at 5 levels (between 1 and 5): all possible configurations were tested. The network also employs two threshold values, 0.1 and 0.05, used alternatively. The learning rate varied between 1.2 and 0.5.

• -. Polynomial modeling [47]: a linear model including all X-block variables and their squared is used.

• -. LASSO [48]. A linear model containing all the X-block parameters is considered; the model is optimized by varying the λ parameter from 0.01 to 0.5 with a step of 0.01.

• -. Random Forest [49]. The optimization is carried out by studying the number of variables randomly sampled as candidates at each split in a range from 1 to the number of columns in the training set minus 1.

• -. Gradient Boosting Modeling [50]. In this case, 3 parameters are optimized: the depth of each tree (from 1 to 5), the number of trees (50, 100, or 150), and the learning rate (0.01, 0.05, 0.1). The minimum number of observations in each node is set at 10. All the combinations of the 4 parameters are tested.

• -. SVM regression [51,52,53]. This model uses a radial basis function (RBF) kernel. The optimization was carried out on two parameters: the cost parameter, C, and the kernel parameter, σ, at five levels (0.01, 0.1, 1, 10, 100). All possible combinations of the two parameters were tested.

• -. k-NN [54]. The number of k nearest neighbors considered in the prediction process was studied from 1 to 15 with step 2. The outcome is based on the average value calculated for the k nearest neighbors.

All the models are optimized by means of R² and RMSE values calculated on the test set, while the best overall model is finally selected according to the results obtained on the production set. In the case of neural networks, the test set is used to stop the training phase.

The best model is then used in two different ways: (i) for estimating the optimal process conditions once the desired mechanical properties of the material are set; and (ii) for re-assigning particular products to the correct steel sub-type by predicting its mechanical properties, particularly important for products characterized by extreme X-block variables, which can be assigned by default to the wrong class (see Section 2.5.6—Step 6).

2.5.5. Step 5: Human Reinforcement

The human reinforcement was applied in this way: (i) all the anomalous values recorded for the mechanical properties and the new coils that are badly predicted by the models are flagged and eliminated from the dataset used for training and validating the models in future; and (ii) samples that in the future present mechanical properties and/or chemical profiles similar to already flagged samples are similarly eliminated from the dataset used for training the models.

2.5.6. Step 6: Prediction of New Productions

When applying the procedure to the production of a coil from the Taranto plant, some issues may arise related to the intended use of the coil indicated by the Taranto plant. For particular applications, some types of steel may show a partial overlap of their chemical profile. The slabs produced at Taranto and delivered to the Novi Ligure plant are accompanied by their elemental profile and the indication of the type of steel they are intended to. Due to the overlapping of the elemental profile of different types of steel, the indication of the type of steel is often not the best possible, thus increasing rework and disposal costs. A preliminary step is therefore focused on the identification of the best type of final product to be achieved from each slab arriving at the Novi Ligure plant, on the basis of its chemical profile. This allows the most effective management of the input material, maximizing the amount of conforming material.

For this particular task, the overall dataset, containing all the steel classes, is split into a training set (75% of the data) and a test set (25% of the data). Then, a Random Forest classification model is built on the training set with the following settings: 500 trees (balancing computational efficiency and prediction accuracy), mtry selects the square root of the total number of predictors at each split, nodesize set to 1 (it allows the trees to grow deeply and model intricate patterns); and maxnodes, left unrestricted (allowing each tree to expand fully until the terminal node condition is satisfied). To assess the performance of the Random Forest model, the test set is used. The final model is used to predict the class for the new production: the three most probable classes for each sample are provided and the Random Forest model is run 3 times with three different training/test sets partitions. The intended use indicated by the Taranto plant is changed only if the three Random Forest iterations predict the same steel class.

2.6. Theoretical Background of the Applied Pre-Processing and Modeling Strategies

2.6.1. Pre-Processing

Outlier detection was carried out by the Median Absolute Deviation (MAD) method [45]. For each variable independently, the median and the absolute deviations of each object from the median are calculated; the MAD is the average of the absolute deviations. Outliers are characterized by absolute deviations from the median higher than MAD*c, where c is a threshold usually set between 2 and 3.5. An object is identified as an outlier if it is considered as such for at least three variables. By changing the threshold value, the sensitivity and specificity of the model in identifying outliers is affected, with a lower value tending to exclude fewer observations (greater inclusiveness) and a higher value making the model more restrictive. A preliminary study was carried out to set the threshold value; experiments were carried out by changing the threshold: (i) in the range [1;2], which represents a less restrictive criterion; and (ii) in the range [3;5], which is more stringent.

The effectiveness in excluding outliers was tested on a reference dataset containing known outlier samples, i.e., observations previously validated as out of standard. It was observed that: (i) the [1;2] range tended not to correctly exclude many outliers; (ii) the [4;5] range, despite having more stringent criterion, incorrectly excluded some valid observations. The best results were obtained with a threshold equal to 3.5 that was therefore selected and maintained for all the calculations. The genetic algorithm (GA) [44] is usually exploited for optimization and selection and is inspired by the natural selection process. It iteratively modifies a population of solutions, where each candidate is defined as a chromosome characterized by a series of genes; in the case of variable selection, each chromosome represents a model, and each gene represents the presence (value = 1) or absence (value = 0) of a variable in the model. The algorithm selects, at each iteration, couples of individuals as parents, from the population, to provide children (evolutionary phase). This phase is driven by the crossover rules, i.e., the way parents are used to provide children, and the crossover probability. Children substitute parents in the current population if they are better. In this way the population evolves over time towards an optimal solution. In order not to focus on local optimal solutions, the crossover alternates with mutation phases, where parents undergo random changes in their genes. This phase is driven by the mutation probability and the way the random changes are applied. The optimization is driven by a fitness function, used to evaluate the quality of a candidate solution (chromosome): in this case a fitness function based on the minimization of the mean squared error (MSE) value in cross-validation was used.

When GA is used for variable selection, each chromosome represents a model with length equal to the number of X-block variables and each gene is a binary value: 1 if the corresponding variable is present in the model and 0 if it is absent. For each model (chromosome) the mean squared error (MSE) on the test set is calculated. The final model is the one with the lowest MSE value. If the MSE value does not improve over five iterations, the GA has converged.

When GA is used for sample selection, each chromosome is a vector of weights, normalized to sum up to 1 and the number of weights must match the number of samples in the training set. The function ensures that at least 80% of the samples have weights above a calculated threshold. If this condition is not met, a penalty is applied. Next, the function creates a linear model using the weighted samples and calculates the mean squared error (MSE) on the test set. If the best fitness value does not improve over five iterations, the GA is considered to have converged.

In general, genetic algorithms proved to be a very effective tool to solve complex optimization problems like feature selection, which has been traditionally performed by employing either filter methods or wrapper methods [55]. In filter methods, the relevance of the predictors is estimated outside of the predictive models and only the predictors that pass a certain criterion are retained. These methods are computationally efficient, but the choice of the variables is not directly related to the predictive performance of the final model; moreover, most filter methods evaluate each predictor separately, therefore redundant (i.e., highly correlated) predictors may be selected. On the other hand, wrapper methods are based on the repeated evaluation of multiple models, either adding or removing one or more variables at each step based on a certain criterion, to maximize the predictive performance and therefore they are more computationally intensive. Another downside is given by the fact that each step is highly conditioned by the previous ones, thus limiting the possibilities of exploring the whole variables’ domain, with the risk of remaining stuck in a local optimum [56]. Instead, with genetic algorithms, many different points (subsets of variables) are selected through random number-generating computation at each iteration, with the best point(s) in the iteration reaching the optimal solution: this approach allows a more thorough exploration of the entire domain and a higher possibility of reaching the global optimum, provided that it has been appropriately implemented [55,57]. Moreover, since the calculation of individual fitness is independent from the other ones, the process can be easily parallelized on a modern multiple-core machine, thus reducing the computational times [56,57].

2.6.2. Modeling Strategies

• -. Artificial neural networks (ANN)

ANNs [46] are inspired by the functioning of the human brain. They are composed of units called artificial neurons, organized into layers: an input layer (with a number of neurons equal to the number of X-block variables), one or more hidden layers (with a number of neurons to be optimized), and an output layer (with a number of neurons equal to the number of Y variables). Neurons in one layer receive the input from the previous layer, weight the information received by each neuron and combine it, and finally transfer it through a transfer function (e.g., sigmoid, ReLU, etc.) to neurons in the next layer. In particular, back-propagation (BP) ANNs [58] are used for regression purposes when complex nonlinear relationships are present in the data. Back-propagation (BP) is a fundamental algorithm used to train neural networks by adjusting the weights of the connections between neurons to minimize the error in the network’s predictions. The process begins with a forward step, where input data are passed through the network, layer by layer, until the output is produced. The difference between the predicted output and the actual target value is then calculated using a loss function, which measures the error. The error is then back-propagated to update the weights in order to reduce the error, according to the following equation:

(1)${\Delta w}_{new}=\eta {\displaystyle \frac{\delta \epsilon }{\delta w}}+\mu \cdot {\Delta w}_{last}$

where η is the learning rate (it controls the size of the change); δε/δw is the gradient of the error ε with respect to the weight w (it indicates the variation in the error with a small weight variation); μ is the momentum (it improves the convergence towards the global optimum); and Δw_last is the change in the weight from the previous iteration.

During the training phase, each sample of the training set is presented to the network and the weights are updated; the training is carried out for a certain number of epochs, an epoch being the presentation to the network of all the samples of the training set. The optimization process involves determining the optimal number of epochs: too few epochs may result in underfitting, while too many epochs may lead to overfitting, where the model becomes too tailored to the training data and performs poorly in prediction. The optimal number of epochs corresponds to the minimum of the error on the test set.

• -. Methods Based on Multiple Regression

Polynomial models [47] extend multiple linear regression by introducing higher order terms, allowing them to consider nonlinear relationships between the variables. Here, polynomial models including quadratic terms were considered.

Least Absolute Shrinkage and Selection Operator (LASSO) [48] is used to perform automatic feature selection by downweighting the coefficients of the variables in the regression model. In this method, a penalty term is added to the residual sum of squares (RSS), which is then multiplied by the regularization parameter λ that controls the amount of regularization applied. Larger λ values increase the penalty, providing a more severe selection.

• -. Methods Based on Decision Trees

Random Forest [49] combines the predictions of several regression trees to improve robustness and accuracy. Each tree is trained on a random subset of the data and features, thus reducing the risk of overfitting. To build a Random Forest, several parameters need to be chosen: (i) the number of trees, usually between 100 and 1000 (a higher number usually leads to better performance as the model averages over more predictions, but increases computational effort); (ii) the number of features considered at each split (limiting the features helps in reducing overfitting and ensures diversity among the trees); (iii) the tree depth, defining the maximum depth of each decision tree (if it is limited, the model is prevented from overly learning specific patterns); (iv) the minimum number of samples required to split an internal node and to be at a leaf node, respectively (they ensure that nodes and leaves have enough data to make reliable decisions); (v) the criterion for measuring the quality of a split (MSE for regression trees); and (vi) bootstrap sampling (for each tree, a random sample with replacement is drawn from the training data). Once all trees are built, predictions are made by aggregating the predictions from all individual trees, using averaging for regression.

Gradient Boosting [50] is another ensemble model that builds decision trees sequentially, where each new tree is trained to correct the errors of the previous one. This method is particularly effective at improving model accuracy by focusing on the data points that are hard to predict. Each tree in the sequence tries to reduce the residual errors of the preceding trees, thus gradually improving the model’s performance. Several parameters have to be selected: (i) the number of trees to be built sequentially (a higher number can provide better performance but increase overfitting); (ii) the learning rate, controlling the contribution of each tree to the final model (smaller values require more trees to achieve the same level of accuracy, but help in preventing overfitting); (iii) the maximum depth of each tree; (iv) the subsample ratio, i.e., the fraction of the training data used to fit each tree (usually between 0.5 and 1); (v) the minimum number of samples required to split a node and to be at a leaf node; and (vi) the loss function (MSE for regression).

• -. Other Methods

Support Vector Machines (SVM) were developed by Boser et al. [59] for classification: they maximize the margin between training data and the decision boundary to identify the optimal hyperplane separating two classes, represented by support vectors. SVM exploits the so-called kernel trick [52,53]: often, it is impossible to linearly separate the two classes in the original system; therefore, data are mapped into a higher-dimensional space by kernel functions where the linear separation is possible. Different kernel functions can be used: linear, polynomial, Gaussian, exponential, and Sigmoid. SVM can also be used for regression, exploiting Support Vector Regression [52]: in this case, a region is defined (tube) around the function that best approximates the function minimizing in the meantime the prediction error. SVR exploits a ε-insensitive loss function (linear or quadratic) that penalizes predictions with errors > ε. Here, a radial basis function kernel is used and two parameters are optimized: the C parameter controls the trade-off between low error on the training set and on the test set, while the σ parameter defines the width of the radial basis function kernel.

k-Nearest Neighbors Regression (k-NN) [54] applies the k-NN principle to regression problems, making predictions exploiting the k nearest neighbor data points and averaging their experimental response. The k parameter, i.e., the number of nearest neighbors, has to be optimized.

2.7. Human Reinforcement

Human reinforcement [60,61,62,63] in the performance of predictive models represents an innovative frontier in artificial intelligence (AI) and machine learning. This approach is based on the premise that, despite significant technological advances, there is still ample room for improvement in predictive models through human intervention. Indeed, humans, with their ability to provide context, interpret ambiguous data, and apply experience-based judgments, can make corrections and optimizations that are beyond the current capabilities of automated systems. Its implementation has applications in a wide range of fields: medicine [64,65], finance [66], cybersecurity, and software engineering [67,68]. This approach brings significant benefits, including reducing bias, increasing the accuracy of predictions, and enhancing the ability of models to generalize from known situations to novel contexts.

However, the effective integration of human reinforcement into predictive models has its challenges, the main issues being related to scalability, since human input requires significant time and resources, and the risk of introducing human bias. Defining strategies for integrating human feedback therefore requires a thorough understanding of both the application domain and machine learning techniques. Here, the interaction between model output and human intervention manifests itself in two main ways: (1) the results produced by the predictive models guide future data collection efforts, highlighting specific areas where existing information proves to be insufficient; and (2) knowledge and experience gained by the Company were used to improve the input provided to the models, thereby refining their predictive ability.

When the models show inadequate performance or unexpected results for certain types of steel, it opens up an opportunity for further investigation. This situation does not merely denote a deficiency in the model but rather signals an area where the available data may not be sufficiently representative or numerous.

2.8. Programming Environment and GUI Interface Development

The GUI interface was developed by Visual Studio 2022 and C# programming language. For the applied algorithms, RStudio was exploited (RStudio 2023.12.0+369) [69] and several R libraries were used:

• -. “doParallel” [70], combined with “foreach” [71], for optimizing processing time by enabling parallelization of computations across multiple processor cores.

• -. “polynom” [72], for creating, manipulating and solving polynomial equations.

• -. As for neural networks, “Keras” [73] provides an interface for neural networks, allowing complex models to be built and trained with just a few lines of code, while “neuralnet” [74] specializes in training and visualizing neural networks with one or more hidden layers.

• -. “readxl” [75] and “writexl” [76] were used to manipulate and export data in Excel format.

• -. “ggplot2” [77], coupled to “gridExtra” [78], “ggfortify” [79], and “GGally” [80], was used for graphical representations.

• -. As for machine learning, “caret” [81] offers a unified interface for hundreds of statistical models, facilitating model training, comparison, and evaluation.

• -. “randomForest” [82], “glmnet” [83], and “gbm” [84] provide efficient implementations of specific algorithms for classification, regression, and boosting.

• -. Feature selection and model optimization were supported by “GA” [85] (genetic algorithms) and “glmnet” [83] (for regularization and variable selection for generalized linear models).

• -. For multivariate analysis, “FactoMineR” [86] and “factoextra” [87] provide tools for data exploration and visualization of factorial analysis, while “missMDA” [88] addresses the problem of missing data in multivariate analysis.

The system was designed to run on platforms with a Microsoft Windows operating system, a choice motivated by reasons of practicality and scalability. Thanks to the internal availability of machines already equipped with Windows, it is possible to easily implement the software to other machines with similar hardware performance, ensuring operational continuity in the event of failures. This choice is accompanied by the internal presence of consolidated tools such as Microsoft Visual Studio for development and Microsoft SQL Server for database management, which ensure smooth and reliable integration.

The structure of the software was designed to maximize flexibility and configurability. Process models and quantities can be easily customized, significantly reducing the work required to adapt the system to different types of plants. This flexibility not only broadens the scope of the software but also makes it a strategic investment for organizations that operate in heterogeneous environments.

In terms of data acquisition, the system supports a wide range of solutions, ensuring adaptability to various operating contexts. It is able to extract information from heterogeneous databases, such as Oracle and MySQL, or receive data via standard communication protocols such as tcp-ip, modbus, opc, and mq websphere. Furthermore, it is possible to acquire manually uploaded or automatically downloaded files, thanks to the use of tools such as Power Automate, or specific applications integrated for Outlook.

The user interface is designed to meet different needs: data can be viewed both through a desktop application and through a web interface. This dual option allows us to easily overcome any difficulties related to the release of the software to users, improving the accessibility and diffusion of the system.

Thanks to these features, the software presents itself as a scalable and highly adaptable solution, able to evolve together with the needs of the organization and to integrate effectively into complex production environments.

This approach is particularly advantageous for different industrial levels, offering significant added value thanks to the software’s ability to predict the mechanical characteristics of steel before production. This functionality allows operators to intervene promptly on the process parameters, optimizing them to obtain results compliant with the required specifications. In this way, not only are costs related to waste and rework reduced, but potential criticalities in the finished material are also minimized, ensuring greater product reliability. This predictive ability not only increases operational efficiency but also represents a strategic tool for improving the overall quality of production, making the system a cutting-edge solution for modern industry, from the optimization of basic processes to the advanced management of complex plants.

Figures S2–S5 in the Supplementary Information show how the data flow works and how the machine learning processes are implemented in the GUI interface.

Moreover, this system, based on iterative learning, does not limit itself to making predictions on mechanical tests, but constantly evolves by updating a table of cases. This table records not only the errors identified autonomously by the system, but also the reports provided by technicians through human reinforcement, creating a continuous cycle of collaborative learning. While monitoring tensile tests on coils and analyzing variations in process data, the system is able to correlate the results with production conditions, identifying recurring anomalies or new deviations from expected behaviors. For example, errors in instrumental data that could go unnoticed in a traditional process are detected by cross-referencing the results of post-production mechanical tests with process parameters. At the same time, any human errors, such as sample exchanges between laboratory tests, are recorded and used to improve validation and control algorithms. The strength of the system lies in its ability to dynamically adapt to the progress of the production process. Thanks to the continuous updating of recorded cases, the system does not require external interventions to remain aligned with variations in production parameters or changes in the treated materials. This allows for the identifying of emerging trends, such as changes in the mechanical characteristics of steels due to changes in raw materials or manufacturing processes. Furthermore, the ability to integrate direct technical reports increases the accuracy of the model, transforming self-learning into a powerful tool for continuous improvement, which not only detects errors, but actively contributes to optimizing the production process.

3. Results

3.1. Dataset and Outlier Removal

The dataset consisted of 8275 samples, separated into different classes of steels as reported in Table 1, LC (in particular LC1, LC5, LC8) and IF steels being the most represented. These samples were described by 82 X-block variables and 3 Y variables.

The developed algorithm was applied to each Y variable separately. Here, we will detail the results obtained for the variable Rp02 (Yield Strength) for the samples belonging to the IF1 class, showing the main steps of the workflow and the outputs provided by the custom-developed software. For the other Y variables and the other classes of steels, only the final results will be shown.

Outliers were detected according to the MAD procedure (Section 2.5.1 and Section 2.6.1): for HSLA steels the % of non-outlier data were always >94% (Table 1); for LC steels the highest % of outliers were recorded for the least represented classes (LC6, LC9); and among IF steels, IF2 recorded the highest % of outliers.

Focusing on IF1 steels, LDA was applied to classify outlier vs. non-outlier samples, randomly selecting a number of non-outlier samples equal to the number of anomalous samples. Figure 3 reports the results provided by the GUI interface: the score of outlier and non-outlier samples on the first discriminant function are reported as a histogram on the x axis (orange for outlier and blue for non-outlier samples).

3.2. Exploratory Data Analysis

After outlier removal, exploratory data analysis is carried out. Figure 4 reports the main results of this phase provided by the custom-developed software on IF1 steels: the distribution of the Yield Strength (Y variable) is shown (Figure 4a). Figure 4b represents instead the correlation matrix including the X-block variables and the Y variable (first row and column): correlations are represented on a color scale from red (−1) to blue (+1) and the correlation matrix allows the identification of the X–block variables most correlated with the Y variable.

PCA is therefore applied on the X-block variables after autoscaling: the % of explained and cumulative explained variance is reported in Figure 4c, while the loading plot of the first two PCs is represented in Figure 4d. Variables in the loading plot are represented as arrows on a color scale from blue (loading close to zero), to red (loading close to one), and the unit circle is also represented: variables close to the circle are almost completely explained by the first two PCs.

3.3. Data Splitting and Sample/Variable Selection by Genetic Algorithms

After outlier removal, the IF1 dataset was split into training (70%, 679 samples), test (15%, 146 samples), and production (15%, 146 samples) sets. The genetic algorithm (GA) was first applied for refining the selection of the sample present in the training set: Figure 5a reports the variation in the RMSE along with the iterations (blue line). The second GA (GA2) was exploited instead for variable selection: its convergence towards the best solution is reported as a red line in Figure 5b.

3.4. Models Calculation and Comparison

The different strategies (Polynomial, Gradient Boosting, Random Forest, k-NN, neural networks, LASSO, and SVM) are then applied for modeling the Y variable on the basis of X-block variables. Each type of model was optimized as described in Section 2.5.4.

Table 2 reports the R², MAE, and RMSE values for the seven models calculated, for the training and the production sets.

Table 3, Table 4 and Table 5 report the results obtained for each type of steel for the best models obtained for each of the three experimental responses (Rp02 in Table 3, Rm in Table 4, and ALL% in Table 5). The models are evaluated through the R², RMSE, and MAE values calculated both in fitting and on the production set, highlighting the models’ effectiveness in real-world scenarios. The tables also report the treatment applied for each type of steel, in particular if they are skinpassed and leveled.

3.5. Human Reinforcement

The human reinforcement was applied in two phases: (i) all the anomalous values recorded for the mechanical properties and the new coils that are badly predicted by the models are flagged and eliminated from the dataset used for training the models in future; (ii) future samples with mechanical properties and/or chemical profiles similar to already flagged samples are similarly eliminated from the dataset used for training the models. Figure 6 reports the improvement recorded after human reinforcement: for each steel class and for each mechanical parameter the % of successful predictions is reported with and without reinforcement. Successful predictions correspond to errors < 5 MPa for Rp02 and Rm, and errors < 0.5 points for ALL%.

3.6. Prediction of New Productions

The built models are used to predict the mechanical properties of new productions and to identify the optimal process settings for achieving target values for the mechanical properties. This step can be accomplished once the intended use of the new coil has been identified. Classification through Random Forest is then used to create a model discriminating all the steel classes based on the historical information on the elemental profile.

When a new coil has to be predicted, the Random Forest model is run three times, and the three most probable classes are provided for each run. The intended use indicated by the Taranto plant is changed only if the three Random Forest iterations predict the same steel class. Table 6 reports the confusion matrix obtained on the test set for one of the iterations calculated.

The diagonal values show the number of correctly classified samples, while off-diagonal values represent misclassifications. Table 7 reports the predictions for three new samples with three different intended uses; for each sample three results for the three runs of the Random Forest algorithm are provided (Run1, Run2, and Run3). As can be seen, the three runs usually provide robust results.

3.7. Application of the Workflow to the Overall Dataset

The workflow was also applied to the overall dataset, including the samples belonging to the three types of steel contemporarily (IF, HSLA, and LC).

Outliers were identified in each class independently, and the data without outliers were then merged. The results on the training and the production sets are reported in Table 8 for the three experimental responses considered.

Figure 7 reports the predicted vs. actual values for the training, test, and production sets for the models reported in Table 8 for each experimental response separately.

4. Discussion

4.1. Outlier Identification

Table 1 shows that the production for the last two years has been characterized by different steel types, LC and IF steels being the most represented. For what regards the identification of the outliers through the MAD procedure, the % of non-outlier samples is usually very high (>92%), the only exceptions being LC9, LC6, IF3, and IF2; in this last case the % of outlier is the highest, about 25% (Table 1).

The comparison of outlier vs. non-outlier samples, identified for IF1 steels by LDA, shows (Figure 3) a very good separation of the two groups of samples: the distributions of the scores of the two groups of samples along the first discriminant direction (LD1) are almost completely separated. The reasons for the separation of the samples in the two classes can be identified looking at the coefficients of the X-block variables on the discriminant function for both groups (outliers and non-outliers): positive coefficients indicate variables that have high values in the corresponding group, while negative coefficients indicate the opposite behavior. The most significant variables for the “non-outlier” group are: the sum of C and N (coeff = 698.03), Nb (coeff = 580.21), V (coeff = 125.59), Cr (coeff = 91.64), and Mn (coeff = 60.74). For what regards the outlier group instead, the most significant variables are: N (coeff = 595.57), C (coeff = 358.14) and C equivalent (coeff = 311.89 and coeff = 222.84), and Si (coeff = 35.86).

These results show that the “non-outlier” group is strongly influenced by a high presence of elements such as niobium, vanadium, and chromium, which improve the mechanical properties and the overall quality of the material. On the contrary, the “Outliers” group is characterized by high concentrations of nitrogen, carbon, and other chemical factors that negatively affect the weldability and performance of the material, leading to a deviation from the quality standards. These results provide a solid basis for targeted interventions aimed at improving the overall quality of the samples.

LDA is used in this context as a tool to identify significant differences between steel samples belonging to distinct groups, such as those defined “ok”, or “not ok”. The main goal is not to attribute a physical meaning to the identified discriminants, but to use LDA to identify anomalies and report samples that deviate from the defined standards. When a sample is classified as “not ok” or has anomalous characteristics compared to historical data, it is recorded in a specific table and reported to the technicians. This report represents a starting point for further investigations into the causes of the deviation, allowing for in-depth analysis of aspects such as production process parameters, chemical composition, or mechanical properties of the material. The system is not limited to immediate reporting but also integrates the results of retroactive analyses: the reported samples are correlated with any detected production criticality. A concrete application example was the reporting of an anomaly related to the concentration of an alloying element in an IF steel: thanks to LDA, it was possible to identify the responsible element and redefine the concentration in the casting sheet.

4.2. Exploratory Data Analysis

In the case of IF1 steels, the Yield Strength (Rp02) shows a quite normal distribution (Figure 4a), indicating the presence of a unique population of samples. For IF1 steels (Figure 4b), the correlation analysis highlights some significant relationships among the studied variables. The strongest correlations, with a value close to one, indicate a high positive relationship between the variables. For example, the correlation between THK_EXIT_G4 and SPESS_USC shows that as the exit thickness of point G4 increases, the final thickness also increases proportionally. A similar behavior is observed between THK_EXIT_G4 and THK_G3_G4, suggesting that the exit thickness is strongly influenced by the conditions in the previous sections of the production line. On the other hand, the weakest correlations reveal a lack of significant relationship between some variables. For example, the relationship between FURN_ALL and RED_G4 shows zero correlation, indicating that the furnace does not impact the thickness reductions in the G4 section. Similarly, the correlation between FORCE_G0 and C_R is also very weak, suggesting that variations in the force applied in the G0 section have little or no impact on changes in the chemical C content.

This analysis provides important insights into understanding the process dynamics. Strong correlations suggest direct dependencies between variables, which could be exploited to improve process control or parameter modeling. In contrast, weak correlations indicate areas where the variables considered have little or no influence on each other, providing insights into which factors could be excluded from further analysis or optimization.

The application of PCA to the dataset shows that the first two PCs account for about 40% of the overall information (Figure 4c). The loading plot of the first two PCs (Figure 4d) highlights how thickness-related variables, such as “EXIT_THK” and “BLACK_THICKNESS”, are closely associated with PC₁ (high negative loading on PC₁ and partial negative weight on PC₂). At positive loadings on PC₁, parameters related to thickness reduction are present. These two groups of variables are obviously negatively correlated to each other. The first PC therefore indicates that this axis primarily represents variations related to the size of the material processed during rolling.

Variables such as “PULL_G4” and “FORCE_G1” show positive loadings along PC₁ and negative ones along PC₂ and show a positive correlation, likely related to tensile dynamics and forces applied along specific sections of the production line.

The second principal component appears dominated by temperature-related variables, such as “FURNACE_TEMP”, and dosage-related variables, such as “DOS_G2”, indicating that PC₂ describes an aspect of the process that is more concerned with thermal control and chemical adjustments than with mechanical or physical material characteristics.

4.3. Samples and Variables Selection by Genetic Algorithms

For what regards the samples selection in the case of IF1 steels, the RMSE was calculated on the test set along with the iterations of the genetic algorithm (Figure 5a). Training data contained 837 samples, while test and production sets contained 279 and 277 samples, respectively. As it can be observed from Figure 5a, the RMSE continuously decreases along with the GA iterations reaching convergence. For IF1 steels, the GA selects 670 final samples in the training set, i.e., the 80.1% of the original samples present in the training set.

For what regards the variables selection for the same class of steels, the second GA (GA2) reached convergence (Figure 5b) and 75 variables were retained over the 82 original ones. The eliminated variables were as follows: Cr_R, Ti_R, THK_G3_G4, FORCE_G0, BEND_G4, POS_G3, POS_G4, DOS_G2, WR_DIA_G4, PULL_ENT_G0, HOTBRIDLE, HEAT_PULL, and EXIT_TLV_PULL.

4.4. Models Calculation and Comparison

The comparison of the models calculated for IF1 steels (Table 2) shows that the worst performances are obtained for Polynomial Regression and artificial neural networks (high RMSE and MAE, and low R² values), indicating limited predictive accuracy. Gradient Boosting and Random Forest provide moderate improvements, with lower RMSE and MAE and higher R², especially on the production set, suggesting better generalization. k-NN and LASSO demonstrate further improvements, achieving lower RMSE and MAE, and higher R² values in both training and production sets, indicating robust performance. SVM stands out as the best-performing model, achieving the lowest RMSE, MAE, and highest R² values in both training and production data. In all the cases the MAE values are lower than the RMSE both on the training and the production sets. However, it is important to note that these are just the metric-based evaluations of the models and do not account for other factors such as computational efficiency, interpretability, or domain-specific considerations, which may also influence model selection.

Table 3, Table 4 and Table 5 report the results obtained for each type of steel for the best models obtained for each of the three experimental responses (Rp02, Rm, and ALL%), evaluated through the R², RMSE, and MAE values calculated both in fitting and on the production set. The values calculated highlight the models’ effectiveness in real-world scenarios. A detailed analysis of the models’ performances reveals that the type of steel and treatment method significantly affects the accuracy of the predictions. Table 3, Table 4 and Table 5 also report the treatment applied for each type of steel, in particular if they are skinpassed and leveled), since steels that have undergone these two treatments show the best performance in terms of lower RMSE and MAE values, particularly in the case of HSLA1 steels.

For LC1, the models generally perform well, delivering robust results for Rp02 and Rm: e.g., Random Forest for Rm achieves good accuracy on the training set, although there is a slight drop in R² for the production set. For ALL%, the Gradient Boosting model proves less effective, with a low R² indicating difficulty in explaining the variance of this property. Nevertheless, the RMSE and MAE values for ALL% remain low, suggesting a reasonable level of precision.

LC5 shows relatively stable results, with Gradient Boosting and Random Forest providing acceptable performance for Rp02 and Rm. However, the RMSE values are relatively high, indicating challenges in maintaining optimal accuracy. For ALL%, the Random Forest model stands out with low RMSE and MAE, even though the R² remains moderate.

For LC6, the LASSO models for Rp02 and Rm provide satisfactory results, with good R² values for both training and production. However, the performance for ALL%, modeled with SVM, is less impressive.

LC8, on the other hand, demonstrates the weakest performance among all steel types. Both Rp02 and Rm show lower R² values compared to other steels, indicating difficulties in accurately predicting these properties. For ALL%, results are also limited.

LC9 emerges as the steel type with the best overall performance, particularly for Rp02. The neural network model for this property achieves very high accuracy, with a high R² on both training and production sets. For Rm and ALL%, the models also provide reliable results.

For steel HSLA1, the Gradient Boosting models perform excellently across all analyzed properties. Specifically, for Rm the model achieves an extremely high R², nearing 0.99 during training and 0.95 on the production set, demonstrating excellent generalization ability. Rp02 and ALL% also show very good results, with R² values exceeding 0.80 on both training and production sets.

In contrast, for HSLA2, the SVM and Random Forest models show more moderate performance. For Rp02 and Rm, the R² is acceptable (around 0.75 for Rp02 and 0.65 for Rm in production), but the model struggles to maintain precision with more complex data. For ALL%, the SVM model shows significantly bad results, with an R² of only 0.41 on the production set, indicating poor representation of the variability for this property.

For HSLA3, the results are mediocre compared to HSLA1. While Random Forest and SVM deliver acceptable RMSE and MAE values, the R² on the production set remains low for all properties, around 0.62–0.65 for Rp02 and Rm, and below 0.50 for ALL%.

For IF1 steel, SVM and the Gradient Boosting models perform well, especially for Rp02 and Rm, where R² values are 0.80 and 0.82, respectively, on the production set. Although RMSE and MAE values are relatively low, results for ALL% show a slight decline, with an R² of 0.78 on the production set. Nevertheless, the Gradient Boosting model for ALL% still maintains a good overall level of precision.

For IF2, performance slightly declines compared to IF1. For Rp02 and Rm, the Random Forest model provides acceptable results, but with R² values of about 0.75–0.81 (production set). For ALL%, the LASSO model performs well during training but drops on the production set (R² = 0.78).

Finally, IF3 stands out for its best overall performance. The Gradient Boosting and Random Forest models achieve excellent results, particularly for Rm, where R² is almost 1 during training and 0.95 on the production set. Rp02 and ALL% also show very good results, with R² values above 0.87 (production set). The extremely low RMSE and MAE values for all properties highlight high predictive precision and excellent generalization ability.

Model performance varies significantly depending on the steel type and the property analyzed. HSLA1 and IF3 emerge as the steel types with the best results, thanks to the high accuracy and consistency of the Gradient Boosting and Random Forest models. On the other hand, HSLA2 and HSLA3 show the weakest performance, highlighting the need for further optimization to achieve more accurate predictions. Overall, Gradient Boosting and Random Forest prove to be the most reliable models, while SVM and LASSO show more variable performance depending on the context. Among the several tested procedures, Random Forest represents by far the most computationally intensive; however, this drawback is counterbalanced by the possibility to model complex relationships. Model complexity can also be effectively addressed by Gradient Boosting and SVM, which are instead low time-demanding. Finally, despite its rapidity, LASSO is selected in a reduced number of cases as the best model since it does not allow us to deal with highly complex datasets.

4.5. Human Reinforcement

Human reinforcement was applied here to improve the sample selection process by the genetic algorithm, specifically targeting the exclusion of outliers. By incorporating human expertise and iterative feedback, the quality and relevance of the samples chosen for the analysis were significantly enhanced. Initially, the algorithm selected a set of samples based on predefined criteria, excluding those identified as outliers. These selections were then reviewed by domain experts, who provided insights and adjustments based on their practical knowledge and experience.

Through iterative feedback loops, the algorithm’s performance was continuously refined. Experts assessed the algorithm’s selections periodically, ensuring that the exclusion of outliers was effective and that the remaining samples were particularly relevant or indicative of the desired outcomes. This collaborative process ensured that the sample pool was not only diverse but also highly pertinent to the specific requirements of the work.

This blend of automated efficiency and human insight created a robust framework that improved the genetic algorithm’s effectiveness. As a result, the algorithm became more focused at identifying optimal samples while effectively excluding outliers, leading to more accurate and reliable outcomes.

Figure 6 shows the improvements achieved by the use of human reinforcement: for all the mechanical properties and for all the steel classes, an improvement in the predictive ability was assessed, particularly for HSLA steels, showing that the models, after reinforcement, were able to provide more reliable results with lower error associated with the predictions.

The comparison between the results obtained without and with (Figure 6) human reinforcement, shows a remarkable improvement in the predictive accuracy of various steel grades after applying human reinforcement, specifically by explaining the model’s incorrect predictions. This intervention allowed the model to “learn” from its mistakes and more accurately adjust its predictions in the second iteration. Initially, the performance across different steels, especially for low carbon (LC) and high-strength low-alloy (HSLA) steels, showed variable degrees of accuracy, with several predictions falling short of expectations. For example, the prediction accuracy for LC1 was 86% for Rp02, 92% for Rm, and only 78% for ALL%. However, after human reinforcement, where the model was informed about its prediction errors and allowed to correct them, these values improved significantly to 89% for Rp02, 94% for Rm, and 92% for ALL%. This indicates that the model was able to refine its predictive capabilities after being taught what it performed wrong.

A similar pattern of improvement is observed in other LC steels. LC5, for instance, initially had moderate accuracy for Rp02 at 72%, while Rm was high at 96%, and ALL% lagged behind at 64%. After human reinforcement, the accuracy for Rp02 jumped to 92%, Rm increased slightly to 98%, and ALL% improved to 90%. This significant increase, particularly in Rp02 and ALL%, demonstrates that by providing the model with feedback on its incorrect predictions, it was able to “learn” from the data more effectively in the next iteration. The model’s improved ability to handle these occurrences suggests that human reinforcement helped it to better interpret the relationships between the features, leading to more precise predictions. In the case of LC5, the improvements were related to lost data in the storage of winding temperatures.

One of the most remarkable improvements can be seen with LC6, where the initial prediction accuracy for Rp02 was just 56%. After applying human reinforcement, this value rose dramatically to 90%. Similarly, Rm and ALL% also saw significant gains. This suggests that explaining the model’s prediction errors helped it understand and account for the complex interactions within the data, resulting in far more accurate predictions in the subsequent iteration.

The IF steels also benefited greatly from the human reinforcement approach. For example, IF1 saw its ALL% prediction accuracy rise from 60% to 91%, while IF2 showed a similar improvement from 56% to 91%. Initially, the model performed better with IF steels due to their more homogeneous nature, but explaining the incorrect predictions further optimized the model’s understanding about how the chemical composition and mechanical properties interact. By receiving targeted feedback, the model could adjust its internal parameters to better align with the specific characteristics of IF steels, leading to much higher accuracy in the second iteration. In the case of both IF1 and IF2, the improvement after human reinforcement was mainly due to lost data on the tensile tests carried out at the laboratory.

The HSLA steels, which initially presented the greatest challenges due to their complex phase structures, also experienced significant improvements. For example, HSLA1 improved from 68% accuracy for Rp02 to 89%, while Rm and ALL% saw similar gains. These improvements suggest that explaining the model’s errors helped it better capture the nuanced phase transformations and mechanical behaviors characteristic of high-strength steels. This refinement was particularly noticeable for HSLA2 and HSLA3, where the initial accuracy was lower, but after human reinforcement, Rp02 accuracy rose to 79% and 80%, respectively. In the case of HSLA1, the improvement was due to lost data in the measurement of the residual magnetic permeability after annealing carried out by the online automatic system.

The underlying reason for these improvements lies in the specific method of human reinforcement used.

This iterative feedback loop allowed the model to refine its understanding of the data, correct its previous errors, and better align its predictions with the actual outcomes. In effect, the model “learned” from its mistakes, improving both its internal feature weighting and its ability to interpret the relationships between the variables.

4.6. Prediction of New Products

When a new coil has to be produced, it is accompanied by an intended use defined by the Taranto plant. To better define the intended use, Random Forest classification is applied: the historical dataset is split into training and test set and the results obtained on the test set are used to evaluate the performance of the Random Forest model. The confusion matrix is reported in Table 6. Some steel types show high accuracy; this is the case of HSLA1 (243 correctly classified samples with minimal misclassifications), IF1 (223 correct classifications with minor misclassifications, as twenty-two samples attributed to IF2 and four to IF3), and IF3 (190 correct predictions and five misclassifications). In some cases, classes show a certain overlap, as for IF2 (partially overlapped with IF3 and IF1) and LC8 (partial overlapping with LC6 and LC9). Other classes show instead an underrepresentation, e.g., LC9, LC5, and LC6. The overall accuracy is high for dominant classes, but refinements are needed for smaller or similar categories to improve classification reliability.

The confusion observed in the matrix is mainly caused by the similarity between the steel types. These steels are often used for the same commercial quality but are tailored for different direct applications. As a result, this slight confusion in classification does not significantly affect the production process. The overlap in classification between these similar steel types is understandable and does not have a meaningful impact on the overall operational efficiency.

The classification model was then used to predict the intended use for three different productions (Table 7): as can be observed, three different runs of the algorithm provide robust results. In these three particular cases, the intended use indicated by the Taranto plant was confirmed.

4.7. Application of the Algorithm to the Overall Dataset

In the case of the application of the workflow on the entire dataset, not focusing on a specific steel type, the results applied on the training set show the good performance of the models, with R² values > 0.75 and RMSE values quite low (Table 8). For what regards the production set, the results appear very promising, with R² values > 0.70 and RMSE values just a little higher than those calculated on the training set, proving that the models can be used for prediction even in the case where the steel class is not defined a priori.

Figure 7 reports the predicted vs. actual values for the training, test, and production sets for the models reported in Table 8, for each experimental response separately. The graphs show the good linearity obtained for all the models notwithstanding the grouping of the samples in the three steel types that can be noticed in most cases. For what regards ALL%, IF steels show the highest values, which are characteristic of this type of product.

5. Conclusions

In conclusion, a workflow for process data analysis in the steel industry has been developed, based on the use of machine learning algorithms to build an interface for data treatment to be directly used online. The proposed approach has a comprehensive connotation, starting from data pre-treatment and cleaning, to model building and prediction, through an automatic procedure. Different machine learning algorithms are compared (Polynomial Regression, LASSO, Random Forests and Gradient Boosting, ANN, SVM, and k-NN), once optimized to provide the models with the best predictive ability. Through the adoption of innovative approaches for the steel industry, such as machine learning and multivariate statistical analysis, we were able to overcome the limitations of traditional methods, providing more accurate and reliable predictions.

The results obtained proved to be very promising for all the types of steel investigated, with very good RMSE, MAE, and R² values both in fitting and in prediction. Moreover, the algorithm shows very good results even when applied to the overall production, including steel samples from different types. The internal variability of IF (Interstitial Free), HSLA (High-Strength Low-Alloy), and LC (Low Carbon) steels significantly affects the elasticity of a mathematical prediction model. IF steels, characterized by an extremely low carbon content and the absence of interstitial elements, have a very uniform microstructure. This homogeneity tends to reduce the variability in the input data, improving the model’s ability to predict mechanical properties such as formability and ductility. In contrast, HSLA steels, which contain alloying elements such as niobium, vanadium, and titanium to improve their strength, introduce greater complexity due to their more heterogeneous microstructure, composed of multiple phases (e.g., bainite, ferrite, and martensite). This structural variability can make the mechanical behavior more difficult to model accurately, requiring more robust and nonlinear algorithms. LC steels, with a moderate carbon content, may present intermediate variability, linked to differences in heat treatment or machining processes. In a mathematical prediction context, such internal differences directly influence the model’s ability to generalize: a dataset that correctly captures these variabilities improves accuracy, while an incomplete modeling may lead to incorrect predictions, especially in extreme stress or strain regimes. Therefore, the choice of the mathematical model must balance the ability to represent the complexity of the material with the need to avoid overfitting due to internal variability. These are the motivations that led the work towards the decision to create sets of different forecasting models for each single steel and type of processing; this allowed us to reach higher fitting and prediction performances.

The models were further refined, above all for what regards the outlier identification, by human reinforcement, proving that the synergy between machine learning and human intervention based on experience can significantly improve the results.

The application here presented is being integrated into Total Quality Tutor (TQT) software, developed in-house in C# language, for predicting the mechanical properties of steel. This integration is a key step toward the development of an online intuitive and accessible platform for the use of predictive models by engineers and technicians in the steel industry.

The integration of models into the TQT will allow users to make predictions about the mechanical properties of steel quickly and accurately, based on data specific to each production. This tool will then be able to serve both for preliminary material design and as a decision support during production, allowing real-time changes to be made to optimize the mechanical properties of finished products.

The system we have implemented has similarities with projects developed in the European Steel Programme [89,90] and with the use of technologies such as 3MA and HACOM [91,92,93], but it stands out for its more preventive approach. While previous systems focused mainly on the online monitoring of the mechanical properties during or after production, our goal is to identify potential problems before the production starts. By integrating our analyses and using the models developed by the TQT system, we can determine the expected mechanical properties of the material in advance, within the limits of the models. This approach allows not only to assess the conformity of the material before processing, but also to proactively act on the process parameters. For example, if the models identify the possibility of non-compliant material properties using standard parameters, it is possible to intervene in real time by adjusting the annealing temperatures or other critical process parameters. This preventive capability represents a significant added value compared to existing systems, which mainly focus on identifying anomalies after the process has already started or concluded. While it is true that there are similarities with previous systems, the goal of TQT is to go further, integrating predictive analysis to anticipate and solve critical issues before they can affect the production, thus ensuring greater efficiency and more rigorous control over the quality of the finished product.

The ultimate goal of our work is to contribute to the creation of a more flexible, efficient, and sustainable manufacturing paradigm in the steel industry, where data-driven decisions and material customization become the norm rather than the exception. Through the continued development and application of sophisticated mathematical models, we can not only improve understanding and control of the mechanical properties of steel but also accelerate innovation in the design and production of high-performance metal components. Additionally, by maintaining an up-to-date database, our models are designed to be self-updating, continuously learning from new data and adapting to changes in production processes.

Author Contributions

Conceptualization, V.Z. and E.R.; methodology, V.Z.; software, V.Z. and D.M.; validation, V.Z. and D.V.; formal analysis, V.Z. and D.V.; investigation, V.Z. and D.V.; resources, V.Z., P.F. and S.M.; data curation, V.Z., D.V., S.C. and E.R.; writing—original draft preparation, V.Z., M.H.B. and E.R.; writing—review and editing, E.R., S.C., M.H.B. and E.M.; visualization, V.Z. and D.M.; supervision, E.R., S.M. and P.F.; project administration, V.Z., S.M., G.P. (Gennaro Papallo), G.P. (Giorgio Porcu) and P.F.; funding acquisition, E.R., S.M. and P.F. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The datasets presented in this article are not readily available because they are they exclusive property of Acciaierie d’Italia S.p.A. Requests to access the datasets should be directed to [email protected].

Acknowledgments

Valerio Zippo expresses a special acknowledgement to Daniele Maestri, David Valenza, Stefano Maggi, Pietro Fossati, Porcu Giorgio, Papallo Gennaro, Sante Pettograsso, Martina De Marco, Eugenia Ghiara, Chiara Rena, Roberto Langiano, Paolo Pollone, Andrea Dario, and Marco Ferrarese for their assistance in the real-world application of the project on the plants.

Conflicts of Interest

Authors Valerio Zippo, Daniele Maestri, Pietro Fossati, David Valenza, Stefano Maggi, Gennaro Papallo and Giorgio Porcu were employed by the company Acciaierie D’italia S.p.a. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 2. Workflow exploited for data analysis and modeling in TQT.

Figure 3. Results of LDA for the comparison of outlier and non-outlier samples in IF1 steels.

Figure 4. Results of exploratory data analysis on IF1 steels: distribution of the Yield Strength (a); correlation matrix of the X- and Y-block variables (b); % explained and cumulative explained variance (c); and loading plot of Principal Component Analysis applied to the dataset (d).

Figure 4. Results of exploratory data analysis on IF1 steels: distribution of the Yield Strength (a); correlation matrix of the X- and Y-block variables (b); % explained and cumulative explained variance (c); and loading plot of Principal Component Analysis applied to the dataset (d).

Figure 4. Results of exploratory data analysis on IF1 steels: distribution of the Yield Strength (a); correlation matrix of the X- and Y-block variables (b); % explained and cumulative explained variance (c); and loading plot of Principal Component Analysis applied to the dataset (d).

Figure 5. Results of the application of genetic algorithms: RMSE variation along with the iterations of the 1st GA used for samples selection (a) and of the 2nd GA used for variable selection (b).

Figure 6. Improvement after human reinforcement: % of successful predictions for each steel class and for each mechanical parameter, with and without reinforcement. Successful predictions: errors [less than] 5 MPa for Rp02 and Rm, and errors [less than] 0.5 points for ALL%.

Figure 7. Predicted vs. actual values calculated for training and production sets and for the best models obtained for Rp02 (a,b), Rm (c,d), and ALL% (e,f). All the best models were calculated with the Random Forest method. Orange = IF; green = LC; purple = HSLA.

Figure 7. Predicted vs. actual values calculated for training and production sets and for the best models obtained for Rp02 (a,b), Rm (c,d), and ALL% (e,f). All the best models were calculated with the Random Forest method. Orange = IF; green = LC; purple = HSLA.

Table 1

Number of samples for each type of steel, their % and the number, and the % of non-outlier samples for each class.

Type of Steel	N° Initial Samples	% Samples Of Each Class	N° Non-Outlier Samples	% Non-Outlier Samples
HSLA	1973	23.83	1909	96.8
Of which: HSLA1	1000	12.08	972	97.2
HSLA2	199	2.40	188	94.5
HSLA3	774	9.35	749	96.8
IF	3000	36.24	2513	83.8
Of which: IF1	1000	12.08	927	92.7
IF2	1000	12.08	758	75.8
IF3	1000	12.08	828	82.8
LC	3302	39.89	3198	96.9
Of which: LC1	1000	12.08	971	97.1
LC5	1000	12.08	996	99.6
LC6	139	1.68	119	85.6
LC8	1000	12.08	968	96.8
LC9	163	1.97	144	88.3
TOT	8275	100	7620

Table 2

RMSE and R² for the 7 models calculated on IF1 steels.

Model	RMSE Train	MAE Train	R2 Train	RMSE Prod	MAE Prod	R2 Prod
Polynomial	12	9.8	0.52	11	9.3	0.50
Neural Network	13	11	0.54	11	9.4	0.53
Gradient Boosting	11	8.8	0.65	10	8.3	0.60
Random Forest	12	9.5	0.68	10	8.2	0.65
k-NN	13	11	0.72	9.9	8.1	0.70
LASSO	13	11	0.75	9.9	8.0	0.73
SVM	9.1	7.6	0.84	9.5	7.9	0.80

Table 3

Results obtained for each type of steel for the best models obtained for Rp02. The models are evaluated through the R², RMSE, and MAE values calculated both on the training and production sets.

Steel	Skinpassed	Leveled	Model	RMSE Train	MAE Train	R2 Train	RMSE Prod.	MAE Prod.	R2 Prod.
HSLA1	YES	YES	Gradient Boosting	14	11	0.95	14	12	0.89
HSLA2	NO	YES	SVM	14	13	0.82	14	13	0.75
HSLA3	YES	YES	Random Forest	16	13	0.65	16	13	0.62
IF1	YES	NO	SVM	9.1	8.0	0.84	9.5	8.2	0.80
IF2	YES	NO	Random Forest	9.6	8.6	0.80	9.8	8.9	0.75
IF3	YES	NO	Random Forest	4.9	4.8	0.97	5.2	5.1	0.92
LC1	YES	YES	SVM	9.1	9.0	0.75	9.4	9.2	0.74
LC5	YES	YES	Gradient Boosting	17	15	0.69	17	15	0.64
LC6	NO	YES	LASSO	12	12	0.77	12	12	0.74
LC8	YES	YES	SVM	15	14	0.68	15	14	0.62
LC9	NO	YES	Neural Network	15	14	0.84	15	14	0.82

Table 4

Results obtained for each type of steel for the best models obtained for Rm. The models are evaluated through the R², RMSE, and MAE values calculated both on the training and production sets.

Steel	Skinpassed	Leveled	Model	RMSE Train	MAE Train	R2 Train	RMSE Prod.	MAE Prod.	R2 Prod.
HSLA1	YES	YES	Gradient Boosting	8.0	6.6	0.99	8.3	7.0	0.95
HSLA2	NO	YES	Random Forest	14	14	0.73	14	14	0.65
HSLA3	YES	YES	SVM	13	12	0.70	13	12	0.65
IF1	YES	NO	Gradient Boosting	6.1	5.7	0.86	6.3	6.1	0.82
IF2	YES	NO	Random Forest	8.3	7.2	0.84	8.7	7.4	0.81
IF3	YES	NO	Gradient Boosting	5.6	4.8	1.00	5.9	5.1	0.95
LC1	YES	YES	Random Forest	7.4	6.6	0.81	7.7	7.0	0.73
LC5	YES	YES	Random Forest	11	8.3	0.69	11	8.6	0.68
LC6	NO	YES	LASSO	13	13	0.76	13	13	0.73
LC8	YES	YES	Gradient Boosting	12	11	0.54	12	11	0.49
LC9	NO	YES	Gradient Boosting	8.2	7.2	0.69	8.6	7.6	0.62

Table 5

Results obtained for each type of steel for the best models obtained for ALL%. The models were evaluated through the R², RMSE, and MAE values calculated both on the training and production sets.

Steel	Skinpassed	Leveled	Model	RMSE Train	MAE Train	R2 Train	RMSE Prod.	MAE Prod.	R2 Prod.
HSLA1	YES	YES	Gradient Boosting	0.90	0.80	0.83	1.2	1.1	0.80
HSLA2	NO	YES	SVM	1.0	0.70	0.47	1.3	1.1	0.41
HSLA3	YES	YES	LASSO	1.2	0.70	0.49	1.5	1.1	0.48
IF1	YES	NO	Gradient Boosting	0.80	0.50	0.80	1.1	0.85	0.78
IF2	YES	NO	LASSO	1.0	0.80	0.84	1.3	1.1	0.78
IF3	YES	NO	Random Forest	0.50	0.20	0.89	0.80	0.59	0.87
LC1	YES	YES	Gradient Boosting	1.1	0.80	0.55	1.5	1.1	0.50
LC5	YES	YES	Random Forest	1.8	1.2	0.60	2.1	1.4	0.55
LC6	NO	YES	SVM	1.5	1.0	0.50	1.7	1.3	0.49
LC8	YES	YES	SVM	1.0	0.60	0.47	1.3	1.0	0.44
LC9	NO	YES	SVM	0.90	0.70	0.62	1.1	0.89	0.58

Table 6

Confusion matrix built on the test set for the Random Forest model. Actual classes are in the rows, while assigned classes are in the columns.

	HSLA1	HSLA2	HSLA3	IF1	IF2	IF3	LC1	LC5	LC6	LC8	LC9
HSLA1	243	0	3	0	0	0	0	0	0	0	0
HSLA2	0	47	0	0	0	0	0	0	0	0	0
HSLA3	0	0	48	0	0	0	0	0	0	0	0
IF1	0	0	0	223	22	4	0	0	0	0	0
IF2	0	0	0	5	162	13	0	0	0	0	0
IF3	0	0	0	3	5	190	0	0	0	0	0
LC1	0	0	0	0	0	0	240	7	0	6	3
LC5	0	0	0	0	0	0	0	72	0	5	1
LC6	0	0	0	0	0	0	0	0	27	1	0
LC8	0	0	0	0	0	0	2	14	2	230	21
LC9	0	0	0	0	0	0	0	1	0	0	11

Table 7

Predictions for three new samples with three different intended uses; for each sample three results for the three runs of the Random Forest algorithm are provided (Run1, Run2, and Run3).

Intended Use from the Taranto Plant	Predicted UseRun1	Predicted UseRun2	Predicted UseRun3
LC5	LC5	LC5	LC8
IF1	IF1	IF1	IF1
LC1	LC1	LC1	LC1

Table 8

Results obtained for all types of steel contemporarily for the best models obtained for each experimental response (Rp02, Rm, and ALL%), evaluated through the R², RMSE, and MAE values calculated both on the training and on the production set.

Steel	Mechanical Properties	Skinpassed	Leveled	Model	N° Initial Samples	N° Used Samples	% Outliers	RMSE Train	MAE Train	R2 Train	RMSE Prod.	MAE Prod.	R2 Prod.
all	Rp02	yes and no mixed	yes and no mixed	Random Forest	8275	5146	49,6	6.2	4.3	0.82	10	7.4	0.78
	Rm							5.6	3.9	0.89	9.1	6.6	0.82
	ALL%							1.1	0.70	0.78	1.4	1.1	0.70

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/technologies13020075/s1, Figure S1: Scheme of the Acciaierie d’Italia production plants and processes carried out at the Novi Ligure plant; Figure S2: Scheme of the data flow for Coils produced by Cold Rolling; Figure S3: Scheme of the workflow and data storage for coils after HDG4; Figure S4: Scheme of the data flow for HDG4; Figure S5: Scheme of the workflow for model calculation and testing.

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