1. Introduction
The prediction of mechanical properties in steel manufacturing holds paramount importance for the steel industry, ensuring both cost-effectiveness and quality. In particular, hot-rolled steel rebars, also known as reinforcing bars (or simply rebars), have been primarily used in reinforcing concrete structures, providing strength and durability to buildings, bridges, and other infrastructure projects. Among the key mechanical properties of interest to steel rebars, one can mention yield strength (YS), ultimate tensile strength (UTS), the UTS/YS ratio, and percent elongation (PE) [
1,
2]. The quantities YS and UTS are important performance indicators of materials under load conditions, representing, respectively, the starting point of permanent deformation and the maximum load the material can withstand before failure. The UTS/YS ratio is a material’s ductility measure, while PE is an indicator of the material’s ability to deform without fracturing [
3,
4].
It is widely known that the aforementioned mechanical properties of steel rebars are heavily dependent on their chemical composition and on parameters related to production processes [
5,
6]. However, these properties are still determined through costly and time-consuming laboratory tests on samples taken from the batch produced. Bearing this in mind, many authors have been using data-driven alternatives to anticipate (or predict) such mechanical properties in an attempt to optimize the manufacturing process. Due to the complexity of the task, these alternatives consist basically of fitting a nonlinear regression model to the available data, using as inputs information from chemical composition and parameters from the production process (e.g., from heat treatment rolling) and as outputs one or more of the quantities of interest (US, UTS, and PE).
Machine learning models have often been chosen for building nonlinear regression models to predict the mechanical properties of products in the steelmaking industry. Examples that are worth mentioning are found in the manufacturing of hot-rolled steel plates [
7], cold-rolled galvanized steel coils [
8], interstitial-free steels [
9], hot-rolled steel rebars [
1,
2], and steelmaking in general [
10,
11,
12,
13]. One of the first successful applications of machine-learning-based regression models to the prediction of the mechanical properties of steel is reported in [
14]. In this work, the authors used support vector regression (SVR) with 29 inputs (19 extracted from chemical composition and 10 from hot-rolling parameters) to predict the mechanical properties of hot-rolled plain carbon steel Q235B, quantified as three output variables (YS, UTS, and PE). Using data collected from the supervisor of the hot-rolling process, the SVR-based approach achieved good performance, according to the authors.
The authors in [
15] introduced a one-hidden-layered multilayer perceptron (MLP) to model and optimize the chemical composition of a steel bar with the goal of predicting its mechanical properties, considering UTS and YS as output variables. This MLP-based regression model was optimized via particle swarm optimization (PSO) in order to exploit better solutions in the search space through iterations. According to the authors, the obtained results were consistent with the actual data. Following a similar paradigm, a single-hidden-layered MLP-based regression model was also developed in [
8] to predict the mechanical properties of a coil, namely, YS and UTS, from its chemical composition, thickness, width, and key galvanizing process parameters, resulting in a total of 23 input variables. An online quality monitoring system was developed with the goal of monitoring the predicted mechanical properties and process parameters of a galvanized coil, helping the quality team in decision making.
The predictive model developed in [
2] is built on 18 inputs derived from the chemical composition (12 inputs) and heat treatment (6 inputs) of steel rebars. The methods employed include multiple linear regression and a two-hidden-layered MLP whose goal is to predict the mechanical properties of steel rebars, namely, YS, UTS (or alternatively, the ratio UTS/YS), and PE. The best performance, measured by R2 values, was obtained by the MLP-based regression model. A two-hidden-layered MLP with 27 inputs is designed in [
7] to predict the mechanical properties (YS, UTS, EL, and impact energy) of industrial steel plates based on the process parameters and the composition of the raw steel. The authors applied this model online to a real steel manufacturing plant.
Four machine learning methods were evaluated in [
16] in the task of predicting the hot ductility of cast steel from chemical composition and thermal conditions. A single-hidden-layered MLP achieved the best performance in comparison with random forest, Gaussian process, and SVR. A single-hidden-layered MLP was also used in [
17] to predict the mechanical properties of ultra-fine-grained Fe-C alloy by fusing the experimental combinations of alloy composition, rolling process parameters, and heat treatment process parameters. In this work, the MLP outperformed the SVR model and an MLP variant trained with a genetic algorithm. In [
18], the UTS of both non-spliced and spliced bars is predicted using nonlinear regression, ridge regression, and MLP, achieving accurate results. In [
19], tree-based machine learning techniques, namely, decision trees and random forests, are implemented to analyze the ultimate strain of non-spliced and spliced steel reinforcements, achieving acceptable results. The authors highlight further that the evaluated tree-based regression models were time-saving and cost-effective compared with more complicated, time-consuming, and expensive experimental examinations.
An ELM-based regression model [
20], a neural network architecture whose input-to-hidden layer weights are randomly sampled and not allowed to be modified during training, was developed in [
21] to predict the mechanical properties of an aluminum alloy strip. The obtained results show that the proposed ELM-based regression model achieved high accuracy and stability in predicting aluminum alloy strips’ YS, UTS, and PE. The main advantage of the ELM over more traditional machine learning methods, such as the MLP and SVR, relies on the very short time required for training the regression model.
Despite its popularity in machine learning, applications of deep learning (DL) models for predicting the mechanical properties of steel are still in their infancy. We hypothesize that this occurs because of the type of input information. Most DL architectures, especially those based on convolutional neural networks (CNNs), require images as inputs. In visual inspection tasks, where image acquisition is usual, the application of CNNs is dominant nowadays. For example, in [
22], a deep learning approach based on a YOLOv3 detector [
23] is used for automatic steel bar detection and counting through images. Thus, to use a CNN, it is necessary to convert the production data into 2D data images, as performed in [
24], for predicting the mechanical properties of hot-rolled steel using chemical composition and process parameters.
Of particular interest to the current paper is the work of Murta et al. [
1], who used the Least Squares Support Vector Regression (LSSVR) [
25] model for predicting the mechanical properties of steel rebar. It was built on 18 inputs and 4 outputs (YS, UTS, UTS/YS ratio, and PE), with the LSSVR model outperforming the MLP-based regression model developed in [
2] on the same dataset. Motivated by this result, we revisit the LSSVR model with the goal of improving its performance on the prediction task of interest. In this context, sparsification approaches are highly important when dealing with support-vector-based models, as the computational complexity typically scales cubically with the size of the training set [
26]. For this purpose, we initially evaluate vector quantization methods [
27,
28] and then introduce a novel approach for using the approximate linear dependence (ALD) method [
29] in the sparsification of the LSSVR model for non-temporal data. Additionally, we make use of the local regression paradigm to develop a novel approach for predicting the mechanical properties of steel rebars. Unlike the single regression model approach, local regression modeling divides the dataset into smaller regions and constructs a separate regression model for each region. This approach has been successfully used in various regression problems, such as identifying failure modes of reinforced concrete shear walls [
30], composite autoclave manufacturing [
31], and polyethylene production [
32].
In summary, in the current paper, we aim at building two LSSVR-based regression models that can be used before the actual manufacturing process takes place so that the mechanical properties of the produced steel rebar resemble the most predicted ones. The main contributions, from the machine learning perspective, consist in the development of two sparse LSSVR-based models, one based on the global modeling paradigm and the other based on the local modeling paradigm. From the perspective of process engineering, the proposed regression models can be used to experiment with different values of the 18 input variables and foresee the resulting four mechanical properties of the steel rebars. It may turn out to be important in the statistical quality control of the produced steel rebars. The fitted regression model can also be used for online (or offline) process monitoring. That is, it can reveal problems in the actual process if there is any disparity between the actual and predicted mechanical properties of the steel rebar. From the perspective of materials engineering, as the regression model can be understood as an emulator of a complex production process, the model can be used to investigate the effect of each input variable on the mechanical properties of the steel produced. Ultimately, the model can be used for teaching purposes.
The remainder of the paper is organized in the following sections: In
Section 2, we provide details on the materials and methods employed in this study. This section encompasses a description of the experimental setup, the materials utilized, and the procedures followed to ensure the reliability and reproducibility of the results. The results are presented and discussed in
Section 3. We conclude the paper by presenting a summary of the contributions and achieved results in
Section 4.