The integration and optimization of continuous casting and rolling processes are fundamental to determining the final quality and production efficiency of steel products. Surface defects originating in the slab, such as slag inclusion, possess a hereditary nature. Even minor instances can propagate through subsequent rolling stages, manifesting as surface defects in the final plate, thereby reducing metal yield and potentially causing severe operational issues like breakout. Therefore, the online prediction of slag inclusion locations on slabs, followed by targeted grinding, is crucial for mitigating downstream quality risks and enhancing economic benefits.
Traditional methods for detecting slag inclusion, such as manual visual inspection or offline sampling analysis, suffer from low efficiency, subjectivity, and an inability to provide real-time predictions. While machine vision-based techniques offer automation, their accuracy is often compromised by surface conditions like oxide scale and flux residues, leading to high false negative rates. Consequently, machine learning (ML) algorithms, renowned for their powerful function approximation and self-learning capabilities, have become a focal point for researchers aiming to develop robust prediction models for surface slag inclusion.
However, a prevalent challenge with existing ML-based prediction models is the discrepancy between high training accuracy and unreliable performance in practical test applications. This often stems from a lack of a systematic approach to optimizing model hyperparameters. This work addresses this gap by developing a predictive model, establishing a critical relationship between training and testing performance metrics, and employing an intelligent optimization algorithm to systematically tune parameters for superior generalization ability.
The formation of surface slag inclusion is influenced by a complex interplay of parameters across the steelmaking process. Inclusions can be exogenous (e.g., ladle slag, refractory materials, mold flux) or endogenous (e.g., deoxidation products). A primary mechanism for surface slag inclusion is the entrapment of slag at the meniscus region due to turbulent fluid flow and uneven heat transfer. Key influencing factors span multiple process stages:
- Converter/BOF Process: Main blow time/oxygen, reblow parameters.
- Secondary Refinement (LF/RH): Treatment time, cycle duration, vacuum parameters, stirring intensity.
- Steel Composition: Content of [C], [Si], [Mn], [P], [S], [Alt], [Als], [Ca].
- Slag Composition: Content of SiO2, CaO, MgO, Al2O3, TiO2.
- Continuous Casting: Tundish conditions, superheat, stopper rod position/fluctuation, SEN immersion depth/age, mold level fluctuation, casting speed/fluctuation, mold flux properties (consumption, viscosity, basicity), mold thermal parameters (water temperature differences, heat flux densities, ratios), oscillation parameters (amplitude, frequency, negative strip time), and operational events (tundish change, flux line change, SEN change).
Approximately 60 such parameters were identified and monitored.
To enable online prediction, a Slab Quality Analysis and Monitoring System was implemented. This system integrates high-frequency data acquisition, manual offline entry, and soft-sensing techniques to collect the identified parameters. A spatio-temporal matching model associates these time-series parameters with individual slabs, calculating integrated features (e.g., mean values) for each parameter per slab. Combined with final plate inspection feedback, this forms the foundational dataset for model development.
1. Analytical Methodology
1.1 Data Preprocessing
Data irregularities such as missing values and outliers are common due to sensor faults or manual errors. Missing values were handled via deletion or mean imputation. For outlier detection and treatment, the robust Z’-Score method was employed. The Z’-score is calculated as:
$$ Z’ = \frac{x_i – M(x)}{1.4826 \times D} $$
where $M(x)$ is the median of the sample data for a feature, and $D$ is the Median Absolute Deviation, $D = |x_i – M(x)|$. Data points with $|Z’| > 3$ are considered outliers. Right-skewed outliers are replaced by $M(x) + 3 \times 1.4826 \times D$, and left-skewed outliers by $M(x) – 3 \times 1.4826 \times D$.
| Issue | Method | Description |
|---|---|---|
| Missing Values | Deletion / Mean Imputation | Removed or filled with feature mean. |
| Outliers | Z’-Score Method ($|Z’|>3$) | Detected and replaced using median-based robust scaling. |
| Class Imbalance | Oversampling (4x) | Minority class (slag inclusion samples) replicated based on correlation stability analysis. |
1.2 Modeling Algorithms
Three prominent machine learning algorithms were evaluated for building the slag inclusion prediction model.
1.2.1 Class-Weighted Support Vector Machine (SVM)
SVM seeks an optimal hyperplane to separate classes. To address the inherent class imbalance (fewer slag inclusion samples), a class-weighted formulation was used. The optimization problem is:
$$ \min_{\omega, b, \xi} \frac{1}{2} \|\omega\|^2 + C_{+}\sum_{y_i=+1}\xi_i + C_{-}\sum_{y_i=-1}\xi_i $$
subject to:
$$ y_i(\omega^T x_i + b) \ge 1 – \xi_i, \quad \xi_i \ge 0, \quad i=1,2,…,n $$
Here, $\omega$ is the weight vector, $b$ is the bias, $\xi_i$ are slack variables, and $C_{+}$ and $C_{-}$ are penalty parameters for the positive (slag inclusion) and negative classes, respectively.
1.2.2 Random Forest (RF)
RF is an ensemble method that constructs multiple decision trees during training and outputs the mode of their predictions. It is robust to overfitting but can become too specific to the training data.
1.2.3 Adaptive Boosting (AdaBoost)
AdaBoost combines multiple weak classifiers (often decision stumps) into a strong classifier by sequentially re-weighting misclassified samples, focusing learning on difficult cases.
| Algorithm | Core Principle | Advantage for Imbalance | Key Hyperparameters |
|---|---|---|---|
| Class-Weighted SVM | Finds max-margin hyperplane; uses class penalties $C_{+}, C_{-}$. | Explicit cost-sensitive learning. | $C_{+}, C_{-}$, kernel parameters. |
| Random Forest (RF) | Ensemble of decorrelated decision trees. | Can balance via class weights in trees. | Number of trees, max depth. |
| AdaBoost | Sequentially boosts weak classifiers. | Focuses on hard-to-classify samples. | Number of estimators, learning rate. |
1.3 Model Hyperparameter Optimization using PSO
The Particle Swarm Optimization (PSO) algorithm was employed to systematically find the optimal hyperparameters (e.g., $C_{+}, C_{-}$ for SVM). In PSO, a swarm of particles (each representing a hyperparameter set) explores the search space. Each particle updates its position based on its own best experience ($P_{best}$) and the swarm’s global best experience ($G_{best}$).
The velocity and position update equations for particle $i$ in dimension $d$ at iteration $k$ are:
$$ V^{k+1}_{id} = \omega V^{k}_{id} + c_1 r_1 (P^{k}_{id} – X^{k}_{id}) + c_2 r_2 (P^{k}_{gd} – X^{k}_{id}) $$
$$ X^{k+1}_{id} = X^{k}_{id} + V^{k+1}_{id} $$
where $\omega$ is inertia weight, $c_1, c_2$ are learning factors, and $r_1, r_2$ are random numbers in [0,1]. The key challenge was defining a fitness function to evaluate particle positions when the true test accuracy is unknown during training.
1.4 Model Evaluation Metrics
For slag inclusion prediction, standard accuracy can be misleading due to class imbalance. Therefore, the following metrics were used, based on the confusion matrix (True Positive TP, False Negative FN, False Positive FP, True Negative TN):
- False Negative Rate (FNR) or Miss Rate: Proportion of actual slag inclusion slabs incorrectly predicted as sound.
$$ FNR = \frac{FN}{TP + FN} $$ - False Positive Rate (FPR): Proportion of actual sound slabs incorrectly predicted as having slag inclusion.
$$ FPR = \frac{FP}{FP + TN} $$ - Fβ Score: Harmonic mean of precision ($Pr=TP/(TP+FP)$) and recall ($Rc=TP/(TP+FN)$), weighted by β. As identifying all defective slabs is critical, β=2 was chosen to emphasize recall.
$$ F_{\beta} = \frac{(1+\beta^2) \cdot Pr \cdot Rc}{\beta^2 \cdot Pr + Rc} $$
1.5 Handling Class Imbalance
The initial dataset contained 194 slabs with slag inclusion and 669 sound slabs. Oversampling was applied to the minority class. The optimal oversampling ratio was determined by analyzing the stabilization point of correlation coefficients between process parameters and slag inclusion occurrence as the dataset was balanced. The correlation stabilized when the defective samples were oversampled by a factor of 4.
2. Model Development and the Training-Testing Relationship
2.1 Preliminary Model Comparison
The three algorithms (SVM, RF, AdaBoost) were trained and tested 5000 times with random hyperparameters and random 70/30 train-test splits. Performance metrics were averaged.
| Algorithm | Training Performance | Testing Performance | ||||
|---|---|---|---|---|---|---|
| FPR | FNR | F2 Score | FPR | FNR | F2 Score | |
| Support Vector Machine (SVM) | 0.14 | 0.11 | 0.85 | 0.23 | 0.19 | 0.70 |
| Random Forest (RF) | ~0.00 | ~0.00 | ~1.00 | 0.21 | 0.31 | 0.59 |
| AdaBoost | 0.11 | 0.15 | 0.84 | 0.18 | 0.25 | 0.65 |
Analysis: RF showed perfect training scores but poor generalization (high test FNR). While AdaBoost had a lower test FPR than SVM, its test FNR was significantly higher. Since minimizing missed detections of slag inclusion is paramount, the SVM model was selected for further development due to its better balance of fitting and generalization, yielding the highest test F2 score.
2.2 Establishing the Relationship: Training Metrics to Test F2 Score
The core innovation lies in modeling the relationship between observable training metrics and the ultimately desired test performance. We analyzed the 5000 SVM training runs and constructed a polynomial regression model to predict the test F2 score ($f$) from the standardized training metrics: False Positive Rate ($t_1$), False Negative Rate ($t_2$), and F2 score ($t_3$). Standardization was performed as $t = (x – \mu)/\sigma$ for each metric.
The derived predictive model is:
$$ f(\mathbf{t}) = 0.62 – 1.19 t_2 t_3 – 0.89 t_3^2 – 0.40 t_2^2 – 0.35 t_1 t_3 – 0.28 t_1 t_2 $$
This model had a mean squared error (MSE) of 0.00256 and a coefficient of determination (R²) of 0.6103, indicating it captures a significant portion of the variance in test performance based on training outcomes.
2.3 Systematic Hyperparameter Optimization with PSO
With the relationship model $f(\mathbf{t})$, PSO could now be effectively used to optimize the SVM hyperparameters ($C_{+}, C_{-}$, etc.). The fitness of a particle (hyperparameter set) was evaluated as follows:
- Train the SVM model with the hyperparameters on the training set.
- Calculate the training metrics (FPR, FNR, F2).
- Standardize these metrics to get $t_1, t_2, t_3$.
- Input $(t_1, t_2, t_3)$ into $f(\mathbf{t})$ to obtain the predicted test F2 score.
- Use this predicted score as the fitness value for the PSO particle.
PSO iteratively updated the particle swarm to maximize $f(\mathbf{t})$. The optimal hyperparameter set found through this process yielded the following results on the actual hold-out test set:
| Dataset | False Positive Rate (FPR) | False Negative Rate (FNR) | F2 Score | Predicted Test F2 by $f(\mathbf{t})$ |
|---|---|---|---|---|
| Training Set | 0.110 | 0.015 | 0.920 | – |
| Test Set (Actual) | 0.229 | 0.186 | 0.727 | 0.752 |
The model successfully identified a high proportion of slabs with slag inclusion (low FNR of 18.6%) while maintaining a reasonable false alarm rate (FPR of 22.9%). The close match between the predicted (0.752) and actual (0.727) test F2 scores validates the utility of the relationship model $f(\mathbf{t})$ for guiding optimization.
3. Online Deployment Strategy
The final PSO-SVM model outputs a probability between 0 and 1 for each slab, indicating the likelihood of surface slag inclusion. For practical deployment, a tiered inspection strategy is recommended based on this probability score ($s$):
| Prediction Score ($s$) | Interpretation | Action |
|---|---|---|
| $s < 0.4$ | Low probability of slag inclusion. | No inspection required. Slab proceeds to rolling. |
| $0.4 \le s < 0.7$ | Moderate probability of slag inclusion. | Trigger sampling inspection on a portion of slabs in this range. |
| $s \ge 0.7$ | High probability of slag inclusion. | Mandatory 100% inspection and grinding if confirmed. |
This strategy balances production efficiency with quality control, ensuring resources are focused on slabs most likely to contain the detrimental slag inclusion defect.
4. Conclusions
This work presents a comprehensive framework for the online prediction of surface slag inclusion in continuous casting slabs. The key findings and contributions are summarized as follows:
- Algorithm Selection: Among SVM, Random Forest, and AdaBoost, the class-weighted Support Vector Machine (SVM) demonstrated the most favorable equilibrium between model fitting capability and generalization power for the slag inclusion prediction task.
- Core Relationship Model: A significant contribution is the establishment of a quantifiable relationship between training performance metrics and the ultimate test performance. The polynomial model $f(\mathbf{t})$ allows for the estimation of the test F2 score based solely on training results (FPR, FNR, F2).
- Systematic Optimization: By integrating this relationship model $f(\mathbf{t})$ as the fitness function within a Particle Swarm Optimization (PSO) routine, a systematic method was created to optimize SVM hyperparameters. This approach directly targets improved generalization ability, even when the true test performance is unknown during the optimization loop.
- Effective Prediction: The optimized PSO-SVM model achieved a test performance with a false negative rate of 18.6% and an F2 score of 0.727. This high recall is crucial for ensuring that the majority of slabs with slag inclusion are correctly identified before rolling.
- Practical Implementation: The proposed tiered inspection strategy based on the model’s prediction score enables efficient and targeted quality control, helping to prevent the hereditary propagation of slag inclusion defects into final rolled products, thereby enhancing product quality stability and metal yield.
This methodology addresses a critical gap in machine learning applications for slab quality prediction by providing a principled way to link training outcomes to expected field performance, thereby enabling the development of more reliable and actionable models for detecting surface slag inclusion.