In modern steel production, the stability and reliability of product quality are paramount. Slag inclusion defects, which originate during the continuous casting process, significantly impair the surface quality and mechanical properties of the final steel products. These defects, often embedded 2 to 10 millimeters beneath the surface, can act as initiation sites for cracks and other imperfections, ultimately affecting the performance of steel in applications ranging from household appliances to aerospace components. Therefore, tracing the root causes of these defects is a critical industrial challenge.
A substantial body of research and practical experience indicates that the stability of the mould level in the continuous casting machine is a primary factor influencing the formation of slag inclusions. Turbulent flow at the meniscus, often driven by level fluctuations, can entrap mould powder or other non-metallic inclusions into the solidifying shell. While numerical modeling and fluid dynamics simulations have provided valuable insights, there remains a significant gap in data-driven, feature-based analyses that directly correlate specific characteristics of mould level fluctuation signals with the occurrence of slag inclusion defects. This study addresses this gap by proposing a comprehensive methodology for mining relevant features from mould level time-series data. Our goal is to move beyond raw signal analysis and identify interpretable, statistically significant features that can distinguish slabs with slag inclusion defects from normal slabs, thereby providing actionable insights for process optimization and defect root cause analysis.
Overall Methodology for Feature Mining
The core objective of this work is to identify features within the mould level fluctuation signal that are strongly correlated with the occurrence of slag inclusion defects. The overall process, as implemented in this study, consists of four main stages: Signal Representation and Preprocessing, Comprehensive Feature Extraction, Statistical Correlation Analysis, and Feature Selection & Validation. This structured approach ensures that the mined features are both robust and interpretable.
1. Signal Representation and Preprocessing
Raw mould level fluctuation data, calculated as the deviation of the actual level from its setpoint, often contains noise and transient anomalies that can obscure underlying patterns relevant to defect formation. We employ two complementary preprocessing techniques to enhance signal quality before feature extraction:
- Piecewise Aggregate Approximation (PAA): This method operates in the time domain to smooth local irregularities. A time series of length $N$ is divided into $n$ segments ($n < N$), and each segment is represented by its mean value. This effectively dampens short-lived, high-amplitude spikes that may be sensor artifacts rather than true process phenomena. The segment size is a key parameter.
- Low-Pass Filtering: This method operates in the frequency domain to remove high-frequency noise. A filter is applied to attenuate signal components above a specified cutoff frequency, preserving the lower-frequency fluctuations that are more likely related to process dynamics like casting speed changes or stopper rod movements.
To determine optimal parameters, we analyze the Dynamic Time Warping (DTW) distance between processed and original signals, alongside visual inspection of the processed signals’ temporal characteristics. Based on this analysis, a PAA window size of 5 and a low-pass filter cutoff frequency of 0.1 (relative to the Nyquist frequency) were selected. We reason that features correlated with slag inclusion may manifest in the original signal, the PAA-smoothed signal (which suppresses local anomalies), and the low-pass filtered signal (which removes global high-frequency noise). Therefore, we perform feature mining on three distinct signal representations: the Raw signal, the PAA-processed signal, and the Low-pass Filtered signal.
2. Comprehensive Feature Extraction
To thoroughly characterize the mould level fluctuation, we extract a broad set of 853 features from both the time and frequency domains for each slab’s signal. This extensive feature set aims to capture various aspects of the signal’s behavior that might be linked to defect formation.
| Feature Domain | Feature Category | Description & Examples | Approx. Count |
|---|---|---|---|
| Time Domain | Global Statistics | Mean, variance, standard deviation, root-mean-square (RMS), kurtosis, skewness, absolute energy. | ~20 |
| Segmented Statistics | Statistics (e.g., mean, std) calculated over different quantiles or fixed segments of the signal (e.g., first/last 30 seconds). | ~50 | |
| Model Coefficients | Coefficients from fitting models like Autoregressive (AR) models. For an AR(10) model: $x_t = c + \sum_{i=1}^{10}\phi_i x_{t-i} + \epsilon_t$. | ~30 | |
| Shape & Pattern Features | Number of peaks, length of longest continuous subsequence above/below a threshold, maximum/minimum derivative, count of crossings of specific level values (e.g., -1mm, +1mm). | ~300 | |
| Specialized Process Features | Count of fluctuations within specific intervals relevant to process control (e.g., [-2, -1) mm, [1, 2) mm), features combining derivative and amplitude. | ~150 | |
| Frequency Domain | Spectral Features | Magnitudes of Fast Fourier Transform (FFT) coefficients, coefficients from Continuous Wavelet Transform (CWT). | ~300 |
| Total Extracted Features | ~853 | ||
3. Statistical Correlation Analysis
For each extracted feature $X_{\varphi}$ (where $\varphi = 1, 2, …, n_{\varphi}$, and $n_{\varphi}=853$), we perform a hypothesis test to assess its correlation with the binary target $Y$ (slag inclusion defect: Yes/No).
- Null Hypothesis $H_{0\varphi}$: Feature $X_{\varphi}$ is not correlated with the prediction of slag inclusion defects.
- Alternative Hypothesis $H_{1\varphi}$: Feature $X_{\varphi}$ is correlated with the prediction of slag inclusion defects.
The test yields a p-value $p_{\varphi}$, quantifying the probability of observing the feature’s distribution given that $H_{0\varphi}$ is true. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting a significant correlation. We use two statistical tests appropriate for different data types:
- Fisher’s Exact Test: Used for Boolean features. The data is arranged in a 2×2 contingency table. The p-value is calculated from the hypergeometric distribution, considering all possible table configurations as or more extreme than the observed one.
- Kolmogorov-Smirnov (K-S) Test: Used for real-valued features. The K-S statistic $D_{n,m}$ measures the maximum vertical distance between the empirical cumulative distribution functions (ECDFs) of the feature for normal slabs ($F_{1,n}(x)$) and defect slabs ($F_{2,m}(x)$):
$$ D_{n,m} = \sup_x | F_{1,n}(x) – F_{2,m}(x) | $$
The p-value is then derived from the distribution of this statistic under the null hypothesis.
4. Feature Selection & Validation
Performing hundreds of hypothesis tests simultaneously increases the risk of false discoveries (Type I errors). We control the False Discovery Rate (FDR) using the Benjamini-Yekutieli procedure. For a desired FDR level $q$, the features are ranked by their p-values $p_{(1)} \leq p_{(2)} \leq … \leq p_{(n_{\varphi})}$. A feature with rank $\varphi$ is considered significant if:
$$ p_{(\varphi)} \leq \frac{\varphi \cdot q}{n_{\varphi} \sum_{\mu=1}^{n_{\varphi}} \frac{1}{\mu}} $$
This step filters out features whose apparent correlation is likely due to chance.
Finally, to validate the effectiveness of the mined feature sets, we build predictive models. A Weighted Random Forest classifier is employed due to its robustness, ability to handle non-linear relationships, and built-in feature importance assessment. The model is trained on the selected features, and its performance is compared against a baseline 1D Convolutional Neural Network (1D-CNN) trained directly on the raw time-series data. This comparison highlights the value of the feature mining process over a purely end-to-end deep learning approach.
Experimental Analysis & Key Findings
Our dataset comprised mould level fluctuation signals for nearly 13,000 slabs, of which 240 were labeled with slag inclusion defects—creating a highly imbalanced classification problem. After preprocessing and extracting 853 features per slab, we applied the statistical correlation analysis and feature selection procedure. The performance of models built on different feature sets was evaluated using the Area Under the ROC Curve (AUC) metric on a held-out test set.
Modeling Performance Comparison
The table below compares the test set AUC of a Weighted Random Forest model trained on various feature sets (selected via our methodology) against a 1D-CNN trained on raw, length-normalized signals.
| Model Type | Input / Feature Set | Number of Features | Test AUC |
|---|---|---|---|
| 1D-CNN (Baseline) | Raw Time-Series Signal | N/A (Raw Data) | 0.527 |
| Raw Signal (Weighted Loss) | N/A (Raw Data) | 0.530 | |
| Weighted Random Forest | All Valid Features (from Raw Signal) | 817 | 0.656 |
| Selected Features (from Raw Signal) | 45 | 0.716 | |
| Selected Features (from PAA Signal) | 45 | 0.648 | |
| Selected Features (from Low-Pass Filtered Signal) | 244 | 0.660 | |
| Selected Features (Raw + Low-Pass Filtered) | 21 | 0.721 | |
| Selected Features (PAA + Low-Pass Filtered) | 34 | 0.702 | |
| Selected Features (Raw + PAA + Low-Pass Filtered) | 12 | 0.660 |
Key Observations from Results:
- Superiority of Mined Features: Models using statistically selected features consistently and significantly outperformed the 1D-CNN baseline trained on raw data (AUC 0.721 vs. 0.530). This demonstrates that our feature mining process successfully distills meaningful information related to slag inclusion formation.
- Interpretability Advantage: Unlike the “black-box” 1D-CNN, the Random Forest model using selected features provides direct interpretability. We can analyze which specific features (e.g., “variance,” “count in interval [-2,-1)”) are most important, offering tangible clues for process engineers.
- Optimal Feature Set: The most effective feature set was derived from the intersection of features selected from the Raw signal and those from the Low-Pass Filtered signal (21 features). This set likely captures genuine process dynamics while being robust to both local anomalies and high-frequency noise.
- Core Feature Subset: The 12 features common to all three signal representations (Raw, PAA, Filtered) represent the most robust and stable indicators strongly associated with slag inclusion defects.
Interpretation of Mined Features and Process Implications
The distribution analysis of the 12 core features provides direct, interpretable insights into how mould level fluctuations contribute to slag inclusion defects. The following table summarizes the key findings and their suggested process implications.
| Feature Category | Example Feature | Observed Trend for Slag Inclusion Slabs | Suggested Process Implication |
|---|---|---|---|
| Overall Variability | Variance ($\sigma^2$), Standard Deviation ($\sigma$) | Higher values on average. | Improve level control system responsiveness to minimize deviation from setpoint. Aim to reduce overall fluctuation variance. |
| Signal Energy | Absolute Energy ($\sum x_t^2$), Root-Mean-Square (RMS) | Higher values on average. | Enhance control to ensure the actual level tracks the setpoint more quickly and accurately, reducing the squared error over time. |
| Extreme Fluctuations | Count of fluctuations in intervals [-2,-1) mm and [1,2) mm | Higher counts. | Implement stricter limits or alarms for deviations exceeding ±1mm. Investigate causes of such sustained deviations (e.g., stopper rod wear, SEN clogging). |
| Distribution Shape | “Variance > Standard Deviation” (Boolean) | More frequently true. | This implies variance > 1, i.e., standard deviation > 1mm. A key goal should be to stabilize level so that $\sigma$ < 1 mm. |
| Temporal Dynamics | 2nd Coefficient ($\phi_2$) of a 10th-order AR model | Less negative/more positive compared to normal slabs. | The level fluctuation in defect slabs has a weaker negative correlation with its value 2 seconds prior. Optimizing control loop parameters may help establish more stable anti-correlated dynamics. |
| Low-Frequency Oscillations | Magnitude of 10th and 16th FFT Coefficients | Higher magnitudes. | Corresponds to low-frequency oscillations (~0.016-0.038 Hz). These may be linked to standing waves, casting speed variations, or oscillation marks. Adjusting mould oscillation frequency/amplitude or investigating rhythmic disturbances is advised. |
| Process Tail Behavior | Index of the 90% Mass Quantile | Distribution shifts towards 1.0 (end of cast). | Indicates severe fluctuations often occur at the very end of a cast sequence, typically during shutdown procedures. Standardizing and optimizing end-of-cast practices is critical to prevent final slab slag inclusion. |
The analysis of these features moves the discussion from a qualitative statement (“unstable level causes slag”) to a quantitative and diagnostic framework. For instance, knowing that slabs with slag inclusion defects frequently have a variance greater than 1 mm² and more fluctuations in the ±1-2 mm band provides specific, measurable targets for process control engineers.
Conclusion
This study presents a systematic, data-driven methodology for mining interpretable features from mould level fluctuation signals that are statistically correlated with slag inclusion defects in continuous casting. By combining signal preprocessing (PAA and low-pass filtering), comprehensive multi-domain feature extraction, rigorous statistical hypothesis testing, and controlled feature selection, we successfully identified a compact set of highly relevant features. The predictive model built on these mined features significantly outperformed a model trained directly on raw time-series data, while offering the crucial advantage of interpretability.
The mined features, such as increased variance, elevated counts in specific deviation bands, the presence of low-frequency oscillations, and poor tail-end control, translate directly into actionable process insights. These findings enable a shift towards proactive quality management, where real-time monitoring of these specific feature values could provide early warnings of conditions conducive to slag inclusion formation. Furthermore, the identified features serve as a valuable guide for prioritizing and tuning mould level control strategies, optimizing mould oscillation parameters, and standardizing casting start-up and shut-down procedures. This feature-based approach provides a powerful complement to traditional modeling and offers a concrete path for reducing defect rates and enhancing steel product quality through data-informed process optimization.