In modern advanced manufacturing, particularly for critical components like high-temperature turbine blades used in heavy-duty gas turbines, achieving consistent and high quality is paramount. These casting parts are typically produced through intricate processes such as investment casting, where numerous process parameters interact in complex ways to determine the final integrity of the component. The traditional post-production inspection paradigm is reactive and costly. With the advent of industrial digitalization, vast amounts of process data are now collected, presenting an opportunity to shift towards proactive quality prediction. However, leveraging this data is fraught with challenges, chief among them being the inherent class imbalance in historical records—defective casting parts are, fortunately, far less frequent than non-defective ones. This imbalance severely hampers the performance of conventional machine learning models, which become biased towards predicting the majority class, rendering them ineffective for the critical task of identifying potential defects. In this work, we address this pivotal issue. We propose a comprehensive methodology that synergizes an advanced data-level oversampling technique with a robust ensemble learning framework to build a highly reliable quality prediction model for casting parts, specifically tailored for the unbalanced datasets prevalent in precision casting operations.
The core challenge in data-driven quality prediction for casting parts stems from the nature of manufacturing data. In a typical investment casting process for turbine blades, hundreds of parameters are logged across stages like core making, wax pattern assembly, shell building, dewaxing, and pouring. The final quality is determined by non-destructive testing methods like Radiographic Testing (RT), resulting in a binary label: “qualified” or “unqualified.” The number of unqualified casting parts is often orders of magnitude smaller than qualified ones, creating a highly imbalanced dataset. Training a classifier directly on such data leads to models with deceptively high overall accuracy but abysmal recall for the minority class (defects). From a practical standpoint, accurately predicting the minority class is often more critical as it allows for preventive interventions, saving significant scrap and rework costs. Therefore, our primary objective is to enhance the model’s performance specifically on the minority class of casting parts without severely compromising the performance on the majority class.
To quantify model performance under imbalance, standard accuracy is misleading. We employ three robust metrics: Area Under the Receiver Operating Characteristic Curve (AUC-ROC), Geometric Mean (G-mean), and the F1-Score. The AUC-ROC evaluates the model’s ability to discriminate between classes across all thresholds. The G-mean is the geometric mean of sensitivity (true positive rate) and specificity (true negative rate), providing a balanced view of performance on both classes:
$$ G_{mean} = \sqrt{\frac{TP}{TP + FN} \times \frac{TN}{TN + FP}} $$
Here, $TP$, $TN$, $FP$, and $FN$ represent True Positives, True Negatives, False Positives, and False Negatives, respectively, with the positive class being the “unqualified” casting parts. The F1-Score is the harmonic mean of Precision and Recall (Sensitivity):
$$ F1 = \frac{2 \times Precision \times Recall}{Precision + Recall} = \frac{2TP}{2TP + FP + FN} $$
Our proposed methodology is a structured pipeline comprising data preprocessing, imbalance handling via a novel oversampling technique, feature selection, and model construction using a stacked ensemble. The first step involves rigorous data preprocessing for the historical process data of the casting parts. This includes handling missing values (e.g., using column mean imputation), encoding categorical variables, and normalizing numerical features to a [0, 1] range using Min-Max scaling to ensure all parameters contribute equally during model training:
$$ x’ = \frac{x – x_{min}}{x_{max} – x_{min}} $$
Furthermore, we perform an initial filtering to remove process parameters that show zero variation across all records, as they carry no discriminative information for predicting the quality of casting parts. The preprocessed dataset is then split into training and testing sets (e.g., 80%-20%) before any imbalance correction is applied to the training set. This ensures that our test set remains a realistic representation of the original, imbalanced production environment, providing a truthful evaluation of the model’s practical viability.
The pivotal step in our pipeline is addressing the class imbalance. We adopt and implement a sophisticated oversampling method called Synthetic Minority based on Probabilistic Distribution (SyMProD). Unlike simpler techniques like SMOTE which can generate noisy samples in overlapping regions, SyMProD intelligently creates synthetic samples for the minority class (unqualified casting parts) by considering the probability density distribution of existing samples. The algorithm proceeds in several stages. First, it applies a Z-score filter to remove outlier or noisy instances from both classes that could degrade the quality of generated samples. For a data point $p$, the Z-score is calculated based on its feature distribution within its class. Points with an absolute Z-score above a Noise Threshold ($NT$) are discarded.
Next, for each remaining minority instance $X_{min}(i)$, the algorithm assesses its position relative to other minority and majority instances. It computes a “closeness factor” $C$ based on the inverse of the sum of Euclidean distances to all other points in the same class. The Euclidean distance between two points $p$ and $q$ in $N$-dimensional space is:
$$ d(p, q) = \sqrt{\sum_{i=1}^{N} (p(i) – q(i))^2} $$
For a minority instance $X_{min}(i)$, its total intra-class distance is $D(X_{min}(i)) = \sum_{j=1}^{n_{min}} d(X_{min}(i), X_{min}(j))$, and its closeness factor is $C(X_{min}(i)) = 1 / D(X_{min}(i))$. The algorithm then finds the $K$ nearest neighbors of $X_{min}(i)$ from both the minority and majority classes. It calculates a minority group proximity factor $\tau_{min}(i)$ and a majority group proximity factor $\tau_{maj}(i)$ by summing the weighted closeness factors of these neighbors, where the weight is the inverse of the distance to the neighbor. A key step is filtering: if $\tau_{min}(i) > \tau_{maj}(i) \times CT$ is not satisfied, where $CT$ is a Cut-off Threshold, the instance $X_{min}(i)$ is considered to be in an overlapping or majority region and is excluded from the subsequent synthesis process. This prevents generating samples in ambiguous areas.
For the filtered minority instances, a probability $P(i)$ is assigned proportional to the ratio of their proximity factors:
$$ \phi(i) = \frac{\tau_{min}(i) + 1}{\tau_{maj}(i) + 1}, \quad P(i) = \frac{\phi(i)}{\sum_{j=1}^{n_{min}} \phi(j)} $$
This probability distribution favors minority instances that are deeply embedded within the minority cluster and far from majority instances. Finally, to generate a new synthetic sample, a minority instance is selected according to $P(i)$. Then, $M$ of its nearest minority neighbors are identified. A synthetic instance $X_{new}$ is created as a convex combination of the selected instance and its $M$ neighbors, weighted by both a set of random coefficients $\beta(j)$ and their assigned probabilities $Pr(j)$:
$$ X_{new} = \sum_{j=1}^{M+1} \beta(j) Pr(j) R(j) $$
where $R(j)$ is the feature vector of the $j$-th participant (the chosen instance and its $M$ neighbors), and $\sum \beta(j)Pr(j) = 1$. This method effectively populates the feature space in the densest and most representative regions of the minority class for the casting parts, creating a balanced training dataset.
Following the creation of a balanced dataset, we perform feature selection to reduce dimensionality and improve model efficiency. We utilize the XGBoost algorithm on the balanced training data to rank all process parameters by their importance in predicting the quality of the casting parts. Parameters with the lowest importance scores are pruned, retaining only the most influential features for the final modeling stage. This step helps in mitigating overfitting and building a more interpretable and faster model.
The final stage is building the predictive model. Instead of relying on a single algorithm, we employ a Stacking ensemble learning framework to combine the strengths of multiple, diverse base learners. In the first layer, we train several distinct classifiers: Random Forest (RF), Support Vector Machine (SVM) with a radial basis function kernel, and XGBoost. These models are chosen for their complementary learning styles. We use 5-fold cross-validation on the balanced training data for each base learner. For each fold, the predictions on the held-out validation fold are collected. Once trained, the base learners generate a new set of features: their prediction scores (e.g., class probabilities) for the entire training data. These meta-features, along with the original target labels, form the dataset for the second-layer meta-learner. We choose LightGBM as the meta-learner due to its high efficiency and accuracy. This Stacking ensemble, denoted as SyMProD-Stacking, learns to optimally combine the predictions from the base models, often leading to superior generalization performance for predicting the quality of new casting parts compared to any single model.
To validate our proposed SyMProD-Stacking methodology, we conducted an extensive experimental study using real-world investment casting data for high-temperature turbine blades. The original dataset contained records for 10,000 casting parts with 31 initial process parameters. After preprocessing and removing non-varying parameters, the dataset was characterized. The class imbalance was severe, with 8,502 qualified and 1,498 unqualified parts, yielding an imbalance ratio of approximately 5.67:1.
| Process Parameter | Min | Max | Mean | Coeff. of Variation |
|---|---|---|---|---|
| Low-Temperature Strength (MPa) | 8.51 | 11.00 | 10.037 | 0.0590 |
| High-Temperature Strength (MPa) | 20.01 | 25.00 | 22.660 | 0.0579 |
| Slurry Viscosity – Layer 2 (MPa·s) | 42.55 | 43.95 | 43.281 | 0.0047 |
| Silicon Content – Layer 3 (%) | 28.25 | 30.41 | 29.324 | 0.0183 |
| Dewaxing Pressure (MPa) | 0.53 | 0.58 | 0.563 | 0.0198 |
| Pouring Temperature (°C) | 1481.00 | 1484.00 | 1482.299 | 0.0007 |
| Pouring Weight (kg) | 28.80 | 29.60 | 29.184 | 0.0068 |
| Remelt Slag Ratio (%) | 0.01 | 0.06 | 0.043 | 0.2518 |
| Melting Vacuum Degree | 0.04 | 0.39 | 0.219 | 0.4695 |
| Crucible Usage Count | 1.00 | 6.00 | 3.326 | 0.4461 |
Our first experiment demonstrated the critical impact of handling imbalance. We compared models trained on the raw imbalanced data versus models trained on data balanced using our SyMProD method (with parameters $K=5$, $M=5$, $NT=3$, $CT=1.2$). The feature selection step reduced the parameters to the 10 most important ones, including pouring temperature, pouring weight, remelt slag ratio, and crucible usage count. Using classifiers like LightGBM, RF, and SVM, the results were stark. While overall accuracy slightly decreased for the balanced data, the prediction accuracy for the crucial minority class (unqualified casting parts) increased dramatically by 75.4%. More importantly, the balanced models showed substantial gains in all three robustness metrics: AUC-ROC increased by 24-28%, G-mean by 30-35%, and F1-score by 32-50%. This confirms that the SyMProD oversampling is essential for building a practically useful predictor for casting parts quality.
We then compared SyMProD against other popular oversampling techniques: SMOTE, ADASYN, and K-Means-SMOTE. Using the same 10 selected features and classifiers (LightGBM, RF, SVM), we evaluated the performance on the test set. The results, averaged over 5-fold cross-validation, are summarized below.
| Classifier | Oversampling Method | AUC-ROC | G-mean | F1-Score |
|---|---|---|---|---|
| LightGBM | SMOTE | 0.724 | 0.697 | 0.512 |
| ADASYN | 0.737 | 0.682 | 0.504 | |
| K-Means-SMOTE | 0.780 | 0.721 | 0.573 | |
| SyMProD | 0.803 | 0.741 | 0.629 | |
| Random Forest | SMOTE | 0.701 | 0.677 | 0.486 |
| ADASYN | 0.696 | 0.654 | 0.507 | |
| K-Means-SMOTE | 0.746 | 0.719 | 0.574 | |
| SyMProD | 0.759 | 0.706 | 0.597 | |
| SVM | SMOTE | 0.712 | 0.681 | 0.497 |
| ADASYN | 0.719 | 0.691 | 0.528 | |
| K-Means-SMOTE | 0.775 | 0.714 | 0.564 | |
| SyMProD | 0.791 | 0.734 | 0.616 |
The table clearly shows that SyMProD consistently achieves the best or near-best performance across all classifiers and metrics for predicting the quality of these casting parts. This validates its effectiveness in generating high-quality synthetic samples that better represent the underlying distribution of the minority class in the complex feature space of casting process parameters.
The final experiment pitted our full SyMProD-Stacking ensemble model against the strongest individual classifiers (each trained on SyMProD-balanced data). The Stacking model used RF, SVM, and XGBoost as base learners and LightGBM as the meta-learner.
| Model | AUC-ROC | G-mean | F1-Score |
|---|---|---|---|
| SyMProD-Stacking (Proposed) | 0.847 | 0.769 | 0.665 |
| LightGBM | 0.803 | 0.741 | 0.629 |
| XGBoost | 0.794 | 0.736 | 0.621 |
| SVM | 0.791 | 0.724 | 0.616 |
| Random Forest | 0.759 | 0.706 | 0.597 |
The results are conclusive. Our proposed SyMProD-Stacking framework outperformed all single models significantly. Compared to the best single model (LightGBM), it achieved improvements of 5.48% in AUC-ROC, 3.78% in G-mean, and 5.72% in F1-score. Compared to the weakest single model (RF), the improvements were even more pronounced: 11.59%, 8.92%, and 11.39%, respectively. This demonstrates the power of the Stacking ensemble to integrate diverse predictive patterns from different algorithms, leading to a more robust and accurate final model for the challenging task of quality prediction for high-temperature turbine blade casting parts.
In conclusion, the quality prediction for high-value, complex casting parts like turbine blades is critically hampered by imbalanced historical data. This work presents a holistic and effective solution to this problem. By integrating a probabilistic oversampling technique (SyMProD) that intelligently generates synthetic minority samples with a powerful Stacking ensemble learning architecture, we develop a predictive model that excels at identifying potential defects. The SyMProD method effectively rebalances the dataset while avoiding noise and overlap, and the Stacking framework leverages model diversity to capture complex, non-linear relationships in the casting process data. Our empirical validation on real industrial data confirms the superiority of this approach, showing marked improvements in key metrics like F1-score and G-mean for the minority class. This methodology provides a practical and powerful tool for manufacturers to transition towards proactive quality control, enabling early detection of process deviations that could lead to defective casting parts, thereby reducing waste, saving costs, and ensuring the reliability of critical components. Future work could explore adapting this framework for multi-class quality grading or integrating it with real-time process control systems for closed-loop quality optimization in the production of casting parts.