In the field of sand casting, predicting the quality of complex castings is crucial due to the prevalence of defects such as cold shuts, porosity, sand inclusions, and shrinkage cavities. These defects are influenced by a combination of process parameters and the three-dimensional (3D) structure of the castings. However, the complex 3D geometry of castings poses significant challenges in quantitative characterization, making it difficult to establish a clear relationship between morphology and quality. Traditional data-driven approaches in sand casting often neglect 3D shape analysis, limiting their ability to identify defect causes in complex regions. To address this, we focus on leveraging multi-source heterogeneous data, including structured process parameters and 3D structural data, to develop a robust quality prediction model. This research aims to extract meaningful features from 3D casting models using advanced deep learning techniques and integrate them with process data for accurate defect prediction. By doing so, we can enhance the understanding of how casting morphology affects quality and improve production outcomes in sand casting.
The sand casting process involves several stages, each contributing to the final quality of the castings. Key steps include sand mixing, molding, core making, melting, and pouring. Each stage generates structured data, such as sand properties (e.g., moisture content, compactability, permeability, and green strength) and melting parameters (e.g., pouring temperature, time, and inoculant addition). Additionally, the 3D models of castings, like steering axles, slewing frames, and axle housings, represent non-structured data that are difficult to quantify. These castings often have intricate geometries, leading to variations in defect occurrence. For instance, steering axles connect wheels and frames, bearing loads and transmitting driving forces, while axle housings protect internal components and support structural integrity. The complexity of these shapes necessitates advanced feature extraction methods to capture relevant morphological characteristics.
| Characteristic | Description |
|---|---|
| Wide Applicability | Not limited by size, thickness, or shape; capable of producing castings over 300 tons. |
| Material Variety | Compatible with various alloy materials, primarily cast iron, cast steel, and aluminum alloys. |
| High Dimensional Accuracy | Superior precision compared to forging and welding processes. |
| Cost-Effectiveness | Low production costs, making it economically viable for large-scale applications. |
To address the challenges in 3D feature extraction, we employ a deep convolutional autoencoder (3D-DCAE) model. Autoencoders are unsupervised learning models that reconstruct input data through an encoding and decoding process, effectively reducing dimensionality while preserving essential features. The 3D-DCAE utilizes 3D convolutional layers to scan the volumetric data of castings, capturing spatial relationships that are missed by traditional 2D approaches. The encoding process transforms the input 3D voxel grid into a latent representation, denoted as \( h \), which encapsulates the key shape features. The decoding process reconstructs the original 3D shape from \( h \), and the model is trained by minimizing the reconstruction error. The loss function, based on mean squared error, is defined as:
$$ L = \frac{1}{N} \sum_{i=1}^{N} \| x_i – \hat{x}_i \|^2 $$
where \( x_i \) is the original 3D data, \( \hat{x}_i \) is the reconstructed data, and \( N \) is the number of samples. This approach allows us to extract compact features that represent the casting morphology, facilitating the integration with process data for quality prediction.
In our implementation, the 3D-DCAE model consists of multiple 3D convolutional and pooling layers in the encoder, followed by deconvolutional layers in the decoder. The input to the model is a voxelized representation of the casting 3D model, with dimensions [depth, height, width]. For example, a typical voxel grid might be of size 64x64x64. The encoder uses 3D convolutional kernels with a stride of 1 and padding to maintain spatial dimensions, followed by max-pooling to reduce size. The decoder mirrors this structure with deconvolutional layers to upsample the latent representation back to the original dimensions. The latent space \( h \) is a flattened vector that serves as the feature set for subsequent analysis. Compared to a 2D convolutional autoencoder (2D-DCAE), which treats depth as channels, the 3D-DCAE preserves spatial continuity across all three dimensions, leading to more accurate reconstructions. Experimental results show that the 3D-DCAE achieves a reconstruction accuracy of 99.76%, significantly outperforming the 2D-DCAE, which struggles with depth-wise correlations.
| Model | Reconstruction Accuracy | Training Time (hours) | Key Advantage |
|---|---|---|---|
| 3D-DCAE | 99.76% | 12 | Captures full 3D spatial features |
| 2D-DCAE | 95.30% | 10 | Faster but less accurate |
The defect prediction model integrates the extracted 3D features with structured process data, such as sand properties and melting parameters, to form a multi-source heterogeneous dataset. Before training, the data undergoes preprocessing, including normalization to scale values between 0 and 1, and one-hot encoding for categorical defect labels. Normalization is critical for accelerating convergence and improving model sensitivity, as it ensures that all features contribute equally to the learning process. The normalization formula is given by:
$$ x_{\text{norm}} = \frac{x – x_{\min}}{x_{\max} – x_{\min}} $$
where \( x \) is the original value, and \( x_{\min} \) and \( x_{\max} \) are the minimum and maximum values in the dataset. The model architecture is a hybrid convolutional neural network (CNN) combined with fully connected layers, designed to handle the heterogeneous input. The network topology includes two 1D convolutional layers with kernel size 3, which scan the input data to capture local patterns, followed by a max-pooling layer to reduce dimensionality and highlight salient features. The output is flattened and passed through a fully connected layer to produce a five-dimensional vector corresponding to the defect types: cold shuts, porosity, sand inclusions, shrinkage cavities, and no defect. The model uses a cross-entropy loss function with a cost-sensitive regularizer to address class imbalance, defined as:
$$ L_{\text{total}} = -\sum_{c=1}^{C} y_c \log(\hat{y}_c) + \lambda \sum_{c=1}^{C} w_c \cdot \text{penalty}(c) $$
where \( y_c \) is the true label, \( \hat{y}_c \) is the predicted probability for class \( c \), \( C \) is the number of classes, \( \lambda \) is a regularization parameter, and \( w_c \) is a weight for class \( c \) to penalize misclassifications of rare defects. Training is performed using mini-batch gradient descent with a batch size of 64, initial learning rate of 0.01, and 80 epochs to ensure stable convergence.
| Parameter | Value |
|---|---|
| Training Set Proportion | 0.8 |
| Test Set Proportion | 0.2 |
| Initial Learning Rate | 0.01 |
| Number of Epochs | 80 |
| Batch Size | 64 |
| Loss Function | Cross-entropy with cost-sensitive regularization |
| Optimization Algorithm | Mini-batch gradient descent |
To evaluate the effectiveness of our approach, we compare the proposed model against traditional methods, such as multilayer perceptron (MLP) and standard CNN. The MLP model achieves accuracies of 92.6% on the training set and 86.1% on the test set, while the standard CNN reaches 93.9% and 90.7%, respectively. In contrast, our model attains 96.5% training accuracy and 93.7% test accuracy, demonstrating superior performance in predicting defects for sand casting. This improvement is attributed to the integration of 3D morphological features, which provide additional insights into how casting geometry influences defect formation. For instance, features like hotspots and concave-convex degrees, extracted by the 3D-DCAE, correlate with defects such as shrinkage cavities and cold shuts, enabling more precise predictions.
In conclusion, this research addresses the challenges in quality prediction for complex sand casting by leveraging multi-source heterogeneous data. We have developed a comprehensive framework that includes data acquisition from sand mixing, molding, melting, and pouring processes, followed by advanced 3D feature extraction using a deep convolutional autoencoder. The integration of these features with process data into a defect prediction model has proven effective, achieving high accuracy in identifying common defects. This approach not only enhances the understanding of morphology-quality relationships but also provides a practical tool for improving sand casting production. Future work could explore real-time application in industrial settings and extend the model to other casting methods.
The sand casting industry can benefit significantly from this data-driven methodology, as it enables proactive quality control and reduces defect rates. By continuously refining the feature extraction and prediction models, we can further optimize the sand casting process for various complex geometries and materials. The use of 3D convolutional autoencoders represents a step forward in handling non-structured data in manufacturing, paving the way for more intelligent and adaptive systems in sand casting and beyond.