Data-Driven Quality Prediction and Process Optimization in Sand Casting Foundry

1. Introduction and Research Context

Sand casting foundry technology remains the most widely applied casting method globally, particularly in the mass production of critical components for automotive, railway, and construction machinery industries. In 2020, the total output of various castings in China reached 51.95 million tons, with sand casting foundry processes accounting for more than 80% of this production. Despite its prevalence, the sand casting foundry industry faces significant quality control challenges due to its multi-step production chain, numerous influencing factors, and substantial parameter variability.

The primary quality issues in sand casting foundry operations include substandard mechanical properties and excessive defects, both of which lead directly to casting scrap. The quantitative relationships between process parameters and final casting quality remain unclear in most sand casting foundry plants. Process parameter settings and controls depend heavily on empirical experience and trial-and-error experiments, making precise parameter adjustments extremely difficult. This severely limits product quality improvement and production efficiency.

In recent years, the informatization level of the sand casting foundry industry has improved substantially. Enterprise Resource Planning (ERP) systems and Manufacturing Execution Systems (MES) now record large volumes of first-line production data, including equipment parameters, process data, environmental conditions, and quality inspection results. However, these data resources remain largely untapped, presenting what is commonly described as “data explosion, knowledge poverty” in the sand casting foundry sector.

This research aims to address these challenges by developing data-driven models for mechanical property prediction and defect prediction in sand casting foundry operations. Specifically, I utilize Back Propagation (BP) neural networks to construct prediction models for typical casting mechanical properties and sand hole defects, then hybridize BP neural networks with genetic algorithms for process parameter optimization. Additionally, I propose an interactive Nelder-Mead simplex search system for scenarios with limited data availability.

2. Data Mining and Analysis for Sand Casting Foundry

2.1 Production Process Analysis

The sand casting foundry production process is characterized by a long production route involving multiple interconnected stages. Through on-site investigation, I mapped the key production and inspection procedures as summarized in Table 1.

Table 1: Key production and inspection procedures in sand casting foundry

The sand casting foundry operations exhibit three distinctive characteristics: (1) lengthy production routes combining multiple processes; (2) numerous influencing factors making defect source identification difficult; and (3) quality inspection often lagging behind production processes.

2.2 Key Factors Affecting Mechanical Properties and Defects

I analyzed the factors affecting casting quality using a fishbone diagram structure, identifying four main categories: personnel, equipment, materials, and process parameters. The key process parameters affecting mechanical properties and defects in sand casting foundry are summarized in Table 2.

Table 2: Key factors affecting mechanical properties and defects

2.3 Production Data Mining Based on ERP System

I utilized the HuaZhu ERP system deployed in a sand casting foundry enterprise in Jiangsu Province, which has accumulated nearly a decade of production data. The system implements a single-piece lifecycle management model, where each casting is assigned a unique single-piece ID serving as the primary key. This enables tracking and correlation of multi-process data throughout production.

Through data mining, I obtained 120,000 raw single-piece records. After analyzing casting names and categories, I identified typical castings with sufficient data quality for research. Table 3 shows the top ten casting names by data volume.

Table 3: Top ten casting names by single-piece data volume

| Casting Name | Single-piece Data Volume |
|—|—|
| Mechanical Seal Gland 1 | 4902 |
| Mechanical Seal Gland 2 | 2878 |
| Valve Cover 1 | 2480 |
| Cover Plate Clamp | 2416 |
| Middle Section | 1910 |
| Mechanical Seal Gland 3 | 1881 |
| Impeller Flange | 1462 |
| Suction Section 1 | 1330 |
| Valve Cover 2 | 1222 |
| Suction Section 2 | 1103 |

I selected the casting “Mechanical Seal Gland SCP300/400HA-GR.03” (made of 304 stainless steel) as the primary research subject due to its substantial data volume and documented quality issues. After cleaning and processing the 4902 raw records, I obtained 696 complete single-piece records. The data cleaning process involved removing duplicate records from identical production batches and filling missing ambient temperature data using web-scraped historical weather data.

Table 4: Statistical analysis of the mechanical seal gland dataset

| Parameter No. | Parameter Name | Maximum | Minimum | Mean | Variance |
|—|—|—|—|—|—|
| 1 | Sand tensile strength (MPa) | 0.863 | 0.189 | 0.387 | 0.168 |
| 2 | Sand compressive strength (MPa) | 3.183 | 0.491 | 1.916 | 0.480 |
| 3 | Molding day temperature (℃) | 32.5 | 1 | 13.711 | 7.987 |
| 4 | Molding weather condition | Sunny, Cloudy, Rainy | | | |
| 5 | C element content (%) | 0.071 | 0.05 | 0.057 | 0.007 |
| 6 | Si element content (%) | 0.885 | 0.37 | 0.545 | 0.155 |
| 7 | Mn element content (%) | 1.444 | 0.92 | 1.143 | 0.162 |
| 8 | P element content (%) | 0.04 | 0.025 | 0.033 | 0.005 |
| 9 | S element content (%) | 0.015 | 0.001 | 0.006 | 0.005 |
| 10 | Cr element content (%) | 18.486 | 17.572 | 18.203 | 0.133 |
| 11 | Ni element content (%) | 9.474 | 8.01 | 8.151 | 0.220 |
| 12 | Mo element content (%) | 0.365 | 0 | 0.032 | 0.076 |
| 13 | Cu element content (%) | 0.345 | 0 | 0.011 | 0.057 |
| 14 | V element content (%) | 0.094 | 0 | 0.003 | 0.016 |
| 15 | Actual pouring temperature (℃) | 1650 | 1564 | 1610.260 | 14.861 |
| 16 | Heat treatment maximum temperature (℃) | 1150 | 630 | 1092.651 | 60.338 |
| 17 | Holding time (h) | 1 | 0.5 | 0.803 | 0.244 |
| 18 | Heat treatment type | Quenching, Solution, Tempering, Normalizing |
| 19 | Sand hole defect status | 629 samples without defect, 67 samples with defect |
| 20 | Yield strength (MPa) | 315 | 215 | 262.865 | 27.240 |
| 21 | Tensile strength (MPa) | 595 | 510 | 538.115 | 21.647 |
| 22 | Elongation after fracture (%) | 75 | 52 | 61.374 | 5.612 |

2.4 Multiple Linear Regression Baseline

Before employing neural networks, I built multiple linear regression models using Minitab 18 software. The regression equation is:

$$Y = a_1X_1 + a_2X_2 + \cdots + a_nX_n + \beta$$ (1)

For yield strength and elongation, I applied Box-Cox transformation to improve normality:

$$\frac{Y^\lambda – 1}{\lambda \times g^{\lambda-1}} = a_1X_1 + a_2X_2 + \cdots + a_nX_n + \beta$$ (2)

Table 5: Overall performance of multiple linear regression models

| Regression Model | S | R² | R²ₐ | R²ₐ (predicted) |
|—|—|—|—|—|
| Yield strength model | 6.82345 | 0.943 | 0.942 | 0.939 |
| Tensile strength model | 6.94769 | 0.900 | 0.897 | 0.889 |
| Elongation model | 2.52120 | 0.804 | 0.799 | 0.787 |

The coefficient of determination R²ₐ(predicted) reached 0.939, 0.889, and 0.787 for yield strength, tensile strength, and elongation respectively. The elongation model performed poorly, suggesting the presence of nonlinear relationships between process parameters and mechanical properties in the sand casting foundry context.

3. BP Neural Network Prediction Models

3.1 BP Neural Network Fundamentals

The Back Propagation (BP) neural network is the most widely applied neural network architecture. It is a multi-layer feedforward network trained using supervised learning. The basic neuron computes:

$$net_i = \sum_{j=1}^{n} w_{ji}x_j + b_i$$ (3)

$$y_i = f(net_i) = f\left(\sum_{j=1}^{n} w_{ji}x_j + b_i\right) = f(W \cdot X + b_i)$$ (4)

The BP algorithm employs gradient descent optimization with two passes: forward propagation and backward propagation. During forward propagation, input data flows from the input layer through hidden layers to the output layer. During backward propagation, prediction errors propagate backward, and each layer’s weights and biases are adjusted to minimize the error.

3.2 Data Preprocessing

For continuous numerical data, I applied normalization to the range [-1, 1]:

$$x_N = \frac{2x – x_{max} – x_{min}}{x_{max} – x_{min}}$$ (5)

For discrete categorical data (weather condition, heat treatment type), I used one-hot encoding. After preprocessing, each sample had 23 input elements and 1 output element, resulting in a 23-node input layer and 1-node output layer. I split the 696 samples into 418 training, 139 validation, and 139 testing samples (60:20:20 ratio).

3.3 Network Structure Optimization

Table 6: Input and output parameters for the tensile strength prediction model

I tested hidden layer node counts from 6 to 50 for single-hidden-layer structures. Table 7 shows representative results.

Table 7: Effect of hidden layer node count on model performance

| Hidden Nodes | MSE | R² | AER |
|—|—|—|—|
| 6 | 50.095 | 0.928 | 0.0026 |
| 7 | 20.149 | 0.964 | 0.0015 |
| 32 | 11.459 | 0.979 | 0.0009 |
| 35 | 20.978 | 0.965 | 0.0012 |
| 36 | 13.643 | 0.976 | 0.0009 |
| 37 | 0.960 | 0.998 | 0.0003 |
| 38 | 14.561 | 0.975 | 0.0009 |
| 50 | 67.858 | 0.903 | 0.0026 |

The single-hidden-layer structure with 37 nodes (23-37-1) provided the best performance. For the double-hidden-layer case, the optimal structure was 23-8-4-1. I also compared five training algorithms: trainlm (Levenberg-Marquardt), trainoss (one-step secant), trainrp (resilient backpropagation), trainscg (scaled conjugate gradient), and traingdx (variable learning rate gradient descent). The LM algorithm (trainlm) consistently outperformed others in terms of MSE, R², and AER.

3.4 Final Model Architecture and Performance

After extensive testing, I determined the optimal network structures for all prediction models, summarized in Table 8.

Table 8: Optimal network structures and parameters for prediction models

| Model Name | Hidden Layers | Structure | Activation Function | Training Algorithm | Learning Rate | Max Epochs |
|—|—|—|—|—|—|—|
| Yield strength model | Single | 23-37-1 | tansig-purelin | LM algorithm | 0.01 | 30000 |
| Tensile strength model | Single | 23-37-1 | tansig-purelin | LM algorithm | 0.01 | 30000 |
| Elongation model | Single | 23-45-1 | tansig-purelin | LM algorithm | 0.01 | 30000 |
| Sand hole defect model | Single | 23-35-1 | Relu-Sigmoid | LM algorithm | 0.01 | 30000 |

Table 9: Performance evaluation of mechanical property prediction models

| Model Name | MSE | R² | AER |
|—|—|—|—|
| Yield strength model | 2.313 | 0.997 | 0.0005 |
| Tensile strength model | 0.960 | 0.998 | 0.0003 |
| Elongation model | 0.197 | 0.994 | 0.0007 |

The coefficient of determination reached 0.997, 0.998, and 0.994 for yield strength, tensile strength, and elongation prediction, respectively. These results substantially outperform the multiple linear regression models, confirming that the sand casting foundry process parameters have complex nonlinear relationships with mechanical properties.

For the sand hole defect prediction model, the confusion matrix is shown in Table 10.

Table 10: Confusion matrix for sand hole defect prediction

| Actual | Predicted: No Defect | Predicted: With Defect |
|—|—|—|
| No defect (629) | 594 | 35 |
| With defect (67) | 9 | 58 |

The overall prediction accuracy reached 93.68% (652/696), including 94.44% (594/629) accuracy for non-defective samples and 86.57% (58/67) accuracy for defective samples.

3.5 Factor Influence Analysis

I employed controlled variable and gradient increment experiments to analyze single-factor effects on mechanical properties. Table 11 summarizes the influence ranges.

Table 11: Single-factor influence ranges on mechanical properties

| Factor | Range | Yield Strength Range (MPa) | Tensile Strength Range (MPa) | Elongation Range (%) |
|—|—|—|—|—|
| C content (%) | 0.05~0.071 | 217.8~238.6 | 527.4~530.8 | 51.1~72.2 |
| Si content (%) | 0.37~0.885 | 217.0~239.0 | 515.6~542.6 | 64.3~66.2 |
| Mn content (%) | 0.92~1.444 | 221.2~223.3 | 511.6~549.9 | 56.6~78.8 |
| P content (%) | 0.025~0.04 | 194.9~255.5 | 517.5~538.2 | 54.6~71.8 |
| Cr content (%) | 17.572~18.486 | 219.8~230.7 | 517.8~536.0 | 58.1~68.1 |
| Ni content (%) | 8.01~9.474 | 220.7~265.7 | 526.5~551.5 | 62.6~66.1 |
| Pouring temp (℃) | 1564~1650 | 219.8~239.6 | 521.9~531.9 | 63.6~68.4 |
| Ambient temp (℃) | 1~32.5 | 216.8~245.7 | 499.2~548.8 | 58.9~72.6 |

3.6 Sensitivity Analysis Using Garson’s Algorithm

I employed Garson’s algorithm for sensitivity analysis, which uses the neural network weight matrices to quantify the relative importance of each input variable. The improved calculation formula is:

$$R_k(i)^* = \frac{\sum_{j=1}^{n}\left(|W_{ij}V_{jk}| / \sum_{i=1}^{n}|W_{ij}|\right)}{\sum_{i=1}^{n}\sum_{j=1}^{n}\left(|W_{ij}V_{jk}| / \sum_{i=1}^{n}|W_{ij}|\right)}$$ (6)

The sensitivity analysis revealed that Cu element content, holding time, sand specimen tensile strength, and P element content were the four most influential factors for tensile strength, though the contributions were relatively evenly distributed among all 23 factors. This finding confirms the production experience that final casting quality in the sand casting foundry depends on nearly every process step.

4. Process Parameter Optimization for Different Data Scenarios

4.1 Relationship Between Data Volume and Prediction Performance

I conducted retrospective testing on the relationship between training data volume and prediction performance using the “Impeller Flange $FLLZG250-24D-082Z” casting (ZG270-500 carbon steel, 1126 complete records). Figure 3 shows the relationship between training set size and R².

Table 12: Training data volume vs. prediction performance

| Training Data Volume | Optimal Hidden Nodes | R² |
|—|—|—|
| 100 | 12 | 0.0995 |
| 200 | 25 | 0.170 |
| 300 | 25 | 0.233 |
| 400 | 27 | 0.524 |
| 500 | 24 | 0.659 |
| 600 | 28 | 0.619 |
| 700 | 32 | 0.835 |
| 800 | 30 | 0.876 |
| 900 | 33 | 0.927 |

The results clearly demonstrate that when the training dataset is too small, the model’s prediction performance is extremely poor. With 700 data points, the coefficient of determination reached 0.9 or above.

Table 13: Dynamic retrospective testing simulating production process

| Training Data Volume | R² |
|—|—|
| 300 | 0.784 |
| 600 | 0.898 |
| 900 | 0.964 |

4.2 Hybrid BP Neural Network and Genetic Algorithm Optimization

For scenarios with sufficient data, I hybridized the BP neural network with a genetic algorithm (GA). The optimization workflow is: user inputs target mechanical properties → GA generates initial population → BP neural network predicts outputs for each individual → fitness function evaluates individuals → selection, crossover, mutation generate next generation → iteration until stopping criteria.

The fitness function is designed as:

$$gap = \begin{cases} w_1 \times |T_{\sigma_s} – \sigma_s| + w_2 \times |T_{R_m} – R_m| + w_3 \times |T_A – A| & \text{①} \\ C_{1max} & \text{②} \end{cases}$$ (7)

$$fitness = C_{2max} – gap$$ (8)

Branch ① executes when no sand hole defects are predicted; branch ② executes when defects are predicted. The GA parameters were: population size M=100, crossover probability pc=0.8, mutation probability pm=0.001, termination generation T=500.

Table 14: GA parameter settings

| Parameter | Value |
|—|—|
| Population size M | 100 |
| Crossover probability pc | 0.8 |
| Mutation probability pm | 0.001 |
| Termination generation T | 500 |
| Encoding method | Binary encoding |

Table 15: Simulation experiment results – user input targets vs. predicted values

| Prediction Item | Target Value | Predicted Value | Difference |
|—|—|—|—|
| Yield strength (MPa) | 315 | 314.80 | 0.20 |
| Tensile strength (MPa) | 530 | 530.22 | 0.22 |
| Elongation (%) | 52 | 52.09 | 0.09 |
| Sand hole defect | No defect | No defect | Consistent |

Table 16: Optimized process parameter combination from simulation

| Parameter | Optimized Value |
|—|—|
| Sand specimen tensile strength (MPa) | 0.675 |
| Sand specimen compressive strength (MPa) | 2.059 |
| Molding day temperature (℃) | 1.7 |
| Molding weather condition | Sunny |
| C content (%) | 0.059 |
| Si content (%) | 0.841 |
| Mn content (%) | 1.213 |
| P content (%) | 0.028 |
| S content (%) | 0.011 |
| Cr content (%) | 17.999 |
| Ni content (%) | 8.077 |
| Mo content (%) | 0.281 |
| Cu content (%) | 0.073 |
| V content (%) | 0.065 |
| Actual pouring temperature (℃) | 1645 |
| Heat treatment maximum temperature (℃) | 1144 |
| Holding time (h) | 0.5 |
| Heat treatment type | Solution |

In the second simulation experiment, I aimed to minimize Ni element usage while maintaining similar mechanical properties. The comparison is shown in Table 17.

Table 17: Historical vs. optimized process parameters for reducing Ni usage

| Parameter | Historical Process | Optimized Process |
|—|—|—|
| Ni content (%) | 9.232 | 8.055 |
| C content (%) | 0.059 | 0.062 |
| Si content (%) | 0.645 | 0.861 |
| Mn content (%) | 1.354 | 1.073 |
| Cr content (%) | 17.572 | 18.333 |
| Heat treatment temperature (℃) | 1100 | 1113.1 |

Table 18: Comparison of mechanical properties

| Property | Historical Detection Value | Optimized Prediction Value |
|—|—|—|
| Yield strength (MPa) | 255 | 255.18 |
| Tensile strength (MPa) | 550 | 549.86 |
| Elongation (%) | 71 | 71.08 |
| Sand hole defect | No defect | No defect |

The results demonstrate that Ni element usage was reduced by 12.7% while achieving similar mechanical properties.

4.3 Nelder-Mead Simplex Search Method for Limited Data

When production data is insufficient, particularly during new product trials, I employed the Nelder-Mead simplex method (NMSM). This method is suitable for nonlinear unconstrained optimization and requires few experiments.

Table 19: Comparison of process parameter optimization methods

The algorithm’s key steps include initialization, determining the worst point x(h), second-worst point x(s), and best point x(l), followed by reflection, expansion, contraction, and shrinkage operations. Reflection points are calculated as:

$$x^{(r)} = \bar{x} + \alpha(\bar{x} – x^{(h)})$$ (9)

Expansion points:

$$x^{(e)} = \bar{x} + \gamma(x^{(r)} – \bar{x})$$ (10)

I validated the algorithm using a numerical function minimization test:

$$\min f(x_1, x_2) = (x_1 – 3)^2 + 2(x_2 + 2)^2, \quad -6 \leq x_i \leq 6$$ (11)

The algorithm converged close to the global optimum (3, -2) within approximately 16 interaction cycles, with function values of 0.125, 0.044, and 0.067 for three random initial simplices.

Table 20: Simplex search process for new inorganic sand parameter optimization

| Experiment No. | Binder (%) | Hardener (%) | Heating Temp (℃) | Heating Time (s) | 24h Tensile Strength (MPa) |
|—|—|—|—|—|—|
| 1 | 1.5 | 30 | 140 | 120 | 0.741 |
| 2 | 1.5 | 40 | 160 | 140 | 1.409 |
| 3 | 1.5 | 50 | 180 | 160 | 2.292 |
| 4 | 2.0 | 30 | 160 | 160 | 1.207 |
| 5 | 2.5 | 40 | 140 | 160 | 1.005 |
| 6 | 2.25 | 50 | 180 | 190 | 3.009 |
| 7 | 2.625 | 60 | 200 | 225 | 3.005 |
| 8 | 1.125 | 45 | 200 | 165 | 1.648 |
| 9 | 1.188 | 62.5 | 200 | 167.5 | 2.490 |
| 10 | 1.531 | 63.75 | 220 | 201.25 | 3.255 |

Within just 10 experiments, the tensile strength improved from the initial range of 0.741-2.292 MPa to a maximum of 3.255 MPa, demonstrating the efficiency of the simplex search method in the sand casting foundry context.

I also proposed and implemented an interactive simplex search system that entirely encapsulates the complex algorithmic logic. The system recommends the next experimental point, accepts user inputs for experimental results, and provides subsequent recommendations, effectively managing experiments through persistent data storage.

5. System Development and Application Testing

5.1 System Architecture

I developed a sand casting foundry process parameter optimization system using UML modeling for requirements analysis. The system follows a three-tier architecture: presentation layer, business logic layer, and data access layer, utilizing the SSM framework (Spring + MyBatis + SpringMVC) with MySQL for data persistence.

Table 21: Core class descriptions in the system

5.2 Application Testing Results

I tested the system using 18 new single-piece records from production. Table 22 presents the prediction errors.

Table 22: Prediction error evaluation for the latest 18 castings

| Prediction Item | Maximum Error Rate | Average Error Rate (AER) |
|—|—|—|
| Yield strength | 2.09% | 0.75% |
| Tensile strength | 1.94% | 0.89% |
| Elongation after fracture | 5.14% | 1.76% |

The system’s main functional modules include: (1) experiment management, allowing users to create, query, and delete experiments; (2) quality prediction for mechanical properties and sand hole defects; (3) process parameter optimization using the hybrid BP-GA method with user-specified target values and weights; and (4) interactive simplex search optimization for limited-data scenarios.

Table 23: Summary of predicted values for a sample casting

| Prediction Item | Predicted Value |
|—|—|
| Yield strength (MPa) | 235.78 |
| Tensile strength (MPa) | 510.73 |
| Elongation after fracture (%) | 63.24 |
| Sand hole defect | No defect |

6. Conclusions and Outlook

This research addressed the critical challenge of unclear quantitative relationships between process parameters and casting quality in the sand casting foundry industry. The main conclusions are:

(1) I completed multi-process data mining for sand casting foundry operations, correlating parameters across production stages using unique single-piece identifiers. This yielded 696 complete records for a 304 steel gland casting and 1126 records for an impeller flange casting.

(2) BP neural network prediction models for yield strength, tensile strength, and elongation achieved coefficient of determination values of 0.997, 0.998, and 0.994 respectively, substantially outperforming linear regression models. The sand hole defect prediction model achieved 93.68% overall accuracy.

(3) The hybrid BP neural network and genetic algorithm approach successfully optimized process parameters according to user requirements. The algorithm reduced Ni usage by 12.7% while maintaining similar mechanical properties.

(4) For limited-data scenarios, the interactive simplex search system enabled efficient process parameter optimization, achieving satisfactory results within 10 experiments for new inorganic sand proportioning in the sand casting foundry application.

(5) The developed system demonstrated high prediction accuracy and provided quantitative relationships between process parameters and mechanical properties, offering valuable guidance for parameter setting and control.

Future research directions include extending the methodology to casting families with similar characteristics, developing automated model training capabilities for new casting types, and employing genetic algorithms for neural network training to achieve more automatic and stable optimization in sand casting foundry operations.