Pulp Chemistry Variables for Gaussian Process Prediction of Rougher Copper Recovery
Abstract
:Highlights
- Model-selected input variables for training the GPR model varies in the presence of pulp chemistry data (pH, Eh, dissolved oxygen and temperature).
- RNCA showed the pulp chemistry feature weight in the order dissolved oxygen > pH > Eh > temperature.
- The GPR predictive model performance improves with the addition of pulp chemistry variables.
- Pulp chemistry parameters are essential in predicting rougher copper recovery, particularly for complex ores.
Abstract
1. Introduction
- How does pulp chemistry variable addition to existing model-selected variables affect rougher copper recovery performance?
- Does the addition of pulp chemistry variables during input variation selection encourage elimination of some originally model-selected flotation process variables in predicting the rougher copper recovery?
- What is the predictive accuracy of a GPR algorithm in predicting rougher copper recovery with and without pulp chemistry variables?
2. Methodology
2.1. Data Collection and Pre-Processing
- Sample from a chosen slurry stream is collected into the PCM® sample vessel;
- The pulp chemistry sensors (e.g., pH, Eh and dissolved oxygen) are contacted for 2 min in the PCM® sample vessel. A time of 2 min was selected as it allows stable sensor readings for each batch slurry sampling;
- The measured data is logged and time-stamped;
- The PCM® sample vessel is then flushed clean for new sample collection. This process is repeated every 3–5 min.
- th standardized observation
- th observation of sample
- mean of sample
- standard deviation of sample
2.2. Model Development
2.3. Model Performance Assessment Criteria
- th true rougher copper recovery value
- mean of true rougher copper recovery
- th predicted rougher copper recovery value
- mean of predicted rougher copper recovery
- maximum true rougher copper recovery value
- minimum true rougher copper recovery value
- total number of observations
3. Results and Discussion
3.1. Variable Selection by RNCA Algorithm
3.2. Model Performance Assessment
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Reference | Model | Pulp Chemistry Data |
---|---|---|
[50] | Neural network | Only pH |
[51] | Neural network | None |
[52] | Probabilistic decision tree and Neural network | None |
[53] | Fuzzy logic | None |
[54] | Neural network, Boosted trees, Random forest, Gaussian process regression, Decision table, Support vector machine, M5p model tree, REPTree, Decision stump and M5 rules | None |
[55] | Neural network | None |
[56] | Neural network | None |
[57] | Neural network | None |
[58] | Neural network | None |
[59] | Support vector regression | None |
[32] | Probabilistic decision tree and Neural network | None |
[60] | Genetic algorithm-Support vector machine | None |
[61] | Genetic algorithm-Support vector machine | None |
[62] | Neural network | Only pH |
[63] | Neural network | None |
[64] | Neural network | Only pH |
[65] | Neural network | None |
[66] | Linear regression, Non-linear regression, Neural network, Radial basis function | None |
[67] | Neural network | Only pH |
[68] | Random forest-firefly algorithm | Only pH |
[69] | Neural network (deep learning) | Only pH |
[21] | Neural network (deep learning) | Only pH |
[70] | Random forest, Long Short-Term Memory and Gated recurrent unit | Only pH |
[71] | Fuzzy logic | None |
This work | Gaussian process regression | pH, Eh, dissolved oxygen, temperature |
Variable | Variable Index | Variable Type | ||
---|---|---|---|---|
Established rougher flotation variables | Feed particle size (% passing 75 μm) | x1 | Input variables | |
Throughput (t/h) | x2 | |||
Xanthate dosage (mL/min) | tank cell 1 | x3 | ||
tank cell 4 | x4 | |||
Frother dosage (mL/min) | tank cell 1 | x5 | ||
tank cell 4 | x6 | |||
Froth depth (mm) | tank cell 1 | x7 | ||
tank cell 2/3 * | x8 | |||
tank cell 4/5 * | x9 | |||
Pulp chemistry variables | pH | x10 | ||
Eh | x11 | |||
Dissolved oxygen | x12 | |||
Temperature | x13 | |||
Rougher copper recovery (%) | Output variable |
Scenarios | Input Variables |
---|---|
1 | Established rougher flotation variables |
2 | Established rougher flotation variables and pulp chemistry variables |
3 | Variables as selected by RNCA algorithm |
K-Fold | Best Lambda Values | Selected Variables |
---|---|---|
5 | 0.0101 | x1, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x13 |
6 | 0.0304 | x1, x2, x3, x5, x6, x9, x10, x11, x12, x13 |
7 | 0.0202 | x1, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x13 |
8 | 0.0152 | x1, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x13 |
9 | 0.0279 | x1, x2, x3, x5, x6, x8, x9, x10, x11, x12, x13 |
10 | 0.0203 | x1, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x13 |
Criteria | Scenario 1 | Scenario 2 | Scenario 3 | |||
---|---|---|---|---|---|---|
Training Dataset | Testing Dataset | Training Dataset | Testing Dataset | Training Dataset | Testing Dataset | |
r | 0.9998 | 0.9528 | 0.9999 | 0.9589 | 0.9999 | 0.9806 |
RMSE | 0.0005 | 0.4897 | 0.0004 | 0.4496 | 0.0005 | 0.3122 |
MAPE | 0.0003 | 0.2761 | 0.0003 | 0.2332 | 0.0003 | 0.1948 |
SI | 0.0005 | 0.0052 | 0.0005 | 0.0048 | 0.0005 | 0.0033 |
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Amankwaa-Kyeremeh, B.; Ehrig, K.; Greet, C.; Asamoah, R. Pulp Chemistry Variables for Gaussian Process Prediction of Rougher Copper Recovery. Minerals 2023, 13, 731. https://doi.org/10.3390/min13060731
Amankwaa-Kyeremeh B, Ehrig K, Greet C, Asamoah R. Pulp Chemistry Variables for Gaussian Process Prediction of Rougher Copper Recovery. Minerals. 2023; 13(6):731. https://doi.org/10.3390/min13060731
Chicago/Turabian StyleAmankwaa-Kyeremeh, Bismark, Kathy Ehrig, Christopher Greet, and Richmond Asamoah. 2023. "Pulp Chemistry Variables for Gaussian Process Prediction of Rougher Copper Recovery" Minerals 13, no. 6: 731. https://doi.org/10.3390/min13060731