A Generalized Method for Modeling the Adsorption of Heavy Metals with Machine Learning Algorithms
Abstract
:1. Introduction
2. Materials and Methods
2.1. Regression Algorithms
- (i).
- support vector regression with radial basis function (SVR-RBF) kernel
- (ii).
- support vector regression with polynomial (SVR-poly) kernel
- (iii).
- random forest (RF) regression
- (iv).
- stochastic gradient boosting (SGB) regression
- (v).
- Bayesian additive regression tree (BART)
2.1.1. SVR-RBF
2.1.2. SVR-Poly
2.1.3. RF Regression
2.1.4. SGB Regression
2.1.5. BART
2.2. Evaluation Metrics
2.2.1. Spearman’s Rank Correlation Coefficient (SPcorr)
2.2.2. Coefficient of Determination (R2)
2.2.3. Mean Absolute Error (MAE)
2.2.4. Root Mean Squared Error (RMSE)
2.3. Dataset
- AD1: Superheated steam-activated granular carbon
- AD2: Ragi husk powder (bio-sorbent)
- AD3: Antep pistachio or Pistacia vera L. (bio-sorbent)
- AD4: Red mud
- AD5: Synthesized functional polydopamine@Fe3O4 nanocomposite (PDA@Fe3O4)
- AD6: Eucalyptus leaves (bio-sorbent)
- AD7: Spirulina (Arthospira) maxima (bio-sorbent)
- AD8: Spirulina (Arthospira) indica (bio-sorbent)
- AD9: Spirulina (Arthospira) platensis (bio-sorbent)
- AD10: Reduced graphene oxide-supported nanoscale zero-valent iron (nZVI/rGO) composites
- AD11: Cupric oxide nanoparticles (CuONPs) prepared with Tamarindus indica pulp extract
- AD12: Cerium hydroxylamine hydrochloride (Ce-HAHCl)
- IP1: Operating temperature, T (°C)
- IP2: Initial pH (-)
- IP3: Initial concentration (mg/L)
- IP4: Contact time (min)
- IP5: Adsorbent dosage (mg)
- IP6: Agitator speed (rpm)
- OP: Removal efficiency (%)
2.4. MLA Modeling
2.4.1. Data Interpolation
2.4.2. Parameter Optimization and Model Selection
Individual Metal
Comprehensive Dataset
2.5. Computing Framework
3. Results
3.1. ML Model Evaluation for Individual Dataset
3.2. ML Model Evaluation for Combined Dataset
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Reference | HM | AD | Experimental Parameters | Modeling Methodology | |||
---|---|---|---|---|---|---|---|
Variable Inputs | Fixed Inputs | Output | Data Points | ||||
[19] | Cr(VI) | AD1 | IP1 IP2 IP3 IP4 IP5 | IP6 | OP | 36 | - RSM: R2 = 0.9986 - ANN: R2 = 0.9911 |
[27] | Cr(VI) | AD2 | IP2 IP3 IP5 | IP1 IP4 IP6 | 16 | - ANN: R2 = 0.996 - RSM: R2 = 0.993 | |
[46] | Pb(II) | AD3 | IP2 IP3 IP4 | IP1 IP5 IP6 | 17 | - RSM: R2 = 0.98383 | |
[16] | Pb(II) | AD4 | IP2 IP4 IP5 | IP1 IP3 IP6 | 15 | - ANN: R2 = 0.898 - RSM: R2 = 0.672 | |
[21] | Hg(II) | AD5 | IP2 IP3 IP4 | IP1 IP5 IP6 | OP | 15 | - LI: R2 = 0.991 - FI: R2 = 0.989 - RSM: R2 = 0.9871 |
[28] | Hg(II) | AD6 | IP2 IP3 IP4 IP5 | IP1 IP6 | 30 | - RSM: R2 = 0.984 - FI: R2 = 0.9849 - LI: R2 = 0.9802 - DRI: R2 = 0.9293 - TI: R2 = 0.8769 | |
[29] | Cd(II) | AD7 | IP2 IP3 IP5 IP6 | IP1 IP4 | 27 | - FI: R2 = 0.998 - LI: R2 = 0.969 - ANN: R2 = 0.965 - RSM: R2 = 0.760 | |
Cd(II) | AD8 | 27 | - FI: R2 = 0.994 - ANN: R2 = 0.967 - RSM: R2 = 0.962 - LI: R2 = 0.953 | ||||
Cd(II) | AD9 | 27 | - ANN: R2 = 0.9955 - FI: R2 = 0.979 - RSM: R2 = 0.974 - LI: R2 = 0.967 | ||||
[22] | Cd(II) | AD10 | IP1 IP2 IP3 IP4 | IP5 IP6 | 29 | - ANN: R2 = 0.9999 - LI: R2 = 0.9909 - FI: R2 = 0.9852 - RSM: R2 = 0.9826 - DRI: R2 = 0.8226 | |
[23] | As(III) | AD11 | IP1 IP2 IP3 IP5 | IP4 IP6 | 31 | - ANN: R2 = 0.9994 - LI: R2 = 0.997 - FI: R2 = 0.805 | |
[25] | As(III) | AD12 | IP1 IP2 IP3 IP4 IP5 IP6 | - | 105 | - ANN: R2 = 0.975 |
Parameter (Unit) | Average | Maximum | Minimum | Standard Deviation | HM-AD |
---|---|---|---|---|---|
IP1 (°C) | 25.0 | 48.8 | 1.2 | 9.4 | Cr(VI)-AD1 |
IP2 (-) | 6.0 | 10.8 | 1.2 | 1.9 | |
IP3 (mg/L) | 150.0 | 268.9 | 31.1 | 47.0 | |
IP4 (min) | 50.0 | 73.8 | 26.2 | 9.4 | |
IP5 (mg) | 1.2 | 2.2 | 0.3 | 0.4 | |
IP6 (rpm) | 150.0 | 150.0 | 150.0 | 0.0 | |
OP (%) | 71.2 | 96.3 | 39.7 | 10.6 | |
IP1 (°C) | 25.0 | 25.0 | 25.0 | 0.0 | Cr(VI)-AD2 |
IP2 (-) | 2.0 | 3.0 | 1.0 | 0.8 | |
IP3 (mg/L) | 19.3 | 25.0 | 2.0 | 4.9 | |
IP4 (min) | 120.0 | 120.0 | 120.0 | 0.0 | |
IP5 (mg) | 3.9 | 60.9 | 1.6 | 10.6 | |
IP6 (rpm) | 180.0 | 180.0 | 180.0 | 0.0 | |
OP (%) | 67.0 | 72.7 | 59.2 | 4.0 | |
IP1 (°C) | 30.0 | 30.0 | 30.0 | 0.0 | Pb(II)-AD3 |
IP2 (-) | 3.8 | 5.5 | 2.0 | 1.2 | |
IP3 (mg/L) | 27.5 | 50.0 | 5.0 | 17.8 | |
IP4 (min) | 62.5 | 120.0 | 5.0 | 45.5 | |
IP5 (mg) | 1000.0 | 1000.0 | 1000.0 | 0.0 | |
IP6 (rpm) | 250.0 | 250.0 | 250.0 | 0.0 | |
OP (%) | 76.0 | 97.3 | 26.5 | 22.5 | |
IP1 (°C) | 23.0 | 23.0 | 23.0 | 0.0 | Pb(II)-AD4 |
IP2 (-) | 5.0 | 7.0 | 3.0 | 1.5 | |
IP3 (mg/L) | 32.1 | 32.1 | 32.1 | 0.0 | |
IP4 (min) | 32.5 | 60.0 | 5.0 | 20.8 | |
IP5 (mg) | 5.6 | 10.0 | 1.3 | 3.3 | |
IP6 (rpm) | 150.0 | 150.0 | 150.0 | 0.0 | |
OP (%) | 80.6 | 96.8 | 38.8 | 20.9 | |
IP1 (°C) | 20.0 | 20.0 | 20.0 | 0.0 | Hg(II)-AD5 |
IP2 (-) | 4.0 | 7.0 | 1.0 | 2.3 | |
IP3 (mg/L) | 60.0 | 100.0 | 20.0 | 30.2 | |
IP4 (min) | 240.0 | 420.0 | 60.0 | 136.1 | |
IP5 (mg) | 10.0 | 10.0 | 10.0 | 0.0 | |
IP6 (rpm) | 400.0 | 400.0 | 400.0 | 0.0 | |
OP (%) | 32.7 | 41.0 | 20.5 | 6.3 | |
IP1 (°C) | 25.0 | 25.0 | 25.0 | 0.0 | Hg(II)-AD6 |
IP2 (-) | 6.0 | 9.0 | 3.0 | 1.1 | |
IP3 (mg/L) | 2.7 | 3.9 | 0.5 | 0.5 | |
IP4 (min) | 47.5 | 90.0 | 5.0 | 15.8 | |
IP5 (mg) | 1.5 | 2.5 | 0.5 | 0.3 | |
IP6 (rpm) | 120.0 | 120.0 | 120.0 | 0.0 | |
OP (%) | 92.6 | 94.7 | 78.5 | 4.2 | |
IP1 (°C) | 25.0 | 25.0 | 25.0 | 0.0 | Cd(II)-AD7 |
IP2 (-) | 7.0 | 8.0 | 6.0 | 0.7 | |
IP3 (mg/L) | 0.0 | 0.0 | 0.0 | 0.0 | |
IP4 (min) | 6.0 | 6.0 | 6.0 | 0.0 | |
IP5 (mg) | 0.2 | 0.2 | 0.1 | 0.0 | |
IP6 (rpm) | 14.0 | 16.0 | 12.0 | 1.4 | |
OP (%) | 62.3 | 73.3 | 56.6 | 3.8 | |
IP1 (°C) | 25.0 | 25.0 | 25.0 | 0.0 | Cd(II)-AD8 |
IP2 (-) | 7.0 | 8.0 | 6.0 | 0.7 | |
IP3 (mg/L) | 0.0 | 0.0 | 0.0 | 0.0 | |
IP4 (min) | 6.0 | 6.0 | 6.0 | 0.0 | |
IP5 (mg) | 0.2 | 0.2 | 0.1 | 0.0 | |
IP6 (rpm) | 14.0 | 16.0 | 12.0 | 1.4 | |
OP (%) | 66.2 | 79.2 | 58.2 | 5.7 | |
IP1 (°C) | 25.0 | 25.0 | 25.0 | 0.0 | Cd(II)-AD9 |
IP2 (-) | 7.0 | 8.0 | 6.0 | 0.7 | |
IP3 (mg/L) | 0.0 | 0.0 | 0.0 | 0.0 | |
IP4 (min) | 6.0 | 6.0 | 6.0 | 0.0 | |
IP5 (mg) | 0.2 | 0.2 | 0.1 | 0.0 | |
IP6 (rpm) | 14.0 | 16.0 | 12.0 | 1.4 | |
OP (%) | 69.9 | 82.5 | 61.8 | 5.6 | |
IP1 (°C) | 30.0 | 40.0 | 20.0 | 6.5 | Cd(II)-AD10 |
IP2 (-) | 6.0 | 7.0 | 5.0 | 0.7 | |
IP3 (mg/L) | 30.0 | 40.0 | 20.0 | 6.5 | |
IP4 (min) | 20.0 | 30.0 | 10.0 | 6.5 | |
IP5 (mg) | 30.0 | 30.0 | 30.0 | 0.0 | |
IP6 (rpm) | 200.0 | 200.0 | 200.0 | 0.0 | |
OP (%) | 60.1 | 77.3 | 44.3 | 8.7 | |
IP1 (°C) | 40.0 | 60.0 | 20.0 | 8.9 | As(III)-AD11 |
IP2 (-) | 7.0 | 12.0 | 2.0 | 2.2 | |
IP3 (mg/L) | 1000.0 | 1900.0 | 100.0 | 402.5 | |
IP4 (min) | 270.0 | 270.0 | 270.0 | 0.0 | |
IP5 (mg) | 75.0 | 135.0 | 15.0 | 26.8 | |
IP6 (rpm) | 100.0 | 100.0 | 100.0 | 0.0 | |
OP (%) | 76.2 | 92.7 | 48.2 | 12.3 | |
IP1 (°C) | 38.5 | 60.0 | 20.0 | 16.3 | As(III)-AD12 |
IP2 (-) | 7.5 | 10.0 | 4.0 | 2.4 | |
IP3 (mg/L) | 23.2 | 50.0 | 10.0 | 15.7 | |
IP4 (min) | 62.3 | 90.0 | 30.0 | 23.4 | |
IP5 (mg) | 7733.3 | 10,000.0 | 6000.0 | 1761.0 | |
IP6 (rpm) | 162.1 | 180.0 | 120.0 | 23.8 | |
OP (%) | 76.6 | 98.9 | 50.0 | 13.9 | |
Overall statistics | |||||
IP1 (°C) | 30.0 | 60.0 | 1.2 | 11.9 | Cr(VI)-AD1 Cr(VI)-AD2 Pb(II)-AD3 Pb(II)-AD4 Hg(II)-AD5 Hg(II)-AD6 Cd(II)-AD7 Cd(II)-AD8 Cd(II)-AD9 Cd(II)-AD10 As(II)-AD11 As(II)-AD12 |
IP2 (-) | 6.0 | 12.0 | 1.0 | 2.3 | |
IP3 (mg/L) | 102.6 | 1900.0 | 0.0 | 261.1 | |
IP4 (min) | 78.7 | 420.0 | 5.0 | 78.9 | |
IP5 (mg) | 1737.0 | 10,000.0 | 0.0 | 3281.4 | |
IP6 (rpm) | 178.7 | 800.0 | 12.0 | 178.1 | |
OP (%) | 68.1 | 98.9 | 0.9 | 21.3 |
Model | Hyperparameter Names | R Package |
---|---|---|
Random Forest | [mtry] | randomForest |
SVR–RBF Kernel | [sigma, C] | kernlab |
SVR–Polynomial Kernel | [degree, scale, C] | kernlab |
Stochastic Gradient Boosting | [n.trees, interaction.depth] | gbm |
Bayesian Additive Regression | [num_trees] | bartMachine |
Combined Dataset (Five Metals) | Percentage | No. Data Points |
---|---|---|
Training | 80% | 2476 |
Test | 20% | 619 |
Total | 100% | 3095 |
Metal | Algorithm | Performance | |||
---|---|---|---|---|---|
MAE | RMSE | SPcorr | R2 | ||
As (III) 1 | SVR-Poly | 2.42 | 5.43 | 0.91 | 0.84 |
Stochastic Gradient Boosting | 1.51 | 3.13 | 0.97 | 0.93 | |
SVR-RBF | 2.41 | 5.30 | 0.92 | 0.84 | |
Random Forest | 1.36 | 3.53 | 0.96 | 0.93 | |
Bayesian Additive Regression Tree | 1.33 | 4.18 | 0.98 | 0.97 | |
As (III) 2 | SVR-Poly | 3.32 | 6.08 | 0.89 | 0.80 |
Stochastic Gradient Boosting | 2.71 | 5.67 | 0.90 | 0.81 | |
SVR-RBF | 3.38 | 5.89 | 0.89 | 0.80 | |
Random Forest | 2.72 | 5.92 | 0.89 | 0.80 | |
Bayesian Additive Regression Tree | 2.57 | 5.83 | 0.89 | 0.79 |
Metal | Algorithm | Performance | |||
---|---|---|---|---|---|
MAE | RMSE | SPcorr | R2 | ||
Cr(IV) 1 | SVR-Poly | 0.38 | 1.08 | 0.94 | 0.89 |
Stochastic Gradient Boosting | 1.51 | 3.13 | 0.97 | 0.93 | |
SVR-RBF | 0.49 | 1.14 | 0.94 | 0.89 | |
Random Forest | 1.36 | 3.53 | 0.96 | 0.93 | |
Bayesian Additive Regression Tree | 0.10 | 0.15 | 0.99 | 0.99 | |
Cr (IV) 2 | SVR-Poly | 2.16 | 3.84 | 0.97 | 0.95 |
Stochastic Gradient Boosting | 2.04 | 4.80 | 0.96 | 0.92 | |
SVR-RBF | 1.62 | 3.04 | 0.98 | 0.96 | |
Random Forest | 1.60 | 4.65 | 0.96 | 0.92 | |
Bayesian Additive Regression Tree | 1.21 | 4.0 | 0.97 | 0.94 |
Metal | Algorithm | Performance | |||
---|---|---|---|---|---|
MAE | RMSE | SPcorr | R2 | ||
Cd (II) 1 | SVR-Poly | 1.06 | 1.77 | 0.97 | 0.95 |
Stochastic Gradient Boosting | 0.58 | 1.32 | 0.98 | 0.97 | |
SVR-RBF | 0.95 | 1.39 | 0.98 | 0.97 | |
Random Forest | 0.66 | 2.00 | 0.96 | 0.92 | |
Bayesian Additive Regression Tree | 0.65 | 1.60 | 0.99 | 0.98 | |
Cd (II) 2 | SVR-Poly | 2.44 | 5.42 | 0.96 | 0.92 |
Stochastic Gradient Boosting | 2.05 | 5.07 | 0.96 | 0.93 | |
SVR-RBF | 2.0 | 3.59 | 0.98 | 0.97 | |
Random Forest | 1.63 | 5.18 | 0.96 | 0.92 | |
Bayesian Additive Regression Tree | 1.16 | 3.22 | 0.98 | 0.97 |
Metal | Algorithm | Performance | |||
---|---|---|---|---|---|
MAE | RMSE | SPcorr | R2 | ||
Hg (II) 1 | SVR-Poly | 0.54 | 0.95 | 0.97 | 0.95 |
Stochastic Gradient Boosting | 0.29 | 0.61 | 0.99 | 0.98 | |
SVR-RBF | 0.42 | 0.90 | 0.98 | 0.96 | |
Random Forest | 0.11 | 0.38 | 0.99 | 0.99 | |
Bayesian Additive Regression Tree | 0.24 | 0.78 | 0.99 | 0.98 | |
Hg (II) 2 | SVR-Poly | 0.61 | 1.67 | 0.94 | 0.88 |
Stochastic Gradient Boosting | 0.26 | 0.75 | 0.98 | 0.97 | |
SVR-RBF | 1.13 | 1.99 | 0.95 | 0.91 | |
Random Forest | 0.23 | 0.85 | 0.95 | 0.97 | |
Bayesian Additive Regression Tree | 0.14 | 0.30 | 0.99 | 0.99 |
Metal | Algorithm | Performance | |||
---|---|---|---|---|---|
MAE | RMSE | SPcorr | R2 | ||
Pb (II) 1 | SVR-Poly | 2.29 | 3.47 | 0.98 | 0.97 |
Stochastic Gradient Boosting | 1.46 | 1.37 | 0.98 | 0.96 | |
SVR-RBF | 1.96 | 3.59 | 0.98 | 0.97 | |
Random Forest | 0.92 | 3.14 | 0.98 | 0.96 | |
Bayesian Additive Regression Tree | 0.61 | 1.37 | 0.99 | 0.99 | |
Pb (II) 2 | SVR-Poly | 1.13 | 1.99 | 1.0 | 1.0 |
Stochastic Gradient Boosting | 0.90 | 2.21 | 0.99 | 0.99 | |
SVR-RBF | 2.29 | 3.47 | 1.0 | 1.0 | |
Random Forest | 0.18 | 0.42 | 0.99 | 0.99 | |
Bayesian Additive Regression Tree | 0.69 | 2.78 | 0.99 | 0.99 |
Model | Train | Test | ||||||
---|---|---|---|---|---|---|---|---|
MAE | RMSE | SPCC | R2 | MAE | RMSE | SPCC | R2 | |
SVR-Poly | 0.0276 | 0.046 | 0.977 | 0.976 | 0.0278 | 0.052 | 0.972 | 0.970 |
SGB | 0.0247 | 0.043 | 0.981 | 0.979 | 0.249 | 0.047 | 0.979 | 0.976 |
SVR-RBF | 0.0267 | 0.043 | 0.981 | 0.978 | 0.0273 | 0.050 | 0.976 | 0.973 |
RF | 0.004 | 0.015 | 0.997 | 0.997 | 0.007 | 0.033 | 0.989 | 0.988 |
BART | 0.023 | 0.048 | 0.990 | 0.974 | 0.025 | 0.054 | 0.983 | 0.969 |
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Hafsa, N.; Rushd, S.; Al-Yaari, M.; Rahman, M. A Generalized Method for Modeling the Adsorption of Heavy Metals with Machine Learning Algorithms. Water 2020, 12, 3490. https://doi.org/10.3390/w12123490
Hafsa N, Rushd S, Al-Yaari M, Rahman M. A Generalized Method for Modeling the Adsorption of Heavy Metals with Machine Learning Algorithms. Water. 2020; 12(12):3490. https://doi.org/10.3390/w12123490
Chicago/Turabian StyleHafsa, Noor, Sayeed Rushd, Mohammed Al-Yaari, and Muhammad Rahman. 2020. "A Generalized Method for Modeling the Adsorption of Heavy Metals with Machine Learning Algorithms" Water 12, no. 12: 3490. https://doi.org/10.3390/w12123490