Machine Learning Models for Predicting Water Quality of Treated Fruit and Vegetable Wastewater
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area, Wash-Water Samples, and Laboratory Analysis
2.2. Multiple Linear Regression
2.3. Generalized Structure of Group Method of Data Handling (GSGMDH)
- The second-order polynomial defined polynomial structure (Equation (7)) has only two input neurons.
- The input neurons in each layer are selected only from adjacent layers.
2.4. Model Performance Evaluation
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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TSSTreated | TPTreated | TNTreated | CODTreated | BODTreated | NH4-NTreated | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Process\ | W | WP | W | WP | W | WP | W | WP | W | WP | W | WP | |
Treatments | 1 | 0.5 | 1 | 0.5 | 1 | 0.5 | 1 | 0.5 | 1 | 0.5 | 0.5 | 1 | |
Bench Scale | C | 0.55 | 0.70 | 0.11 | 0.29 | 0.44 | 0.14 | 0.33 | 0.29 | 0.33 | 0.13 | 0.33 | 0.14 |
DAF | 0.73 | 0.80 | 0.67 | 0.43 | 0.67 | 0.29 | 0.56 | 0.43 | 0.22 | 0.25 | 0.44 | 0.29 | |
EC&F | 0.45 | 0.60 | 1 | 0.57 | 0.78 | 0.57 | 0.89 | 0.86 | 0.56 | 0.75 | 0.56 | 0.71 | |
C&F | 1 | 0.90 | 0.44 | 0.86 | 0.56 | 0.43 | 0.67 | 0.63 | 0.44 | 0.5 | 0.22 | 0.38 | |
HC | 0.27 | 0.50 | - | - | - | - | - | - | - | - | - | ||
S | 0.09 | 0.10 | - | - | - | - | - | - | - | - | - | - | |
Full Scale | MBR + RO + UV | - | 1 | - | 1 | - | 1 | - | 1 | - | 1 | - | 1 |
POND | 0.18 | 0.40 | 0.89 | - | 0.89 | - | 0.22 | 0.14 | 0.78 | 0.38 | 0.89 | 0.57 | |
SET1 | 0.36 | 0.30 | 0.33 | 0.71 | 0.33 | 0.86 | 0.44 | 0.57 | 0.89 | 0.63 | 0.78 | 0.86 | |
SET1G | 0.91 | - | 0.78 | - | 1 | - | 0.78 | - | 1 | - | 0.67 | - | |
SET3 | 0.82 | 0.20 | 0.22 | 0.14 | 0.22 | 0.71 | 1 | 0.71 | 0.67 | 0.88 | 1 | 0.43 | |
SETBIO4 | 0.64 | - | 0.56 | - | 0.11 | - | 0.11 | - | 0.11 | - | 0.11 | - |
MLR Equations | Equation Number |
---|---|
(13) | |
(14) | |
(15) | |
(16) | |
(17) |
Process | Treatment | pHRaw | BODRaw | CODRaw | NH4-NRaw | TNRaw | TPRaw | TSSRaw | TSRaw | TDSRaw | |
---|---|---|---|---|---|---|---|---|---|---|---|
TSSTreated | −0.08 | −0.42 | 0.02 | −0.04 | 0.16 | 0.05 | 0.22 | 0.13 | 0.24 | 0.32 | 0.05 |
BODTreated | −0.53 | −0.29 | −0.2 | 0.9 | 0.62 | 0.09 | 0.36 | 0.04 | 0.05 | 0.28 | 0.61 |
CODTreated | −0.58 | −0.26 | −0.11 | 0.65 | 0.56 | 0.07 | 0.19 | −0.01 | 0.04 | 0.40 | 0.62 |
TPTreated | −0.55 | −0.35 | −0.19 | 0.07 | 0.16 | 0.48 | 0.19 | 0.88 | 0.08 | 0.07 | 0.02 |
TNTreated | −0.23 | −0.43 | 0.17 | 0.34 | 0.49 | 0.58 | 0.50 | 0.40 | 0.10 | 0.27 | 0.35 |
NH4-NTreated | −0.13 | −0.46 | −0.07 | 0.18 | 0.41 | 0.85 | 0.37 | 0.27 | 0.56 | 0.14 | −0.05 |
Raw Wash-water Quality Parameters | (mg/L) | TSSRaw | TDSRaw | TSRaw | CODRaw | BODRaw | TNRaw | TPRaw | NH4-NRaw |
min | 24 | 364 | 468 | 20 | 5 | 0.9 a | 1.30 | 0.09 | |
mean | 2498 | 1532 | 3795 | 1556 | 387 | 15 | 16.5 | 3.1 | |
max | 42,920 | 8740 | 13,855 | 12,400 | 3760 | 101 | 179 | 35 b | |
Treated Wash-water Quality Parameters | (mg/L) | TSSTreated | CODTreated | BODTreated | TNTreated | TPTreated | NH4-NTreated | ||
min | 0 | 2 | 2 | 0.03 | 0.04 | 0 | |||
mean | 452 | 632 | 177 | 9.4 | 5.6 | 4.5 | |||
max | 7160 | 8300 | 2300 | 53.1 | 90 | 70 | |||
Effluent requirements for wastewater discharge in Canada | (mg/L) | TSS | TDS | TS | BOD | TP | NH4-N | ||
Drinking Water c | - | 500 | - | - | 0.01 | 0.02 g | |||
Sanitary /Sewer Discharge d | 350 | - | - | 300 | 10 | - | |||
PWQO e | 25 f | - | - | 20 f | 0.02 |
R | RMSE | MAPE | |||
---|---|---|---|---|---|
TSSTreated | GSGMDH | Train (122 *) | 0.86 | 442 | 985 |
Test (46) | 0.82 | 501 | 1131 | ||
MLR | Train (122) | 0.30 | 736 | 65 | |
Test (46) | 0.54 | 706 | 364 | ||
BODTreated | GSGMDH | Train (120) | 0.99 | 36 | 106 |
Test (52) | 0.99 | 31 | 89 | ||
MLR | Train (120) | 0.83 | 159 | 558 | |
Test (52) | 0.67 | 199 | 443 | ||
CODTreated | GSGMDH | Train (123) | 0.85 | 573 | 261 |
Test (54) | 0.91 | 619 | 192 | ||
MLR | Train (123) | 0.54 | 890 | 820 | |
Test (54) | 0.73 | 575 | 943 | ||
TPTreated | GSGMDH | Train (62) | 0.73 | 8.99 | 428 |
Test (28) | 0.91 | 5.66 | 457 | ||
MLR | Train (62) | 0.59 | 6.40 | 58 | |
Test (28) | 0.80 | 12.8 | 63 | ||
TNTreated | GSGMDH | Train (57) | 0.96 | 3.49 | 310 |
Test (29) | 0.96 | 4.08 | 127 | ||
MLR | Train (57) | 0.58 | 7.60 | 68 | |
Test (29) | 0.70 | 10.9 | 54 |
Input Parameters for all Following Models: x1 = Process, x2 = BODRaw, x3 = CODRaw, x4 = NH4−NRaw, x5 = TNRaw, x6 = TPRaw, x7 = TSSRaw, x8 = TSRaw, x9 = TDSRaw, x10 = Treatment | |
---|---|
TSS | TSS = (|1.528 − 30.083 ∗ x11 − 15.482 ∗ x1 − 4.522 ∗ x10 + 35.961 ∗ x1 ∗ x11 + 53.634 ∗ x10 ∗ x11 − 2.429 ∗ x10 ∗ x1 + 58.95 ∗ x11 ∗ x11 + 45.6 ∗ x1 ∗ x1 + 6.614 ∗ x10 ∗ x10 − 1.355 ∗ x10 ∗ x1 ∗ x11 + 5.404 ∗ x1 ∗ x11 ∗ x11 − 23.609 ∗ x1 ∗ x1 ∗ x11 − 107.196 ∗ x10 ∗ x11 ∗ x11 + 1.459 ∗ x10 ∗ x1 ∗ x1 − 33.867 ∗ x10 ∗ x10 ∗ x11 + 0.353 ∗ x10 ∗ x10 ∗ x1 − 49.415 ∗ x11 ∗ x11 ∗ x11 − 30.274 ∗ x1 ∗ x1 ∗ x1 − 2.809 ∗ x10 ∗ x10 ∗ x10|) ∗ 7160 |
Where: x11 = 0.137 − 0.639 ∗ x5 − 0.1419 ∗ x10 − 0.7245 ∗ x10 ∗ x5 + 3.46 ∗ x5 ∗ x5 − 0.0056 ∗ x10 ∗ x10 − 4.203 ∗ x10 ∗ x5 ∗ x5 + 1.914 ∗ x10 ∗ x10 ∗ x5 − 0.274 ∗ x5 ∗ x5 ∗ x5 − 0.0313 ∗ x10 ∗ x10 ∗ x10 | |
BOD | BOD = (|0.008 + 0.841 ∗ x21 + 0.044 ∗ x9 − 0.128 ∗ x5 − 3.982 ∗ x9 ∗ x21 − 0.17 ∗ x5 ∗ x21 − 1.682 ∗ x5 ∗ x9 + 5.71 ∗ x21 ∗ x21 + 0.0196 ∗ x9 ∗ x9 + 0.943 ∗ x5 ∗ x5 + 3.0926 ∗ x5 ∗ x9 ∗ x21 − 2.853 ∗ x9 ∗ x21 ∗ x21 + 5.668 ∗ x9 ∗ x9 ∗ x21 − 2.219 ∗ x5 ∗ x21 ∗ x21 − 5.524 ∗ x5 ∗ x9 ∗ x9 − 1.328 ∗ x5 ∗ x5 ∗ x21 + 11.933 ∗ x5 ∗ x5 ∗ x9 − 6.199 ∗ x21 ∗ x21 ∗ x21 + 0.218 ∗ x9 ∗ x9 ∗ x9 − 3.512 ∗ x5 ∗ x5 ∗ x5|) ∗ 2298 + 2 |
Where: x11 = −0.554 − 0.426 ∗ x10 + 0.42 ∗ x2 + 1.623 ∗ x1 − 1.652 ∗ x2 ∗ x10 + 0.224 ∗ x1 ∗ x10 + 1.517 ∗ x1 ∗ x2 + 0.724 ∗ x10 ∗ x10 + 1.265 ∗ x2 ∗ x2 − 0.766 ∗ x1 ∗ x1 + 1.322 ∗ x1 ∗ x2 ∗ x10 − 0.289 ∗ x2 ∗ x10 ∗ x10 + 1.185 ∗ x2 ∗ x2 ∗ x10 − 0.586 ∗ x1 ∗ x10 ∗ x10 − 1.6 ∗ x1 ∗ x2 ∗ x2 + 0.17 ∗ x1 ∗ x1 ∗ x10 − 1.447 ∗ x1 ∗ x1 ∗ x2 − 0.115 ∗ x10 ∗ x10 ∗ x10 − 0.622 ∗ x2 ∗ x2 ∗ x2 − 0.3 ∗ x1 ∗ x1 ∗ x1 | |
and: x21 = −0.005 + 0.172 ∗ x11 + 0.071 ∗ x9 + 0.794 ∗ x2 + 7.808 ∗ x9 ∗ x11 + 25.691 ∗ x2 ∗ x11 − 3.26 ∗ x2 ∗ x9 − 21.654 ∗ x11 ∗ x11 − 0.7863662692 ∗ x9 ∗ x9 − 9.392 ∗ x2 ∗ x2 − 48.61 ∗ x2 ∗ x9 ∗ x11 + 17.523 ∗ x9 ∗ x11 ∗ x11 + 2.059 ∗ x9 ∗ x9 ∗ x11 − 17.201 ∗ x2 ∗ x11 ∗ x11 − 6.373 ∗ x2 ∗ x9 ∗ x9 − 20.94 ∗ x2 ∗ x2 ∗ x11 + 28.041 ∗ x2 ∗ x2 ∗ x9 + 43.899 ∗ x11 ∗ x11 ∗ x11 + 1.773 ∗ x9 ∗ x9 ∗ x9 + 8.693 ∗ x2 ∗ x2 ∗ x2 | |
COD | COD = = (|0.000423 + 0.073 ∗ x12 + 0.79 ∗ x11 − 6.087 ∗ x11 ∗ x12 + 1.742 ∗ x12 ∗ x12 + 5.405 ∗ x11 ∗ x11 − 9.309 ∗ x11 ∗ x12 ∗ x12 + 30.949 ∗ x11 ∗ x11 ∗ x12 − 0.46 ∗ x12 ∗ x12 ∗ x12 − 22.407 ∗ x11 ∗ x11 ∗ x11|) ∗ 8298 + 2 |
Where: x11 = −0.059 + 0.131 ∗ x10 + 1.3484 ∗ x9 − 0.694 ∗ x2 − 2.875 ∗ x9 ∗ x10 + 2.066 ∗ x2 ∗ x10 + 5.147 ∗ x2 ∗ x9 + 0.067 ∗ x10 ∗ x10 − 3.47 ∗ x9 ∗ x9 + 1.432 ∗ x2 ∗ x2 − 0.608 ∗ x2 ∗ x9 ∗ x10 + 1.315 ∗ x9 ∗ x10 ∗ x10 + 1.326 ∗ x9 ∗ x9 ∗ x10 − 1.818 ∗ x2 ∗ x10 ∗ x10 − 15.481 ∗ x2 ∗ x9 ∗ x9 − 0.94 ∗ x2 ∗ x2 ∗ x10 + 8.23 ∗ x2 ∗ x2 ∗ x9 − 0.104 ∗ x10 ∗ x10 ∗ x10 + 6.812 ∗ x9 ∗ x9 ∗ x9 − 3.527 ∗ x2 ∗ x2 ∗ x2 | |
and: x12 = −1.119 − 6.106 ∗ x10 − 34.025 ∗ x2 − 5.377 ∗ x1 − 1.72 ∗ x2 ∗ x10 + 13 ∗ x1 ∗ x10 + 103.148 ∗ x1 ∗ x2 + 2.854 ∗ x10 ∗ x10 + 1.817 ∗ x2 ∗ x2 + 27.183 ∗ x1 ∗ x1 + 2.378 ∗ x1 ∗ x2 ∗ x10 − 0.7980132594 ∗ x2 ∗ x10 ∗ x10 + 0.834 ∗ x2 ∗ x2 ∗ x10 − 1.312 ∗ x1 ∗ x10 ∗ x10 − 1.213 ∗ x1 ∗ x2 ∗ x2 − 7.666 ∗ x1 ∗ x1 ∗ x10 − 69.104 ∗ x1 ∗ x1 ∗ x2 − 0.924 ∗ x10 ∗ x10 ∗ x10 − 1.167 ∗ x2 ∗ x2 ∗ x2 − 20.56 ∗ x1 ∗ x1 ∗ x1 | |
TP | TP = (|−0.055 − 1.609 ∗ x11 + 0.619 ∗ x10 + 1.528 ∗ x4 − 10.509 ∗ x10 ∗ x11 + 26.087 ∗ x4 ∗ x11 − 1.137 ∗ x4 ∗ x10 + 51.713 ∗ x11 ∗ x11 − 0.738 ∗ x10 ∗ x10 − 16.005 ∗ x4 ∗ x4 + 37.421 ∗ x4 ∗ x10 ∗ x11 − 42.84 ∗ x10 ∗ x11 ∗ x11 + 8.358 ∗ x10 ∗ x10 ∗ x11 − 929.104 ∗ x4 ∗ x11 ∗ x11 − 0.0658 ∗ x4 ∗ x10 ∗ x10 + 473.109 ∗ x4 ∗ x4 ∗ x11 − 3.534 ∗ x4 ∗ x4 ∗ x10 + 322.282 ∗ x11 ∗ x11 ∗ x11 + 0.263 ∗ x10 ∗ x10 ∗ x10 − 39.329 ∗ x4 ∗ x4 ∗ x4|) ∗ 89.96 + 0.04 |
where: x11 = −2.442 + 7.202 ∗ x1 + 0.533 ∗ x4 + 0.896 ∗ x4 ∗ x1 − 4.397 ∗ x1 ∗ x1 − 3.009 ∗ x4 ∗ x4 − 4.066 ∗ x4 ∗ x1 ∗ x1 + 21.622 ∗ x4 ∗ x4 ∗ x1 − 0.2734052233 ∗ x1 ∗ x1 ∗ x1 − 15.831 ∗ x4 ∗ x4 ∗ x4 | |
TN | TN = (|0.079 − 0.157 ∗ x11 + 0.747 ∗ x5 − 1.742 ∗ x9 + 8.214 ∗ x5 ∗ x11 − 5.488 ∗ x9 ∗ x11 − 10.891 ∗ x9 ∗ x5 + 1.884 ∗ x11 ∗ x11 + 2.472 ∗ x5 ∗ x5 + 14.098 ∗ x9 ∗ x9 + 3.182 ∗ x9 ∗ x5 ∗ x11 − 4.938 ∗ x5 ∗ x11 ∗ x11 − 6.586 ∗ x5 ∗ x5 ∗ x11 − 8.161 ∗ x9 ∗ x11 ∗ x11 − 19.931 ∗ x9 ∗ x5 ∗ x5 + 7.19 ∗ x9 ∗ x9 ∗ x11 + 45.043 ∗ x9 ∗ x9 ∗ x5 + 1.522 ∗ x11 ∗ x11 ∗ x11 + 0.609 ∗ x5 ∗ x5 ∗ x5 − 22.436 ∗ x9 ∗ x9 ∗ x9|) ∗ 60.83 + 0.03 |
Where: x11 = 0.124 + 0.296 ∗ x4 + 0.339 ∗ x9 − 0.06 ∗ x10 − 7.27 ∗ x9 ∗ x4 − 7.826 ∗ x10 ∗ x4 + 0.627 ∗ x10 ∗ x9 + 42.361 ∗ x4 ∗ x4 − 1.624 ∗ x9 ∗ x9 − 0.143 ∗ x10 ∗ x10 + 18.159 ∗ x10 ∗ x9 ∗ x4 − 196.991 ∗ x9 ∗ x4 ∗ x4 + 71.295 ∗ x9 ∗ x9 ∗ x4 + 0.209 ∗ x10 ∗ x4 ∗ x4 + 0.382 ∗ x10 ∗ x9 ∗ x9 + 1.765 ∗ x10 ∗ x10 ∗ x4 − 1.498 ∗ x10 ∗ x10 ∗ x9 − 2.397 ∗ x4 ∗ x4 ∗ x4 + 0.785 ∗ x9 ∗ x9 ∗ x9 + 0.258 ∗ x10 ∗ x10 ∗ x10 |
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Mundi, G.; Zytner, R.G.; Warriner, K.; Bonakdari, H.; Gharabaghi, B. Machine Learning Models for Predicting Water Quality of Treated Fruit and Vegetable Wastewater. Water 2021, 13, 2485. https://doi.org/10.3390/w13182485
Mundi G, Zytner RG, Warriner K, Bonakdari H, Gharabaghi B. Machine Learning Models for Predicting Water Quality of Treated Fruit and Vegetable Wastewater. Water. 2021; 13(18):2485. https://doi.org/10.3390/w13182485
Chicago/Turabian StyleMundi, Gurvinder, Richard G. Zytner, Keith Warriner, Hossein Bonakdari, and Bahram Gharabaghi. 2021. "Machine Learning Models for Predicting Water Quality of Treated Fruit and Vegetable Wastewater" Water 13, no. 18: 2485. https://doi.org/10.3390/w13182485
APA StyleMundi, G., Zytner, R. G., Warriner, K., Bonakdari, H., & Gharabaghi, B. (2021). Machine Learning Models for Predicting Water Quality of Treated Fruit and Vegetable Wastewater. Water, 13(18), 2485. https://doi.org/10.3390/w13182485